Showing papers on "Superpotential published in 2014"

Gauge Theories Labelled by Three-Manifolds

Abstract: We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N=2 gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independence of the SL(2) Chern-Simons partition function on the choice of triangulation translates to a statement that S^3_b partition functions of two mirror 3d N=2 gauge theories are equal. Three-dimensional N=2 field theories associated to 3-manifolds can be thought of as theories that describe boundary conditions and duality walls in four-dimensional N=2 SCFTs, thus making the whole construction functorial with respect to cobordisms and gluing.

$\mathcal{N} = 2$ quantum field theories and their BPS quivers

Abstract: We explore the relationship between four-dimensional $\mathcal{N} = 2$ quantum field theories and their associated BPS quivers. For a wide class of theories including super-Yang-Mills theories, Argyres-Douglas models, and theories defined by M5-branes on punctured Riemann surfaces, there exists a quiver which implicitly characterizes the field theory. We study various aspects of this correspondence including the quiver interpretation of flavor symmetries, gauging, decoupling limits, and field theory dualities. In general a given quiver describes only a patch of the moduli space of the field theory, and a key role is played by quantum mechanical dualities, encoded by quiver mutations, which relate distinct quivers valid in different patches. Analyzing the consistency conditions imposed on the spectrum by these dualities results in a powerful and novel mutation method for determining the BPS states. We apply our method to determine the BPS spectrum in a wide class of examples, including the strong coupling spectrum of super-Yang-Mills with an ADE gauge group and fundamental matter, and trinion theories defined by M5-branes on spheres with three punctures.

Analytic classes of metastable de Sitter vacua

Abstract: In this paper, we give a systematic procedure for building locally stable dS vacua in $$ \mathcal{N}=1 $$ supergravity models motivated by string theory. We assume that one of the superfields has a Kahler potential of no-scale type and impose a hierarchy of supersymmetry breaking conditions. In the no-scale modulus direction the supersymmetry breaking is not small, in all other directions it is of order ϵ. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by ϵ and the cosmological constant. These regions exist regardless of the details of the other moduli, provided the superpotential can be tuned such that the off-diagonal blocks of the mass matrix are parametrically small. We test and support this general dS landscape construction by explicit analytic solutions for the STU model. The Minkowski limits of these dS vacua either break supersymmetry or have flat directions in agreement with a no-go theorem that we prove, stating that a supersymmetric Minkowski vacuum without flat directions cannot be continuously deformed into a non-supersymmetric vacuum. We also describe a method for finding a broad class of stable supersymmetric Minkowski vacua that can be F-term uplifted to dS vacua and which have an easily controllable SUSY breaking scale.

Supersymmetric Janus solutions in four dimensions

Abstract: We use maximal gauged supergravity in four dimensions to construct the gravity dual of a class of supersymmetric conformal interfaces in the theory on the worldvolume of multiple M2-branes. We study three classes of examples in which the (1+1)-dimensional defects preserve (4, 4), (0, 2) or (0, 1) supersymmetry. Many of the solutions have the maximally supersymmetric AdS 4 vacuum dual to the $ \mathcal{N} $ = 8 ABJM theory on both sides of the interface. We also find new special classes of solutions including one that interpolates between the maximally supersymmetric vacuum and a conformal fixed point with $ \mathcal{N} $ = 1 supersymmetry and G2 global symmetry. We find another solution that interpolates between two distinct conformal fixed points with $ \mathcal{N} $ = 1 supersymmetry and G2 global symmetry. In eleven dimensions, this G2 to G2 solution corresponds to a domain wall across which a magnetic flux reverses orientation.

Yukawas and discrete symmetries in F-theory compactifications without section

Abstract: In the case of F-theory compactifications on genus-one fibrations without section there are naturally appearing discrete symmetries, which we argue to be associated to geometrically massive U(1) gauge symmetries. These discrete symmetries are shown to induce non-trivial selection rules for the allowed Yukawa couplings in SU(N) gauge theories. The general discussion is exemplified using a concrete Calabi-Yau fourfold realizing an SU(5) GUT model. We observe that M2 instanton effects appear to play a key role in the generation of new superpotential terms and in the dynamics close to phase transition loci.

An Index Formula for Supersymmetric Quantum Mechanics

Abstract: We derive a localization formula for the refined index of gauged quantum mechanics with four supercharges. Our answer takes the form of a residue integral on the complexified Cartan subalgebra of the gauge group. The formula captures the dependence of the index on Fayet-Iliopoulos parameters and the presence of a generic superpotential. The residue formula provides an efficient method for computing cohomology of quiver moduli spaces. Our result has broad applications to the counting of BPS states in four-dimensional N=2 systems. In that context, the wall-crossing phenomenon appears as discontinuities in the value of the residue integral as the integration contour is varied. We present several examples illustrating the various aspects of the index formula.

Linking Starobinsky-type inflation in no-scale supergravity to MSSM

Abstract: A novel realization of the Starobinsky inflationary model within a moderate extension of the Minimal Supersymmetric Standard Model (MSSM) is presented. The proposed superpotential is uniquely determined by applying a continuous R and a 2 discrete symmetry, whereas the Kahler potential is associated with a no-scale-type SU(54,1)/SU(54) × U(1)R × 2 Kahler manifold. The inflaton is identified with a Higgs-like modulus whose the vacuum expectation value controls the gravitational strength. Thanks to a strong enough coupling (with a parameter cT involved) between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton with cT ≥ 76 and the corresponding effective theory being valid up to the Planck scale. The inflationary observables turn out to be in agreement with the current data and the inflaton mass is predicted to be 3·1013GeV. At the cost of a relatively small superpotential coupling constant, the model offers also a resolution of the μ problem of MSSM for cT ≤ 4500 and gravitino heavier than about 104GeV. Supplementing MSSM by three right-handed neutrinos we show that spontaneously arising couplings between the inflaton and the particle content of MSSM not only ensure a sufficiently low reheating temperature but also support a scenario of non-thermal leptogenesis consistently with the neutrino oscillation parameters.

Landscaping with fluxes and the E8 Yukawa Point in F-theory

Abstract: Integrality in the Hodge theory of Calabi-Yau fourfolds is essential to nd the vacuum structure and the anomaly cancellation mechanism of four dimensional F-theory compactications. We use the Griths-Frobenius geometry and homological mirror symmetry to x the integral monodromy basis in the primitive horizontal subspace of Calabi-Yau fourfolds. The Gamma class and supersymmetric localization calculations in the 2d gauged linear sigma model on the hemisphere are used to check and extend this method. The result allows us to study the superpotential and the Weil-Petersson metric and an associated tt* structure over the full complex moduli space of compact fourfolds for the rst time. We show that integral

Scalar Hairy Black Holes in General Dimensions

Abstract: We obtain a class of asymptotic flat or (anti)--de Sitter [(A)dS] hairy black holes in $D$-dimensional Einstein gravity coupled to a scalar with a certain scalar potential. For a given mass, the theory admits both the Schwarzschild-Tangherlini and the hairy black holes with different temperature and entropy, but satisfying the same first law of thermodynamics. For some appropriate choice of parameters, the scalar potential can be expressed in terms of a superpotential, and it can arise in gauged supergravities. In this case, the solutions develop a naked curvature singularity and become the spherical domain walls. Uplifting the solutions to $D=11$ or 10, we obtain solutions that can be viewed as spherical M-branes or D3-branes. We also add electric charges to these hairy black holes. All these solutions contain no scalar charges in that the first law of thermodynamics is unmodified. We also try to construct new AdS black holes carrying scalar charges, with some moderate success in that the charges are pre-fixed in the theory instead of being some continuous integration constants.

A note on the magnitude of the flux superpotential

Abstract: The magnitude of the flux superpotential W flux plays a crucial role in determining the scales of IIB string compactifications after moduli stabilisation. It has been argued that values of W flux ≪ 1 are preferred, and even required for physical and consistency reasons. This note revisits these arguments. We establish that the couplings of heavy Kaluza-Klein modes to light states scale with the internal volume as g ~ M KK /M P ~ $ \mathcal{V} $ −2/3 ≪ 1 and argue that consistency of the superspace derivative expansion requires gF/M 2 ~ m 3/2 /M KK ≪ 1, where F is the auxiliary field of the light fields and M the ultraviolet cutoff. This gives only a mild constraint on the flux superpotential, W flux ≪ $ \mathcal{V} $ 1/3, which can be easily satisfied for $ \mathcal{O} $ (1) values of W flux. This regime is also statistically favoured and makes the Bousso-Polchinski mechanism for the vacuum energy hierarchically more efficient.

Natural inflation in supergravity and beyond

Abstract: Supergravity models of natural inflation and its generalizations are presented. These models are special examples of the class of supergravity models proposed in [R. Kallosh and A. Linde, J. Cosmol. Astropart. Phys. 11 (2010) 011; R. Kallosh, A. Linde, and T. Rube, Phys. Rev. D 83, 043507 (2011)], which have a shift symmetric K\"ahler potential, superpotential linear in goldstino, and stable Minkowski vacua. We present a class of supergravity models with arbitrary potentials modulated by sinusoidal oscillations, similar to the potentials associated with axion monodromy models. We show that one can implement natural inflation in supergravity even in the models of a single axion field with axion parameters $O(1)$. We also discuss the irrational axion landscape in supergravity, which describes a potential with an infinite number of stable Minkowski and metastable dS minima.

The Challenge of Realizing F-term Axion Monodromy Inflation in String Theory

Abstract: A systematic analysis of possibilities for realizing single-field F-term axion monodromy inflation via the flux-induced superpotential in type IIB string theory is performed. In this well-defined setting the conditions arising from moduli stabilization are taken into account, where we focus on the complex-structure moduli but ignore the Kaehler moduli sector. Our analysis leads to a no-go theorem, if the inflaton involves the universal axion. We furthermore construct an explicit example of F-term axion monodromy inflation, in which a single axion-like field is hierarchically lighter than all remaining complex-structure moduli.

Dynamical R-parity violation.

Abstract: We present a new paradigm for supersymmetric theories with R-parity violation (RPV). At high scale, R parity is conserved in the visible sector but spontaneously broken in the supersymmetry-breaking sector. The breaking is then dynamically mediated to the visible sector and is manifested via nonrenormalizable operators at low energy. Consequently, RPV operators originate from the Kahler potential rather than the superpotential, and are naturally suppressed by the supersymmetry-breaking scale, explaining their small magnitudes. A new set of nonholomorphic RPV operators is identified and found to often dominate over the standard RPV ones. We study the relevant low-energy constraints arising from baryon-number violating processes, proton decay, and flavor changing neutral currents, which may all be satisfied if a solution to the standard model flavor puzzle is incorporated. The chiral structure of the RPV operators implies new and distinct collider signatures, indicating the need to alter current techniques in searching for RPV at the LHC.

Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1 \times D^2$

Abstract: We study three dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-Matter theories on the direct product of a circle and a two dimensional hemisphere ($S^1 \times D^2$) with specified boundary conditions by the method of localization. We construct boundary interactions to cancel the supersymmetric variation of the three dimensional superpotential term and the Chern-Simons term and show inflows of the bulk-boundary anomalies. It finds that the boundary conditions induce two dimensional $\mathcal{N}=(0,2)$ type supersymmetry on the boundary torus. We also study the relation between the 3d-2d coupled partition function of our model and three dimensional holomorphic blocks.

BPS States in Supersymmetric Chiral Models with Higher Derivative Terms

Abstract: We study the higher derivative chiral models with four supercharges and Bogomol'nyi--Prasad--Sommerfield (BPS) states in these models. The off-shell Lagrangian generically includes higher powers of the auxiliary fields $F$, which causes distinct on-shell branches associated with the solutions to the auxiliary fields equation. We point out that the model admits a supersymmetric completion of arbitrary higher derivative bosonic models of a single complex scalar field, and an arbitrary scalar potential can be introduced even without superpotentials. As an example, we present a supersymmetric extension of the Faddeev--Skyrme model without four time derivatives, in contrast to the previously proposed supersymmetric Faddeev--Skyrme-like model containing four time derivatives. In general, higher derivative terms together with a superpotential result in deformed scalar potentials. We find that higher derivative corrections to $1/2$ BPS domain walls and $1/2$ BPS lumps are exactly canceled out, while the $1/4$ BPS lumps (as compact baby Skyrmions) depend on a characteristic feature of the higher derivative models. We also find a new $1/4$ BPS condition for domain wall junctions, which generically receives higher derivative corrections.

On Gaussian random supergravity

Abstract: We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kahler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with |F| ≪ M susy or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log(P ) ∝ − N. We argue that random supergravities lead to potentially interesting inflationary dynamics.

Supersymmetric Quantum Mechanics

Abstract: This bachelor thesis contains an introduction into supersymmetric quantum mechanics(SUSYQM). SUSYQM provides a different way of solving quantum mechanical problems. The thesis explains the basic concepts of SUSYQM, such as the factorization of a Hamiltonian, the definition of its superpotential and the shape invariant potentials. The SUSYQM framework was applied to some problems such as the infinite square well potential, the harmonic oscillator, the radial solution to the Hydrogen atom and isospectral deformation of potentials.

D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation

Abstract: We analyze the quantum-corrected moduli space of D7-brane position moduli with special emphasis on inflationary model building. D7-brane deformation moduli are key players in two recently proposed inflationary scenarios: The first, D7-brane chaotic inflation, is a variant of axion monodromy inflation which allows for an effective 4d supergravity description. The second, fluxbrane inflation, is a stringy version of D-term hybrid inflation. Both proposals rely on the fact that D7-brane coordinates enjoy a shift-symmetric Kahler potential at large complex structure of the Calabi-Yau threefold, making them naturally lighter than other fields. This shift symmetry is inherited from the mirror-dual Type IIA Wilson line on a D6-brane at large volume. The inflaton mass can be provided by a tree-level term in the flux superpotential. It induces a monodromy and, if tuned to a sufficiently small value, can give rise to a large-field model of inflation. Alternatively, by a sensible flux choice one can completely avoid a tree-level mass term, in which case the inflaton potential is induced via loop corrections. The positive vacuum energy can then be provided by a D-term, leading to a small-field model of hybrid natural inflation. In the present paper, we continue to develop a detailed understanding of the D7-brane moduli space focusing among others on shift-symmetry-preserving flux choices, flux-induced superpotential in Type IIB/F-theory language, and loop corrections. While the inflationary applications represent our main physics motivation, we expect that some of our findings will be useful for other phenomenological issues involving 7-branes in Type IIB/F-theory constructions.

Type IIA supergravity and M -theory on manifolds with SU(4) structure

Abstract: We give the general form of supersymmetric backgrounds with two real supercharges of M-theory and type IIA supergravity (with non-zero Romans mass in general) of the form $\mathbb{R}^{1,d} \times \M_8$, d=1,2, on eight-dimensional manifolds with SU(4) structure. We point out a subtlety in the integrability theorems for low-dimensional supersymmetric compactifications. As a special case we examine Calabi-Yau flux vacua and we show that unbroken supersymmetry does not in general require the four-form flux to be (2,2) or primitive. Our results could be used to construct novel higher-dimensional analogues of the Klebanov-Strassler geometry. In the case of M-theory large-volume Calabi-Yau flux vacua our results are in agreement with partial supersymmetry breaking in three-dimensional N=2 supergravity. Alternatively, the conditions for supersymmetry can be expressed in terms of a real `superpotential' in accordance with three-dimensional N=1 supergravity. We present explicit examples of M-theory flux vacua on K3 \times K3, which however do not appear to possess F-theory duals with four-dimensional Poincare invariance.

On new maximal supergravity and its BPS domain-walls

Abstract: We revise the SU(3)-invariant sector of $ \mathcal{N} $ = 8 supergravity with dyonic SO(8) gaugings. By using the embedding tensor formalism, analytic expressions for the scalar potential, superpotential(s) and fermion mass terms are obtained as a function of the electromagnetic phase ω and the scalars in the theory. Equipped with these results, we explore non-supersymmetric AdS critical points at ω ≠ 0 for which perturbative stability could not be analysed before. The ω-dependent superpotential is then used to derive first-order flow equations and obtain new BPS domain-wall solutions at ω ≠ 0. We numerically look at steepest-descent paths motivated by the (conjectured) RG flows.

Induced-gravity inflation in no-scale supergravity and beyond

Abstract: Supersymmetric versions of induced-gravity inflation are formulated within Supergravity (SUGRA) employing two gauge singlet chiral superfields. The proposed superpotential is uniquely determined by applying a continuous R and a discrete n symmetry. We select two types of logarithmic Kahler potentials, one associated with a no-scale-type SU(2,1)/SU(2)× U(1)R×n Kahler manifold and one more generic. In both cases, imposing a lower bound on the parameter c involved in the coupling between the inflaton and the Ricci scalar curvature — e.g. c 76, 105, 310 for n=2,3 and 6 respectively —, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity. In the case of no-scale SUGRA we show that, for every n, the inflationary observables remain unchanged and in agreement with the current data while the inflaton mass is predicted to be 31013 GeV. Beyond no-scale SUGRA the inflationary observables depend mildly on n and crucially on the coefficient involved in the fourth order term of the Kahler potential which mixes the inflaton with the accompanying non-inflaton field.

A Note on Asymmetric Thick Branes

Abstract: We study asymmetric thick braneworld scenarios, generated after adding a constant to the superpotential associated with the scalar field. We study in particular models with odd and even polynomial superpotentials, and we show that asymmetric brane can be generated irrespective of the potential being symmetric or asymmetric. We study in addition the nonpolynomial sine-Gordon like model, also constructed with the inclusion of a constant in the standard superpotential, and we investigate gravitational stability of the asymmetric brane. The results suggest robustness of the new braneworld scenarios and add further possibilities of the construction of asymmetric branes.

de Sitter vacua from nonperturbative flux compactifications

Abstract: In this work we present stable de Sitter solutions of =1 supergravity in a geometric type IIB duality frame with the addition of non-perturbative contributions. Contrary to the standard approach we retain the moduli dependence of both the tree level superpotential and its non-perturbative contribution. This provides the possibility for a single-step approach that stabilises all moduli simultaneously in a de Sitter vacuum. By means of a genetic algorithm we find explicit solutions where different scales are separated and hierarchies are investigated.

Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills

Abstract: Twisted compactification of the 6d $ \mathcal{N} $ = (2, 0) theories on a punctured Riemann surface give a large class of 4d $ \mathcal{N} $ = 1 and $ \mathcal{N} $ = 2 gauge theories, called class $ \mathcal{S} $ . We argue that nonperturbative dynamics of class $ \mathcal{S} $ theories are described by 5d maximal Super-Yang-Mills (SYM) twisted on the Riemann surface. In a sense, twisted 5d SYM might be regarded as a “Lagrangian” for class $ \mathcal{S} $ theories on $ {{\mathbb{R}}^{1,2 }}\times {S^1} $ . First, we show that twisted 5d SYM gives generalized Hitchin’s equations which was proposed recently. Then, we discuss how to identify chiral operators with quantities in twisted 5d SYM. Mesons, or holomorphic moment maps, are identified with operators at punctures which are realized as 3d superconformal theories T ρ [G] coupled to twisted 5d SYM. “Baryons” are identified qualitatively through a study of 4d $ \mathcal{N} $ = 2 Higgs branches. We also derive a simple formula for dynamical superpotential vev which is relevant for BPS domain wall tensions. With these tools, we examine many examples of 4d $ \mathcal{N} $ = 1 theories with several phases such as confining, Higgs, and Coulomb phases, and show perfect agreements between field theories and twisted 5d SYM. Spectral curve is an essential tool to solve generalized Hitchin’s equations, and our results clarify the physical information encoded in the curve.

M5 brane and four dimensional \mathcal{N} = 1 theories I

Abstract: Four dimensional $ \mathcal{N} $ = 1 theories are engineered by compactifying six dimensional (2, 0) theory on a Riemann surface with regular punctures. A generalized Hitchin’s equation involving two Higgs fields is proposed as the BPS equation for $ \mathcal{N} $ = 1 compactification. The puncture is interpreted as the singular boundary condition of this equation, and regular puncture is shown to be labeled by a nilpotent commuting pair. In this paper, we focus on a subset of regular puncture which is described by rotating branes representing $ \mathcal{N} $ =2 puncture. As an application, we show that Seiberg duality of SU(N) SQCD with N f = 2N and certain superpotential term is realized as different degeneration limits of the same punctured Riemann surface, and find four more dual theories.

The Landscape of M-theory Compactifications on Seven-Manifolds with $G_2$ Holonomy

Abstract: We study the physics of globally consistent four-dimensional $\mathcal{N}=1$ supersymmetric M-theory compactifications on $G_2$ manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these manifolds. We study a rich example that exhibits $U(1)^3$ gauge symmetry and a spectrum of massive charged particles that includes a trifundamental. Applying recent mathematical results to this example, we compute membrane instanton corrections to the superpotential and spacetime topology change in a compact model; the latter include both the (non-isolated) $G_2$ flop and conifold transitions. The conifold transition spontaneously breaks the gauge symmetry to $U(1)^2$, and associated field theoretic computations of particle charges make correct predictions for the topology of the deformed $G_2$ manifold. We discuss physical aspects of the abelian $G_2$ landscape broadly, including aspects of Higgs and Coulomb branches, membrane instanton corrections, and some general aspects of topology change.