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Publication# Vacuum Stability in Supersymmetric Effective Theories

Abstract

The main topics discussed in this thesis are supersymmetric low-energy effective theories and metastability conditions in generic non-renormalizable models with global and local supersymmetry. In the first part we discuss the conditions under which the low-energy expansion in space-time derivatives preserves supersymmetry implying that heavy multiplets can be more efficiently integrated out directly at the superfield level. These conditions translate into the requirements that also fermions and auxiliary fields should be small compared to the heavy mass scale. They apply not only to the matter sector, but also to the gravitational one if present, and imply in that case that the gravitino mass should be small. We finally give a simple prescription to integrate out heavy chiral and vector superfields consisting respectively in imposing stationarity of the superpotential and of the Kähler potential; the procedure holds in the same form both for global and local supersymmetry. In the second part we study general criteria for the existence of metastable vacua which break global supersymmetry in models with local gauge symmetries. In particular we present a strategy to define an absolute upper bound on the mass of the lightest scalar field which depends on the geometrical properties of the Kähler target manifold. This bound can be saturated by properly tuning the superpotential and its positivity therefore represents a necessary and sufficient condition for the existence of metastable vacua. It is derived by looking at the subspace of all those directions in field space for which an arbitrary supersymmetric mass term is not allowed and scalar masses are controlled by supersymmetry-breaking splitting effects. This subspace includes not only the direction of supersymmetry breaking, but also the directions of gauge symmetry breaking and the lightest scalar is in general a linear combination of fields spanning all these directions. Our purpose is to show that the largest value for the lightest mass is in general achieved when the lightest scalar is a combination of the Goldstone and the Goldstino partners. We conclude by computing the effects induced by the integration of heavy multiplets on the light masses. In particular we focus on the sGoldstino partners and we show that heavy chiral multiplets induce a negative level-repulsion effect that tends to compromise vacuum stability, whereas heavy vector multiplets in general induce a positive-definite contribution. Our results find application in the context of string-inspired supergravity models, where metastability conditions can be used to discriminate among different compactification scenarios and supersymmetric effective theories can be used to face the problem of moduli stabilization.

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Leonardo Brizi, Claudio Scrucca

We study the scalar mass matrix of general supersymmetric theories with local gauge symmetries, and derive an absolute upper bound on the lightest scalar mass. This bound can be saturated by suitably tuning the superpotential, and its positivity therefore represents a necessary and sufficient condition for the existence of metastable vacua. It is derived by looking at the subspace of all those directions in field space for which an arbitrary supersymmetric mass term is not allowed and scalar masses are controlled by supersymmetry-breaking splitting effects. This subspace includes not only the direction of supersymmetry breaking, but also the directions of gauge symmetry breaking and the lightest scalar is in general a linear combination of fields spanning all these directions. We present explicit results for the simplest case of theories with a single local gauge symmetry. For renormalizable gauge theories, the lightest scalar is a combination of the Goldstino partners and its square mass is always positive. For more general non-linear sigma models, on the other hand, the lightest scalar can involve also the Goldstone partner and its square mass is not always positive.

2011,

We reconsider the general question of how to characterize most efficiently the low-energy effective theory obtained by integrating out heavy modes in globally and locally supersymmetric theories. We consider theories with chiral and vector multiplets and identify the conditions under which all approximately supersymmetric low-energy effective theory can exist. These conditions translate into the requirements that all the derivatives, fermions and auxiliary fields should be small in units of the heavy mass scale. They apply not only to the matter sector, but also to the gravitational one if present, and imply in that case that the gravitino mass should he small. We then show how to determine the unique exactly supersymmetric theory that approximates this effective theory at the lowest order in the counting of derivatives, fermions and auxiliary fields, by working both at the superfield level and with component fields. As a result we give a simple prescription tor integrating out heavy superfields in an algebraic and manifestly supersymmetric way, which turns out to hold in the same form both for globally and locally supersymmetric theories. meaning that the process of integrating out heavy modes commutes with the process of switching on gravity. More precisely, for heavy chiral and vector multiplets one has to impose respectively stationarity of the superpotential and the Kahler potential. (C) 2009 Elsevier B.V. All rights reserved.

2009Christopher John Andrey, Claudio Scrucca

We elaborate on the idea that five-dimensional models where sequestering is spoiled due to contact interactions induced by vector multiplets may still be mildly sequestered if a global version of the gauge symmetry associated to the latter survives in the hidden sector. Interestingly, it has been argued that although in such a situation non-trivial current current contact interactions are induced by the heavy vector modes, these do not induce soft scalar masses, as a consequence of the global symmetry. We perform a detailed study of how this hybrid mechanism can be implemented in supergravity and string models, focusing on the prototypical case of heterotic M-theory orbifolds. We emphasize that in general the mechanism works only up to subleading effects suppressed by the ratio between the global symmetry breaking scale in the hidden sector and the vector mass scale or the Planck scale. We also argue that this mild sequestering mechanism allows to rehabilitate the scenario of dilaton domination of supersymmetry breaking, which is incompatible with dilaton stabilization in its original version, by exploiting the fact that hidden brane fields do contribute to the cosmological constant but not to soft terms, thanks to the global symmetry. (C) 2010 Elsevier B.V. All rights reserved.

2010