Showing papers on "Section (fiber bundle) published in 2016"

Properties of the Binary Black Hole Merger GW150914

Abstract: On September 14, 2015, the Laser Interferometer Gravitational-wave Observatory (LIGO) detected a gravitational-wave transient (GW150914); we characterise the properties of the source and its parameters. The data around the time of the event were analysed coherently across the LIGO network using a suite of accurate waveform models that describe gravitational waves from a compact binary system in general relativity. GW150914 was produced by a nearly equal mass binary black hole of $36^{+5}_{-4} M_\odot$ and $29^{+4}_{-4} M_\odot$ (for each parameter we report the median value and the range of the 90% credible interval). The dimensionless spin magnitude of the more massive black hole is bound to be $0.7$ (at 90% probability). The luminosity distance to the source is $410^{+160}_{-180}$ Mpc, corresponding to a redshift $0.09^{+0.03}_{-0.04}$ assuming standard cosmology. The source location is constrained to an annulus section of $590$ deg$^2$, primarily in the southern hemisphere. The binary merges into a black hole of $62^{+4}_{-4} M_\odot$ and spin $0.67^{+0.05}_{-0.07}$. This black hole is significantly more massive than any other known in the stellar-mass regime.

Compensating strong coupling with large charge

Abstract: We study some (conformal) field theories with global symmetries in the sector where the value of the global charge $Q$ is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone's theorem in the non-relativistic regime. We also derive the unexpected result, first presented in [Hellerman et al. 2015], that the effective field theory describing such sector of fixed $Q$ contains effective couplings $\lambda_{\text{eff}}\sim \lambda^b /Q^{a}$, where $\lambda$ is the original coupling. Hence, large charge leads to weak coupling. In the last section of the paper we present an outline of how to compute anomalous dimensions of the $O(n)$ model in this limit.

Fluxes in F-theory compactifications on genus-one fibrations

Abstract: We initiate the construction of gauge fluxes in F-theory compactifications on genus-one fibrations which only have a multi-section as opposed to a section. F-theory on such spaces gives rise to discrete gauge symmetries in the effective action. We generalize the transversality conditions on gauge fluxes known for elliptic fibrations by taking into account the properties of the available multi-section. We test these general conditions by constructing all vertical gauge fluxes in a bisection model with gauge group $$ \mathrm{S}\mathrm{U}(5)\times {\mathrm{\mathbb{Z}}}_2 $$ . The non-abelian anomalies are shown to vanish. These flux solutions are dynamically related to fluxes on a fibration with gauge group SU(5)×U(1) by a conifold transition. Considerations of flux quantization reveal an arithmetic constraint on certain intersection numbers on the base which must necessarily be satisfied in a smooth geometry. Combined with the proposed transversality conditions on the fluxes these conditions are shown to imply cancellation of the discrete $$ {\mathrm{\mathbb{Z}}}_2 $$ gauge anomalies as required by general consistency considerations.

Optimized Active Single-Miller Capacitor Compensation With Inner Half-Feedforward Stage for Very High-Load Three-Stage OTAs

Abstract: This paper introduces a new effective single-Miller capacitor compensation topology for three-stage amplifiers with very large capacitive loads, realized through an active-feedback capacitor together with an inner half-feedforward stage. Moreover, an optimized design strategy which profitably exploits the two left half-plane zeros is presented. To improve the amplifier large signal transient response, the topology also includes an external feedforward path, that only marginally affects the frequency compensation, and a novel slew-rate enhancer section. To validate the solutions presented, a three-stage OTA driving a 10-nF load has been designed and implemented in a standard 0.35- $\mu\text{m}$ CMOS technology. The amplifier occupies less than 0.003-mm2 of die area, provides 2.7-MHz gain-bandwidth product and 0.55-V/ $\mu\text{s}$ average slew-rate, while consuming only 25- $\mu\text{A}$ quiescent current.

Higgs Bundles and Characteristic Classes

Abstract: Sixty years ago Hirzebruch observed how the vanishing of the Stiefel–Whitney class w2 led to integrality of the \(\hat{A}\)-genus of an algebraic variety [Hirz1]. This was one motivation for the Atiyah–Singer index theorem but also for my own thesis about Dirac operators and Kahler manifolds. Indeed the interaction between topology and algebraic geometry which he developed has been a constant theme in virtually all my work.

Virtual signed Euler characteristics

Abstract: Roughly speaking, to any space $M$ with perfect obstruction theory we associate a space $N$ with symmetric perfect obstruction theory. It is a cone over $M$ given by the dual of the obstruction sheaf of $M$, and contains $M$ as its zero section. It is locally the critical locus of a function. More precisely, in the language of derived algebraic geometry, to any quasi-smooth space $M$ we associate its $(-1)$-shifted cotangent bundle $N$. By localising from $N$ to its $\mathbb C^*$-fixed locus $M$ this gives five notions of virtual signed Euler characteristic of $M$: (1) The Ciocan-Fontanine-Kapranov/Fantechi-G\"ottsche signed virtual Euler characteristic of $M$ defined using its own obstruction theory, (2) Graber-Pandharipande's virtual Atiyah-Bott localisation of the virtual cycle of $N$ to $M$, (3) Behrend's Kai-weighted Euler characteristic localisation of the virtual cycle of $N$ to $M$, (4) Kiem-Li's cosection localisation of the virtual cycle of $N$ to $M$, (5) $(-1)^{vd}$ times by the topological Euler characteristic of $M$. Our main result is that (1)=(2) and (3)=(4)=(5). The first two are deformation invariant while the last three are not.

Birational boundedness of low dimensional elliptic Calabi-Yau varieties with a section.

Abstract: We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi-Yau manifolds $Y\rightarrow X$ with a section, provided that $\dim(Y)\leq 5$ and $X$ is not of product-type. As a consequence, we obtain that there are finitely many possibilities for the Hodge diamond of such manifolds. The result follows from log birational boundedness of klt pairs $(X, \Delta)$ with $K_X+\Delta$ numerically trivial and not of product-type, in dimension at most $4$.

E$_{8(8)}$ Exceptional Field Theory: Geometry, Fermions and Supersymmetry

Abstract: We present the supersymmetric extension of the recently constructed E$_{8(8)}$ exceptional field theory -- the manifestly U-duality covariant formulation of the untruncated ten- and eleven-dimensional supergravities. This theory is formulated on a (3+248) dimensional spacetime (modulo section constraint) in which the extended coordinates transform in the adjoint representation of E$_{8(8)}$. All bosonic fields are E$_{8(8)}$ tensors and transform under internal generalized diffeomorphisms. The fermions are tensors under the generalized Lorentz group SO(1,2)$\times$SO(16), where SO(16) is the maximal compact subgroup of E$_{8(8)}$. Vanishing generalized torsion determines the corresponding spin connections to the extent they are required to formulate the field equations and supersymmetry transformation laws. We determine the supersymmetry transformations for all bosonic and fermionic fields such that they consistently close into generalized diffeomorphisms. In particular, the covariantly constrained gauge vectors of E$_{8(8)}$ exceptional field theory combine with the standard supergravity fields into a single supermultiplet. We give the complete extended Lagrangian and show its invariance under supersymmetry. Upon solution of the section constraint the theory reduces to full D=11 or type IIB supergravity.

Cubic fourfolds fibered in sextic del Pezzo surfaces

Abstract: We exhibit new examples of rational cubic fourfolds, parametrized by a countably infinite union of codimension-two subvarieties in the moduli space. Our examples are fibered in sextic del Pezzo surfaces over the projective plane; they are rational whenever the fibration has a rational section.

Gauge Groups and Matter Fields on Some Models of F-theory without Section

Abstract: We investigate F-theory on an elliptic Calabi-Yau 4-fold without a section to the fibration. To construct an elliptic Calabi-Yau 4-fold without a section, we introduce families of elliptic K3 surfaces which do not admit a section. A product K3 × K3, with one of the K3’s chosen from these families of elliptic K3 surfaces without a section, realises an elliptic Calabi-Yau 4-fold without a section. We then compactify F-theory on such K3 × K3’s. We determine the gauge groups and matter fields which arise on 7-branes for these models of F-theory compactifications without a section. Since each K3 × K3 constructed does not have a section, gauge groups arising on 7-branes for F-theory models on constructed K3 × K3’s do not have U(1)-part. Interestingly, exceptional gauge group E 6 appears for some cases.

Analytical formulas for short bunch wakes in a flat dechirper

Abstract: We develop analytical models of the longitudinal and transverse wakes, on and off axis for a flat, corrugated beam pipe with realistic parameters, and then compare them with numerical calculations, and generally find good agreement. These analytical ``first order'' formulas approximate the droop at the origin of the longitudinal wake and of the slope of the transverse wakes; they represent an improvement in accuracy over earlier, ``zeroth order'' formulas. In example calculations for the RadiaBeam/LCLS dechirper using typical parameters, we find a 16% droop in the energy chirp at the bunch tail compared to simpler calculations. With the beam moved to $200\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ from one jaw in one dechirper section, one can achieve a 3 MV transverse kick differential over a $30\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ length.

M\"obius disjointness for non-uniquely ergodic skew products

Abstract: For $\tau>2$, let $T$ be a $C^\tau$ skew product map of the form $(x+\alpha,y+h(x))$ on $\mathbb T^2$ over a rotation of the circle. We show that if $T$ preserves a measurable section, then it is disjoint to the Mobius sequence. This in particular implies that any non-uniquely ergodic $C^\tau$ skew product map on $\mathbb T^2$ has a finite index factor that is disjoint to the Mobius sequence.

Radius of convexity of partial sums of odd functions in the close-to-convex family

Abstract: We consider the class of all analytic and locally univalent functions $f$ of the form $f(z)=z+\sum_{n=2}^\infty a_{2n-1} z^{2n-1}$, $|z| -\frac{1}{2}. $$ We show that every section $s_{2n-1}(z)=z+\sum_{k=2}^na_{2k-1}z^{2k-1}$, of $f$, is convex in the disk $|z|<\sqrt{2}/3$. We also prove that the radius $\sqrt{2}/3$ is best possible, i.e. the number $\sqrt{2}/3$ cannot be replaced by a larger one.

7-dimensional ${\cal N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory

Abstract: We show how to construct seven-dimensional half-maximally supersymmetric consistent truncations of 11-/10-dimensional SUGRA using $\mathrm{SL}(5)$ exceptional field theory Such truncations are defined on generalised $\mathrm{SU}(2)$-structure manifolds and give rise to seven-dimensional half-maximal gauged supergravities coupled to $n$ vector multiplets and thus with scalar coset space $\mathbb{R}^+ \times \mathrm{O}(3,n)/\mathrm{O}(3)\times\mathrm{O}(n)$ The consistency conditions for the truncation can be written in terms of the generalised Lie derivative and take a simple geometric form We show that after imposing certain "doublet" and "closure" conditions, the embedding tensor of the gauged supergravity is given by the intrinsic torsion of generalised $\mathrm{SU}(2)$-connections and automatically satisfies the linear constraint of seven-dimensional half-maximal gauged supergravities, as well as the quadratic constraint when the section condition is satisfied

The Global Sections of the Chiral de Rham Complex on a Kummer Surface

Abstract: The chiral de Rham complex is a sheaf of vertex algebras {\Omega}^ch_M on any nonsingular algebraic variety or complex manifold M, which contains the ordinary de Rham complex as the weight zero subspace. We show that when M is a Kummer surface, the algebra of global sections is isomorphic to the N = 4 superconformal vertex algebra with central charge 6. Previously, CP^n was the only manifold where a complete description of the global section algebra was known.

Measurement Uncertainty Budget of the PMV Thermal Comfort Equation

Abstract: Fanger’s predicted mean vote (PMV) equation is the result of the combined quantitative effects of the air temperature, mean radiant temperature, air velocity, humidity activity level and clothing thermal resistance. PMV is a mathematical model of thermal comfort which was developed by Fanger. The uncertainty budget of the PMV equation was developed according to GUM in this study. An example is given for the uncertainty model of PMV in the exemplification section of the study. Sensitivity coefficients were derived from the PMV equation. Uncertainty budgets can be seen in the tables. A mathematical model of the sensitivity coefficients of $$T_{\mathrm{a}}$$ , $$h_{\mathrm{c}}$$ , $$T_{\mathrm{mrt}}$$ , $$T_{\mathrm{cl}}$$ , and $$P_{\mathrm{a}}$$ is given in this study. And the uncertainty budgets for $$h_{\mathrm{c}}$$ , $$T_{\mathrm{cl}}$$ , and $$P_{\mathrm{a}}$$ are given in this study.

Dynamical behavior and Jacobi stability analysis of wound strings

Abstract: We numerically solve the equations of motion (EOM) for two models of circular cosmic string loops with windings in a simply connected internal space. Since the windings cannot be topologically stabilized, stability must be achieved (if at all) dynamically. As toy models for realistic compactifications, we consider windings on a small section of $$\mathbb {R}^2$$ , which is valid as an approximation to any simply connected internal manifold if the winding radius is sufficiently small, and windings on an $$S^2$$ of constant radius $$\mathcal {R}$$ . We then use Kosambi–Cartan–Chern (KCC) theory to analyze the Jacobi stability of the string equations and determine bounds on the physical parameters that ensure dynamical stability of the windings. We find that, for the same initial conditions, the curvature and topology of the internal space have nontrivial effects on the microscopic behavior of the string in the higher dimensions, but that the macroscopic behavior is remarkably insensitive to the details of the motion in the compact space. This suggests that higher-dimensional signatures may be extremely difficult to detect in the effective $$(3+1)$$ -dimensional dynamics of strings compactified on an internal space, even if configurations with nontrivial windings persist over long time periods.

Conjectures on counting associative 3-folds in $G_2$-manifolds

Abstract: There is a strong analogy between compact, torsion-free $G_2$-manifolds $(X,\varphi,*\varphi)$ and Calabi-Yau 3-folds $(Y,J,g,\omega)$ We can also generalize $(X,\varphi,*\varphi)$ to 'tamed almost $G_2$-manifolds' $(X,\varphi,\psi)$, where we compare $\varphi$ with $\omega$ and $\psi$ with $J$ Associative 3-folds in $X$, a special kind of minimal submanifold, are analogous to $J$-holomorphic curves in $Y$ Several areas of Symplectic Geometry -- Gromov-Witten theory, Quantum Cohomology, Lagrangian Floer cohomology, Fukaya categories -- are built using 'counts' of moduli spaces of $J$-holomorphic curves in $Y$, but give an answer depending only on the symplectic manifold $(Y,\omega)$, not on the (almost) complex structure $J$ We investigate whether it may be possible to define interesting invariants of tamed almost $G_2$-manifolds $(X,\varphi,\psi)$ by 'counting' compact associative 3-folds $N\subset X$, such that the invariants depend only on $\varphi$, and are independent of the 4-form $\psi$ used to define associative 3-folds We conjecture that one can define a superpotential $\Phi_\psi:{\mathcal U}\to\Lambda_{>0}$ 'counting' associative $\mathbb Q$-homology 3-spheres $N\subset X$ which is deformation-invariant in $\psi$ for $\varphi$ fixed, up to certain reparametrizations $\Upsilon:{\mathcal U}\to{\mathcal U}$ of the base ${\mathcal U}=$Hom$(H_3(X;{\mathbb Z}),1+\Lambda_{>0})$, where $\Lambda_{>0}$ is a Novikov ring Using this we define a notion of '$G_2$ quantum cohomology' These ideas may be relevant to String Theory or M-Theory on $G_2$-manifolds We also discuss Donaldson and Segal's proposal in arXiv:09023239, section 62, to define invariants 'counting' $G_2$-instantons on tamed almost $G_2$-manifolds $(X,\varphi,\psi)$, with 'compensation terms' counting weighted pairs of a $G_2$-instanton and an associative 3-fold, and suggest some modifications to it

A Maximal Extension of the Best-Known Bounds for the Furstenberg-S\'ark\"ozy Theorem

Abstract: We show that if $h\in \mathbb{Z}[x]$ is a polynomial of degree $k \geq 2$ such that $h(\mathbb{N})$ contains a multiple of $q$ for every $q\in \mathbb{N}$, known as an $\textit{intersective polynomial}$, then any subset of $\{1,2,\dots,N\}$ with no nonzero differences of the form $h(n)$ for $n\in\mathbb{N}$ has density at most a constant depending on $h$ and $c$ times $(\log N)^{-c\log\log\log\log N}$, for any $c 0$, $\mu=\mu(\text{deg}(g),\text{deg}(h))>0$, and $\mu(2,2)=1/2$. We also include a brief discussion of sums of three or more polynomials in the final section.

Elliptic bindings for dynamically convex Reeb flows on the real projective three-space

Abstract: The first result of this paper is that every contact form on \(\mathbb {R}P^3\) sufficiently \(C^\infty \)-close to a dynamically convex contact form admits an elliptic–parabolic closed Reeb orbit which is 2-unknotted, has self-linking number \(-1/2\) and transverse rotation number in (1 / 2, 1]. Our second result implies that any p-unknotted periodic orbit with self-linking number \(-1/p\) of a dynamically convex Reeb flow on a lens space of order p is the binding of a rational open book decomposition, whose pages are global surfaces of section. As an application we show that in the planar circular restricted three-body problem for energies below the first Lagrange value and large mass ratio, there is a special link consisting of two periodic trajectories for the massless satellite near the smaller primary—lunar problem—with the same contact-topological and dynamical properties of the orbits found by Conley (Commun Pure Appl Math 16:449–467, 1963) for large negative energies. Both periodic trajectories bind rational open book decompositions with disk-like pages which are global surfaces of section. In particular, one of the components is an elliptic–parabolic periodic orbit.

F-theory Models without Section on Calabi-Yau 4-folds

Abstract: We consider F-theory models compactified on genus-one fibered Calabi-Yau 4-folds without a section to the fibrations. We consider two families of genus-one fibered Calabi-Yau 4-folds: i)hypersurface of multidegree (3,2,2,2) in $\mathbb{P}^2\times\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$, and ii)double cover of $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$ branched along multidegree (4,4,4,4) 3-fold. By construction, these Calabi-Yau 4-folds have genus-one fibrations. We give explicit equations for these families of Calabi-Yau 4-folds, and confirm that the spaces given by the equations do not admit a section to the fibration. The irreducible components of the discriminant loci of the Calabi-Yau 4-folds we consider in this paper intersect with one another. So, 7-branes wrapped on distinct components intersect with one another, and matters localise along the matter curves. We determine the forms of the discriminant components. We then determine the fiber types on the discriminant components, to deduce the gauge groups on the 7-branes wrapped on the components. For some discriminant component, the gauge group enhances when the component coincides with other components so 7-branes wrapped on them become coincident. Gauge groups $E_6$ and $E_7$ appear for some enhanced cases. For some models, we find that the Jacobians of genus-one fibered Calabi-Yau 4-folds have the Mordell-Weil groups of rank 0. We determine the Mordell-Weil groups of the Jacobians of these models. We determine the potential matter spectra on the bulk, and matters localised along matter curves. We also determine Yukawa couplings which result from the interaction of a matter field on the bulk and two matter fields localised along a matter curve. We compute the generations of chiral matters on the bulk, and matters localised along a matter curve.

XYZ-like Spectra from Laplace Sum Rule at N2LO in the Chiral Limit

Abstract: We present new compact integrated expressions of QCD spectral functions of heavy-light molecules and four-quark $XYZ$-like states at lowest order (LO) of perturbative (PT) QCD and up to $d=8$ condensates of the Operator Product Expansion (OPE). Then, by including up to next-to-next leading order (N2LO) PT QCD corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results from QCD spectral sum rules (QSSR), on the $XYZ$-like masses and decay constants which suffer from the ill-defined heavy quark mass. PT N3LO corrections are estimated using a geometric growth of the PT series and are included in the systematic errors. Our optimal results based on stability criteria are summarized in Tables 11 to 14 and compared, in Section 10, with experimental candidates and some LO QSSR results. We conclude that the masses of the $XZ$ observed states are compatible with (almost) pure $J^{PC}=1^{+\pm}, 0^{++}$ molecule or/and four-quark states. The ones of the $1^{-\pm}, 0^{-\pm}$ molecule / four-quark states are about 1.5 GeV above the $Y_{c,b}$ mesons experimental candidates and hadronic thresholds. We also find that the couplings of these exotics to the associated interpolating currents are weaker than that of ordinary $D,B$ mesons ($f_{DD}\approx 10^{-3}f_D$) and may behave numerically as $1/ \bar m_b^{3/2}$ (resp. $1/ \bar m_b$) for the $1^{+},0^{+}$ (resp. $1^{-}, 0^{-}$) states which can stimulate further theoretical studies of these decay constants.

Lagrangian sections on mirrors of toric Calabi-Yau 3-folds

Abstract: We construct Lagrangian sections of a Lagrangian torus fibration on a 3-dimensional conic bundle, which are SYZ dual to holomorphic line bundles over the mirror toric Calabi-Yau 3-fold. We then demonstrate a ring isomorphism between the wrapped Floer cohomology of the zero-section and the regular functions on the mirror toric Calabi-Yau 3-fold. Furthermore, we show that in the case when the Calabi-Yau 3-fold is affine space, the zero section generates the wrapped Fukaya category of the mirror conic bundle. This allows us to complete the proof of one direction of homological mirror symmetry for toric Calabi-Yau orbifold quotients of the form $\mathbb{C}^3/\Check{G}$. We finish by describing some elementary applications of our computations to symplectic topology.

Compactness criteria and new impulsive functional dynamic equations on time scales

Abstract: In this paper, we introduce the concept of Δ-sub-derivative on time scales to define e-equivalent impulsive functional dynamic equations on almost periodic time scales. To obtain the existence of solutions for this type of dynamic equation, we establish some new theorems to characterize the compact sets in regulated function space on noncompact intervals of time scales. Also, by introducing and studying a square bracket function $[x(\cdot),y(\cdot) ]:\mathbb{T}\rightarrow\mathbb{R}$ on time scales, we establish some new sufficient conditions for the existence of almost periodic solutions for e-equivalent impulsive functional dynamic equations on almost periodic time scales. The final section presents our conclusion and further discussion of this topic.

A note on actions of some monoids

Abstract: Smooth actions of the multiplicative monoid $(\mathbb{R},\cdot)$ of real numbers on manifolds lead to an alternative, and for some reasons simpler, definition of a vector bundle, a double vector bundle and related structures like a graded bundle [Grabowski and Rotkiewicz, J. Geom. Phys. 2011]. For these reasons it is natural to study smooth actions of certain monoids closely related with the monoid $(\mathbb{R},\cdot)$ . Namely, we discuss geometric structures naturally related with: smooth and holomorphic actions of the monoid of multiplicative complex numbers, smooth actions of the monoid of second jets of punctured maps $(\mathbb{R},0)\rightarrow (\mathbb{R},0)$, smooth action of the monoid of real 2 by 2 matrices and smooth actions of multiplicative reals on a supermanifold. In particular cases we recover the notions of a holomorphic vector bundle, a complex vector bundle and a non-negatively graded manifold.

Quantized Brans-Dicke theory: Phase transition, strong coupling limit, and general relativity

Abstract: We show that Friedmann-Robertson-Walker geometry with a flat spatial section in quantized (Wheeler deWitt quantization) Brans-Dicke (BD) theory reveals a rich phase structure owing to anomalous breaking of a classical symmetry, which maps the scale factor $a\ensuremath{\mapsto}\ensuremath{\lambda}a$ for some constant $\ensuremath{\lambda}$. In the weak coupling ($\ensuremath{\omega}$) limit, the theory goes from a symmetry preserving phase to a broken phase. The existence of a phase boundary is an obstruction to another classical symmetry [see V. Faraoni, Phys. Rev. D 59, 084021 (1999).] (which relates two BD theories with different couplings) admitted by BD theory with scale invariant matter content, i.e., ${{T}^{\ensuremath{\mu}}}_{\ensuremath{\mu}}=0$. Classically, this prohibits the BD theory from reducing to general relativity (GR) for scale invariant matter content. We show that a strong coupling limit of both BD and GR preserves the symmetry involving the scale factor. We also show that with scale invariant matter content (radiation, i.e., $P=\frac{1}{3}\ensuremath{\rho}$), the quantized BD theory does reduce to GR as $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$, which is in sharp contrast to classical behavior. This is a first known illustration of a scenario where quantized BD theory provides an example of anomalous symmetry breaking and resulting binary phase structure. We make a conjecture regarding the strong coupling limit of the BD theory in a generic scenario.

Limits of the circles-in-the-sky searches in the determination of cosmic topology of nearly flat universes

Abstract: An important observable signature of a detectable nontrivial spatial topology of the Universe is the presence in the cosmic microwave background sky of pairs of matching circles with the same distributions of temperature fluctuations---the so-called circles in the sky. Most of the recent attempts to find these circles, including the ones undertaken by the Planck Collaboration, were restricted to antipodal or nearly antipodal circles with radii $\ensuremath{\lambda}\ensuremath{\ge}15\ifmmode^\circ\else\textdegree\fi{}$. In the most general search, pairs of circles with deviation from antipodality angles $0\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}169\ifmmode^\circ\else\textdegree\fi{}$ and radii $10\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}\ensuremath{\lambda}\ensuremath{\le}90\ifmmode^\circ\else\textdegree\fi{}$ were investigated. No statistically significant pairs of matching circles were found in the searches so far undertaken. Assuming that the negative result of general search can be confirmed through analysis made with data from Planck and future cosmic microwave background experiments, we examine the question as to whether there are nearly flat universes with compact topology, satisfying Planck constraints on cosmological parameters, that would give rise to circles in the sky whose observable parameters $\ensuremath{\lambda}$ and $\ensuremath{\theta}$ fall outside the parameter ranges covered by this general search. We derive the expressions for the deviation from antipodality and for the radius of the circles associated to a pair of elements ($\ensuremath{\gamma}$, ${\ensuremath{\gamma}}^{\ensuremath{-}1}$) of the holonomy group $\mathrm{\ensuremath{\Gamma}}$ which define the spatial section of any positively curved universe with a nontrivial compact topology. We show that there is a critical position that maximizes the deviation from antipodality and prove that, no matter how nearly flat the Universe is, it can always have a nontrivial spatial topology that gives rise to circles whose deviation from antipodality $\ensuremath{\theta}$ is larger than 169\ifmmode^\circ\else\textdegree\fi{} and whose radii of the circles $\ensuremath{\lambda}$ are smaller than 10\ifmmode^\circ\else\textdegree\fi{} for some observers's positions. This makes it apparent that slightly positively curved nearly flat universes with cosmological parameters within Planck bounds can be endowed with a nontrivial spatial topology with values of the observable parameters $\ensuremath{\lambda}$ and $\ensuremath{\theta}$ outside the ranges covered by the searches for circles carried out so far with either WMAP or Planck data. Thus, these circles-in-the-sky searches carried out so far are not sufficient to exclude the possibility of a universe with a detectable nontrivial cosmic topology. We present concrete examples of lens spaces universes whose associated circles have both, or at least one, value of the observable parameters ($\ensuremath{\lambda}$, $\ensuremath{\theta}$) outside the ranges covered by these searches. We also present a brief discussion of the implications of our results in view of unavoidable practical limits of the circles-in-the-sky method.

Quantum Serre theorem as a duality between quantum D-modules

Abstract: We give an interpretation of quantum Serre theorem of Coates and Givental as a duality of twisted quantum D-modules. This interpretation admits a non-equivariant limit, and we obtain a precise relationship among (1) the quantum D-module of X twisted by a convex vector bundle E and the Euler class, (2) the quantum D-module of the total space of the dual bundle E∨ → X, and (3) the quantum D-module of a submanifold Z ⊂ X cut out by a regular section of E . When E is the anticanonical line bundle K−1 X , we identify these twisted quantum D-modules with second structure connections with different parameters, which arise as Fourier–Laplace transforms of the quantum D-module of X. In this case, we show that the duality pairing is identified with Dubrovin’s second metric (intersection form).

Convex Regions of Stationary Spacetimes and Randers Spaces. Applications to Lensing and Asymptotic Flatness

Abstract: By using stationary-to-Randers correspondence (SRC, see Caponio et al in Rev Mat Iberoamericana 27:919–952, 2011), a characterization of light and time-convexity of the boundary of a region of a standard stationary $$(n+1)$$ -spacetime is obtained, in terms of the convexity of the boundary of a domain in a Finsler $$n$$ or $$(n+1)$$ -space of Randers type The latter convexity is analyzed in depth and, as a consequence, the causal simplicity and the existence of causal geodesics confined in the region and connecting a point to a stationary line are characterized Applications to asymptotically flat spacetimes include the light-convexity of hypersurfaces $$S^{n-1}(r)\times \mathbb {R} $$ , where $$S^{n-1}(r)$$ is a sphere of large radius in a spacelike section of an end, as well as the characterization of their time-convexity with natural physical interpretations The lens effect of both light rays and freely falling massive particles with a finite lifetime, (ie, the multiplicity of such connecting curves) is characterized in terms of the focalization of the geodesics in the underlying Randers manifolds

Concircular vector fields and pseudo-Kaehler manifolds

Abstract: A vector field on a pseudo-Riemannian manifold N is called concircular if it satisfies ΔXv = μX for any vector X tangent to N, where ∆ is the Levi-Civita connection of N. A concircular vector field satisfying ∆Xv = µX is called a nontrivial concircular vector field if the function µ is non-constant. A concircular vector field ν is called a concurrent vector field if the function μ is a non-zero constant. In this article we prove that every pseudo-Kaehler manifold of complex dimension > 1 does not admit a non-trivial concircular vector field. We also prove that this result is false whenever the pseudo-Kaehler manifold is of complex dimension one. In the last section we provide some remarks on pseudo-Kaehler manifolds which admit a concurrent vector field.