Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...
The thesis is dedicated to two groups of questions arising in modern particle physics and cosmology. The first group concerns with the problem of stability of the electroweak (EW) vacuum in different environments. Due to its phenomenological significance, ...
We formulate the Nahm transform in the context of parabolic Higgs bundles on P^1 and extend its scope in completely algebraic terms. This transform requires parabolic Higgs bundles to satisfy an admissibility condition and allows Higgs fields to have poles ...
A simple extension of the minimal left-right symmetric supersymmetric grand unified theory model is constructed by adding two pairs of superfields. This naturally violates the partial Yukawa unification predicted by the minimal model. After including super ...
We analyze the moduli space of spontaneously broken N = 8 supergravity theories in 4 dimensions with classical Minkowski vacua. We find that all the known classical vacua, as well as the several new ones we construct here, can be connected by sending some ...
We study N = 2 vacua in spontaneously broken N = 4 electrically gauged supergravities in four space-time dimensions. We argue that the classification of all such solutions amounts to solving a system of purely algebraic equations. We then explicitly constr ...
We construct a simple class of N=2 gauged supergravity theories that admit metastable de Sitter vacua, generalizing the recent work done in the context of rigid supersymmetry. The setup involves one hypermultiplet and one vector multiplet spanning suitably ...
The Higgs-dilaton cosmological model is able to describe simultaneously an inflationary expansion in the early Universe and a dark energy dominated stage responsible for the present day acceleration. It also leads to a nontrivial relation between the spect ...
We use the embedding tensor formalism to analyse maximally symmetric backgrounds of N = 2 gauged supergravities which have the full N = 2 supersymmetry. We state the condition for N = 2 vacua and discuss some of their general properties. We show that if th ...
We consider breaking of supersymmetry in intersecting D-brane configurations by slight deviation of the angles from their supersymmetric values. We compute the masses generated by radiative corrections for the ad joint scalars on the brane world-volumes. I ...
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 ...
We perform a general study of the issue of metastability for supersymmetry-breaking vacua in theories with N=1 and N=2 global supersymmetry. This problem turns out to capture all the important qualitative features of the corresponding question in theories ...
We develop a method for constructing metastable de Sitter vacua in N = 1 supergravity models describing the no-scale volume moduli sector of Calabi-Yau string compactifications. We consider both heterotic and orientifold models. Our main guideline is the n ...
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 i ...
We study the stability of vacua with spontaneously broken supersymmetry in N = 2 supergravity theories with only hypermultiplets. Focusing on the projection of the scalar mass matrix along the sGoldstino directions, we are able to derive a universal upper ...
We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit vacua with spontaneously broken supersymmetry and realistic cosmological constant. We find that the existence of such viable vacua implies som ...
We analyze the general structure of soft scalar masses emerging in superstring models involving anomalous U(1) symmetries, with the aim of characterizing more systematically the circumstances under which they can happen to be flavor universal. We consider ...
