Showing papers on "Superpotential published in 2016"

N=1 Deformations and RG Flows of N=2 SCFTs

Abstract: We study certain N=1 preserving deformations of four-dimensional N=2 superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an N=1 chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced N=2 supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the $(A_1, A_n)$ Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the $(A_1, A_n)$ theories and find agreements with the previous results. Furthermore, we study the cases, including the $T_N$ and $R_{0,N}$ theories of class $\mathcal{S}$ and some of rank-one SCFTs, where the deformation gives genuine N=1 fixed points.

Disordered quivers and cold horizons

Abstract: We analyze the low temperature structure of a supersymmetric quiver quantum mechanics with randomized superpotential coefficients, treating them as quenched disorder. These theories describe features of the low energy dynamics of wrapped branes, which in large number backreact into extremal black holes. We show that the low temperature theory, in the limit of a large number of bifundamentals, exhibits a time reparametrization symmetry as well as a specific heat linear in the temperature. Both these features resemble the behavior of black hole horizons in the zero temperature limit. We demonstrate similarities between the low temperature physics of the random quiver model and a theory of large N free fermions with random masses.

Open string multi-branched and Kahler potentials

Abstract: We consider type II string compactifications on Calabi-Yau orientifolds with fluxes and D-branes, and analyse the F-term scalar potential that simultaneously involves closed and open string modes. In type IIA models with D6-branes this potential can be directly computed by integrating out Minkowski three-forms. The result shows a multi-branched structure along the space of lifted open string moduli, in which discrete shifts in special Lagrangian and Wilson line deformations are compensated by changes in the RR flux quanta. The same sort of discrete shift symmetries are present in the superpotential and constrain the Kahler potential. As for the latter, inclusion of open string moduli breaks the factorisation between complex structure and Kahler moduli spaces. Nevertheless, the 4d Kahler metrics display a set of interesting relations that allow to rederive the scalar potential analytically. Similar results hold for type IIB flux compactifications with D7-brane Wilson lines.

Accidental symmetries and the conformal bootstrap

Abstract: We study an $$ \mathcal{N}=2 $$ supersymmetric generalization of the three-dimensional critical O(N) vector model that is described by N + 1 chiral superfields with superpotential W = g 1 X∑ i Z 1 2 + g 2 X 3. By combining the tools of the conformal bootstrap with results obtained through supersymmetric localization, we argue that this model exhibits a symmetry enhancement at the infrared superconformal fixed point due to g 2 flowing to zero. This example is special in that the existence of an infrared fixed point with g 1 , g 2 ≠ 0, which does not exhibit symmetry enhancement, does not generally lead to any obvious unitarity violations or other inconsistencies. We do show, however, that the F-theorem excludes the models with g 1 , g 2 ≠ 0 for N > 5. The conformal bootstrap provides a stronger constraint and excludes such models for N > 2. We provide evidence that the g 2 = 0 models, which have the enhanced O(N) × U(1) symmetry, come close to saturating the bootstrap bounds. We extend our analysis to fractional dimensions where we can motivate the nonexistence of the g 1 , g 2 ≠ 0 models by studying them perturbatively in the 4 − ϵ expansion.

Bootstrapping O(N ) vector models with four supercharges in 3 ≤ d ≤ 4

Abstract: We analyze the conformal bootstrap constraints in theories with four super-charges and a global O(N ) × U(1) flavor symmetry in 3 ≤ d ≤ 4 dimensions. In particular, we consider the 4-point function of O(N )-fundamental chiral operators Z i that have no chiral primary in the O(N )-singlet sector of their OPE. We find features in our numerical bounds that nearly coincide with the theory of N + 1 chiral super-fields with superpotential W = X∑ = 1 Z 2 as well as general bounds on SCFTs where ∑ = 1 Z 2 vanishes in the chiral ring.

3d N=2 mirror symmetry, pq-webs and monopole superpotentials

Abstract: D3 branes stretching between webs of (p,q) 5branes provide an interesting class of 3d N=2 theories. For generic pq-webs however the low energy field theory is not known. We use 3d mirror symmetry and Type IIB S-duality to construct Abelian gauge theories corresponding to D3 branes ending on both sides of a pq-web made of many coincident NS5's intersecting one D5. These theories contain chiral monopole operators in the superpotential and enjoy a non trivial pattern of global symmetry enhancements. In the special case of the pq-web with one D5 and one NS5, the 3d low energy SCFT admits three dual formulations. This triality can be applied locally inside bigger quiver gauge theories. We prove our statements using partial mirror symmetry `a la Kapustin-Strassler, showing the equality of the S^3_b partition functions and studying the quantum chiral rings.

Electric Dipole Moments in Natural Supersymmetry

Abstract: We discuss electric dipole moments (EDMs) in the framework of CP-violating natural supersymmetry (SUSY). Recent experimental results have significantly tightened constraints on the EDMs of electrons and of mercury, and substantial further progress is expected in the near future. We assess how these results constrain the parameter space of natural SUSY. In addition to our discussion of SUSY, we provide a set of general formulas for two-loop fermion EDMs, which can be applied to a wide range of models of new physics. In the SUSY context, the two-loop effects of stops and charginos respectively constrain the phases of $A_t \mu$ and $M_2 \mu$ to be small in the natural part of parameter space. If the Higgs mass is lifted to 125 GeV by a new tree-level superpotential interaction and soft term with CP-violating phases, significant EDMs can arise from the two-loop effects of $W$ bosons and tops. We compare the bounds arising from EDMs to those from other probes of new physics including colliders, $b \to s \gamma$, and dark matter searches. Importantly, improvements in reach not only constrain higher masses, but require the phases to be significantly smaller in the natural parameter space at low mass. The required smallness of phases sharpens the CP problem of natural SUSY model building.

3d $ \mathcal{N} $ = 2 mirror symmetry, pq-webs and monopole superpotentials

Abstract: D3 branes stretching between webs of (p,q) 5branes provide an interesting class of 3d $$ \mathcal{N} $$ = 2 theories. For generic pq-webs however the low energy field theory is not known. We use 3d mirror symmetry and Type IIB S-duality to construct Abelian gauge theories corresponding to D3 branes ending on both sides of a pq-web made of many coincident N S5’s intersecting one D5. These theories contain chiral monopole operators in the superpotential and enjoy a non trivial pattern of global symmetry enhancements. In the special case of the pq-web with one D5 and one N S5, the 3d low energy SCFT admits three dual formulations. This triality can be applied locally inside bigger quiver gauge theories. We prove our statements using partial mirror symmetry a la Kapustin-Strassler, showing the equality of the S 3 partition functions and studying the quantum chiral rings.

The super-GUT CMSSM revisited

Abstract: We revisit minimal supersymmetric SU(5) grand unification (GUT) models in which the soft supersymmetry-breaking parameters of the minimal supersymmetric Standard Model (MSSM) are universal at some input scale, $$M_\mathrm{in}$$ , above the supersymmetric gauge-coupling unification scale, $$M_\mathrm{GUT}$$ . As in the constrained MSSM (CMSSM), we assume that the scalar masses and gaugino masses have common values, $$m_0$$ and $$m_{1/2}$$ , respectively, at $$M_\mathrm{in}$$ , as do the trilinear soft supersymmetry-breaking parameters $$A_0$$ . Going beyond previous studies of such a super-GUT CMSSM scenario, we explore the constraints imposed by the lower limit on the proton lifetime and the LHC measurement of the Higgs mass, $$m_\mathrm{h}$$ . We find regions of $$m_0$$ , $$m_{1/2}$$ , $$A_0$$ and the parameters of the SU(5) superpotential that are compatible with these and other phenomenological constraints such as the density of cold dark matter, which we assume to be provided by the lightest neutralino. Typically, these allowed regions appear for $$m_0$$ and $$m_{1/2}$$ in the multi-TeV region, for suitable values of the unknown SU(5) GUT-scale phases and superpotential couplings, and with the ratio of supersymmetric Higgs vacuum expectation values $$\tan \beta \lesssim 6$$ .

Symplectically invariant flow equations for N = 2, D = 4 gauged supergravity with hypermultiplets

Abstract: We consider N = 2 supergravity in four dimensions, coupled to an arbitrary number of vector- and hypermultiplets, where abelian isometries of the quaternionic hyperscalar target manifold are gauged. Using a static and spherically or hyperbolically symmetric ansatz for the fields, a one-dimensional effective action is derived whose variation yields all the equations of motion. By imposing a sort of Dirac charge quantization condition, one can express the complete scalar potential in terms of a superpotential and write the action as a sum of squares. This leads to first-order flow equations, that imply the second-order equations of motion. The first-order flow turns out to be driven by Hamilton’s characteristic function in the Hamilton-Jacobi formalism, and contains among other contributions the superpotential of the scalars. We then include also magnetic gaugings and generalize the flow equations to a symplectically covariant form. Moreover, by rotating the charges in an appropriate way, an alternative set of non-BPS first-order equations is obtained that corresponds to a different squaring of the action. Finally, we use our results to derive the attractor equations for near-horizon geometries of extremal black holes.

Asymptotically safe grand unification

Abstract: Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.

The Super-GUT CMSSM Revisited

Abstract: We revisit minimal supersymmetric SU(5) grand unification (GUT) models in which the soft supersymmetry-breaking parameters of the minimal supersymmetric Standard Model (MSSM) are universal at some input scale, $M_{in}$, above the supersymmetric gauge coupling unification scale, $M_{GUT}$. As in the constrained MSSM (CMSSM), we assume that the scalar masses and gaugino masses have common values, $m_0$ and $m_{1/2}$ respectively, at $M_{in}$, as do the trilinear soft supersymmetry-breaking parameters $A_0$. Going beyond previous studies of such a super-GUT CMSSM scenario, we explore the constraints imposed by the lower limit on the proton lifetime and the LHC measurement of the Higgs mass, $m_h$. We find regions of $m_0$, $m_{1/2}$, $A_0$ and the parameters of the SU(5) superpotential that are compatible with these and other phenomenological constraints such as the density of cold dark matter, which we assume to be provided by the lightest neutralino. Typically, these allowed regions appear for $m_0$ and $m_{1/2}$ in the multi-TeV region, for suitable values of the unknown SU(5) GUT-scale phases and superpotential couplings, and with the ratio of supersymmetric Higgs vacuum expectation values $\tan \beta \lesssim 6$.

Matter-coupled de Sitter supergravity

Abstract: The de Sitter supergravity describes the interaction of supergravity with general chiral and vector multiplets and also one nilpotent chiral multiplet. The extra universal positive term in the potential, generated by the nilpotent multiplet and corresponding to the anti-D3 brane in string theory, is responsible for the de Sitter vacuum stability in these supergravity models. In the flat-space limit, these supergravity models include the Volkov–Akulov model with a nonlinearly realized supersymmetry. We generalize the rules for constructing the pure de Sitter supergravity action to the case of models containing other matter multiplets. We describe a method for deriving the closed-form general supergravity action with a given potential K, superpotential W, and vectormatrix fAB interacting with a nilpotent chiral multiplet. It has the potential V = eK(|F2|+|DW|2-3|W|2), where F is the auxiliary field of the nilpotent multiplet and is necessarily nonzero. The de Sitter vacuums are present under the simple condition that |F2|-3|W|2 > 0. We present an explicit form of the complete action in the unitary gauge.

Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

Abstract: In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries on the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.

The heterotic superpotential and moduli

Abstract: We study the four-dimensional effective theory arising from ten-dimensional heterotic supergravity compactified on manifolds with torsion. In particular, given the heterotic superpotential appropriately corrected at O(α′) to account for the Green-Schwarz anomaly cancellation mechanism, we investigate properties of four-dimensional Minkowski vacua of this theory. Considering the restrictions arising from F-terms and D-terms we identify the infinitesimal massless moduli space of the theory. We show that it agrees with the results that have recently been obtained from a ten-dimensional perspective where super-symmetric Minkowski solutions including the Bianchi identity correspond to an integrable holomorphic structure, with infinitesimal moduli calculated by its first cohomology. As has recently been noted, interplay of complex structure and bundle deformations through holomorphic and anomaly constraints can lead to fewer moduli than may have been expected. We derive a relation between the number of complex structure and bundle moduli removed from the low energy theory in this way, and give conditions for there to be no complex structure moduli or bundle moduli remaining in the low energy theory. The link between Yukawa couplings and obstruction theory is also briefly discussed.

δN formalism from superpotential and holography

Abstract: We consider the superpotential formalism to describe the evolution of D scalar fields during inflation, generalizing it to include the case with non-canonical kinetic terms. We provide a characterization of the attractor behaviour of the background evolution in terms of first and second slow-roll parameters (which need not be small). We find that the superpotential is useful in justifying the separate universe approximation from the gradient expansion, and also in computing the spectra of primordial perturbations around attractor solutions in the δN formalism. As an application, we consider a class of models where the background trajectories for the inflaton fields are derived from a product separable super- potential. In the perspective of the holographic inflation scenario, such models are dual to a deformed CFT boundary theory, with D mutually uncorrelated deformation opera- tors. We compute the bulk power spectra of primordial adiabatic and entropy cosmological perturbations, and show that the results agree with the ones obtained by using conformal perturbation theory in the dual picture.

P fluxes and exotic branes

Abstract: We consider the $$ \mathcal{N} $$ = 1 superpotential generated in type-II orientifold models by non-geometric fluxes In particular, we focus on the family of P fluxes, that are related by T-duality transformations to the S-dual of the Q flux We determine the general rule that transforms a given flux in this family under a single T-duality transformation This rule allows to derive a complete expression for the superpotential for both the IIA and the IIB theory for the particular case of a $$ {T}^6/\left[{\mathbb{Z}}_2\times {\mathbb{Z}}_2\right] $$ orientifold We then consider how these fluxes modify the generalised Bianchi identities In particular, we derive a fully consistent set of quadratic constraints coming from the NS-NS Bianchi identities On the other hand, the P flux Bianchi identities induce tadpoles, and we determine a set of exotic branes that can be consistently included in order to cancel them This is achieved by determining a universal transformation rule under T-duality satisfied by all the branes in string theory

Coupling the Inflationary Sector to Matter

Abstract: We describe the coupling of matter fields to an inflationary sector of supergravity, the inflaton Φ and a stabilizer S, in models where the Kahler potential has a flat inflaton direction. Such models include, in particular, advanced versions of the hyperbolic α-attractor models with a flat inflaton direction Kahler potential, providing a good fit to the observational data. If the superpotential is at least quadratic in the matter fields U i , with restricted couplings to the inflaton sector, we prove that under certain conditions: i) The presence of the matter fields does not affect a successful inflationary evolution. ii) There are no tachyons in the matter sector during and after inflation. iii) The matter masses squared are higher than 3H 2 during inflation. The simplest class of theories satisfying all required conditions is provided by models with a flat direction Kahler potential, and with the inflaton Φ and a stabilizer S belonging to a hidden sector, so that matter fields have no direct coupling to the inflationary sector in the Kahler potential and in the superpotential.

On inflation, cosmological constant, and SUSY breaking

Abstract: We consider a broad class of inflationary models of two unconstrained chiral superfields, the stabilizer S and the inflaton Φ, which can describe inflationary models with nearly arbitrary potentials. These models include, in particular, the recently introduced theories of cosmological attractors, which provide an excellent fit to the latest Planck data. We show that by adding to the superpotential of the fields S and Φ a small term depending on a nilpotent chiral superfield P one can break SUSY and introduce a small cosmological constant without affecting main predictions of the original inflationary scenario.

Symplectically invariant flow equations for N=2, D=4 gauged supergravity with hypermultiplets

Abstract: We consider N=2 supergravity in four dimensions, coupled to an arbitrary number of vector- and hypermultiplets, where abelian isometries of the quaternionic hyperscalar target manifold are gauged. Using a static and spherically or hyperbolically symmetric ansatz for the fields, a one-dimensional effective action is derived whose variation yields all the equations of motion. By imposing a sort of Dirac charge quantization condition, one can express the complete scalar potential in terms of a superpotential and write the action as a sum of squares. This leads to first-order flow equations, that imply the second-order equations of motion. The first-order flow turns out to be driven by Hamilton's characteristic function in the Hamilton-Jacobi formalism, and contains among other contributions the superpotential of the scalars. We then include also magnetic gaugings and generalize the flow equations to a symplectically covariant form. Moreover, by rotating the charges in an appropriate way, an alternative set of non-BPS first-order equations is obtained that corresponds to a different squaring of the action. Finally, we use our results to derive the attractor equations for near-horizon geometries of extremal black holes.

General sGoldstino Inflation

Abstract: We prove that all inflationary models, including those with dark energy after the end of inflation, can be embedded in minimal supergravity with a single chiral superfield. Moreover, the amount of supersymmetry breaking is independently tunable due to a degeneracy in the choice for the superpotential. The inflaton is a scalar partner of the Goldstino in this set-up. We illustrate our general procedure with two examples that are favoured by the Planck data.

Mirror symmetry for the Landau-Ginzburg A-model $M=\mathbb C^n, W=z_1 \cdots z_n$

Abstract: We calculate the category of branes in the Landau-Ginzburg A-model with background $M=\mathbb C^n$ and superpotential $W=z_1 \cdots z_n$ in the form of microlocal sheaves along a natural Lagrangian skeleton. Our arguments employ the framework of perverse schobers, and our results confirm expectations from mirror symmetry.

On inflation, cosmological constant, and SUSY breaking

Abstract: We consider a broad class of inflationary models of two unconstrained chiral superfields, the stabilizer $S$ and the inflaton $\Phi$, which can describe inflationary models with nearly arbitrary potentials. These models include, in particular, the recently introduced theories of cosmological attractors, which provide an excellent fit to the latest Planck data. We show that by adding to the superpotential of the fields $S$ and $\Phi$ a small term depending on a nilpotent chiral superfield $P$ one can break SUSY and introduce a small cosmological constant without affecting main predictions of the original inflationary scenario.

Starobinsky-type inflation with products of Kähler manifolds

Abstract: We present a novel realization of Starobinsky-type inflation within Supergravity using two chiral superfields. The proposed superpotential is inspired by induced-gravity models. The Kahler potential contains two logarithmic terms, one for the inflaton T and one for the matter-like field S, parameterizing the SU(1, 1)/U(1)× SU(2)/U(1) Kahler manifold. The two factors have constant curvatures −m/n and 2/n2, where n, m are the exponents of T in the superpotential and Kahler potential respectively, and 0 < n2 ≤ 6. The inflationary observables depend on the ratio 2n/m only. Essentially they coincide with the observables of the original Starobinsky model. Moreover, the inflaton mass is predicted to be 3 · 1013 GeV.

Non-standard charged Higgs decay at the LHC in Next-to-Minimal Supersymmetric Standard Model

Abstract: We consider next-to-minimal supersymmetric standard model (NMSSM) which has a gauge singlet superfield. In the scale invariant superpotential we do not have the mass terms and the whole Lagrangian has an additional Z 3 symmetry. This model can have light scalar and/or pseudoscalar allowed by the recent data from LHC and the old data from LEP. We investigate the situation where a relatively light charged Higgs can decay to such a singlet-like pseudoscalar and a W ± boson giving rise to a final state containing τ and/or b-jets and lepton(s). Such decays evade the recent bounds on charged Higgs from the LHC, and according to our PYTHIA-FastJet based simulation can be probed with 10 fb−1 at the LHC center of mass energy of 13 and 14 TeV.

$P$ fluxes and exotic branes

Abstract: We consider the ${\cal N}=1$ superpotential generated in type-II orientifold models by non-geometric fluxes. In particular, we focus on the family of $P$ fluxes, that are related by T-duality transformations to the S-dual of the $Q$ flux. We determine the general rule that transforms a given flux in this family under a single T-duality transformation. This rule allows to derive a complete expression for the superpotential for both the IIA and the IIB theory for the particular case of a $T^6/[\mathbb{Z}_2 \times \mathbb{Z}_2 ]$ orientifold. We then consider how these fluxes modify the generalised Bianchi identities. In particular, we derive a fully consistent set of quadratic constraints coming from the NS-NS Bianchi identities. On the other hand, the $P$ flux Bianchi identities induce tadpoles, and we determine a set of exotic branes that can be consistently included in order to cancel them. This is achieved by determining a universal transformation rule under T-duality satisfied by all the branes in string theory.