Superpotential

About: Superpotential is a research topic. Over the lifetime, 3836 publications have been published within this topic receiving 137867 citations.

Constructing gauge theory geometries from matrix models

Abstract: We use the matrix model ? gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the = 1 U(N) gauge theory with adjoint and symmetric or anti-symmetric matter, broken by a tree level superpotential to a product subgroup involving U(Ni) and SO(Ni) or Sp(Ni/2) factors. The relevant geometry is encoded by a non-hyperelliptic Riemann surface, which we extract from the exact loop equations. We also show that O(1/N) corrections can be extracted from a logarithmic deformation of this surface. The loop equations contain explicitly subleading terms of order 1/N, which encode information of string theory on an orientifolded local quiver geometry.

Massive wavefunctions, proton decay and FCNCs in local F-theory GUTs

Abstract: We study the coupling of MSSM fields to heavy modes through cubic superpotential interactions in F-theory SU(5) GUTs. The couplings are calculated by integrating the overlap of two massless and one massive wavefunctions. The overlap integral receives contributions from only a small patch around a point of symmetry enhancement thereby allowing the wavefunctions to be determined locally on flat space, drastically simplifying the calculation. The cubic coupling between two MSSM fields and one of the massive coloured Higgs triplets present in SU(5) GUTs is calculated using a local eight-dimensional SO(12) gauge theory. We find that for the most natural regions of local parameter space the coupling to the triplet is comparable to or stronger than in minimal four-dimensional GUTs thereby, for those regions, reaffirming or strengthening constraints from dimension-five proton decay. We also identify possible regions in local parameter space where the couplings to the lightest generations are substantially suppressed compared to minimal four-dimensional GUTs. We further apply our results and techniques to study other phenomenologically important operators arising from coupling to heavy modes. In particular we calculate within a toy model flavour non-universal soft masses induced by integrating out heavy modes which lead to FCNCs.

Reheating and Supersymmetric Flat-Direction Baryogenesis

Abstract: We re-examine Affleck-Dine baryo/leptogenesis from the oscillation of condensates along flat directions of the supersymmetric standard model, which attained large vevs at the end of inflationary epoque. The key observation is that superpotential interactions couple the flat directions to other fields, which acquire masses induced by the flat-direction vev that may be sufficiently small for them to be kinematically accessible to inflaton decay. The resulting plasma of inflaton decay products then may act on the flat directions via these superpotential Yukawa couplings, inducing thermal masses and supersymmetry-breaking A terms. In such cases the flat directions start their oscillations at an earlier time than usually estimated. The oscillations are also terminated earlier, due to evaporation of the flat direction condensate produced by its interaction with the plasma of inflaton decay products. In these cases we find that estimates for the resulting baryon/lepton asymmetry of the universe are substantially altered. We identify scenarios for the Yukawa couplings to the flat directions, and the order and mass scale of higher-dimensional superpotential interactions that set the initial flat direction vev, that might lead to acceptable baryo/leptogenesis.

Supersymmetric vacua in random supergravity

Abstract: We determine the spectrum of scalar masses in a supersymmetric vacuum of a general $ \mathcal{N}=1 $ supergravity theory, with the Kahler potential and superpotential taken to be random functions of N complex scalar fields. We derive a random matrix model for the Hessian matrix and compute the eigenvalue spectrum. Tachyons consistent with the Breitenlohner-Freedman bound are generically present, and although these tachyons cannot destabilize the supersymmetric vacuum, they do influence the likelihood of the existence of an ‘uplift’ to a metastable vacuum with positive cosmological constant. We show that the probability that a supersymmetric AdS vacuum has no tachyons is formally equivalent to the probability of a large fluctuation of the smallest eigenvalue of a certain real Wishart matrix. For normally-distributed matrix entries and any N, this probability is given exactly by $ P=\exp \left( {{{{-2{N^2}{{{\left| W \right|}}^2}}} \left/ {{m_{\mathrm{susy}}^2}} \right.}} \right) $ , with W denoting the superpotential and m susy the supersymmetric mass scale; for more general distributions of the entries, our result is accurate when N ≫ 1. We conclude that for $ \left| W \right|\gtrsim {{{{m_{\mathrm{susy}}}}} \left/ {N} \right.} $ , tachyonic instabilities are ubiquitous in configurations obtained by uplifting supersymmetric vacua.