Finite-temperature supersymmetry: the Wess-Zumino model

We investigate the breakdown of supersymmetry at finite temperature. While it has been proven that temperature always breaks supersymmetry, the nature of this breaking is less clear. On the one hand, a study of the Ward-Takahashi identities suggests a spontaneous breakdown of supersymmetry without the existence of a Goldstino, while on the other hand it has been shown that in any supersymmetric plasma there should exist a massless fermionic collective excitation, the phonino. Aim of this work is to unify these two approaches. For the Wess-Zumino model, it is shown that the phonino exists and contributes to the supersymmetric Ward-Takahashi identities in the right way displaying that supersymmetry is broken spontaneously with the phonino as the Goldstone fermion.     

Spontaneous supersymmetry breaking and superconductivity in a non-relativistic model

The conjecture that supersymmetry breaking implies superconductivity is supported by the analysis of a class of supersymmetric non-relativistic models involving only fermions. Here the investigation is extened to a non-relativistic model involving both fermions and bosons, which in a sense is the non-relativistic version of the Wess-Zumino model. A sufficient condition is established for the validity of the conjecture. This condition can be possibly violated at most in a two-dimensional subspace of the three-dimensional space of the coupling constants.     

Dynamical supersymmetry breaking in a finite field theoretical model

We present a supersymmetric field theory in two or three space-time dimensions with an internal symmetry of the O(N) type. In the large-N limit the model is finite and supersymmetry is spontaneously broken. The fields representing the order parameters of the broken supersymmetry phase acquire dynamics through quantum corrections. In particular the Goldstone fermion is a zero-mass fermionic bound state.     

Spontaneous breaking of anti-de sitter supersymmetry

We compute the one-loop effective potential of the Wess-Zumino model in Anti-de Sitter space. The effect of the background geometry is determined exactly. After the renormalization of the kinetic action and the insertion of a linear counterterm in the superpotential, we solve the quantum-corrected equations of motion, obtaining the vacuum solutions in the semiclassical approximation. The vacuum expectation values of theA andB fields are shifted by finite terms which depend upon the boundary conditions for the field propagators. Despite this result, we show with complete generality that supersymmetry is preserved to the one-loop order at each classically supersymmetric extremum of the effective potential.     

Simulating the Wess-Zumino supersymmetry model in optical lattices

We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in 2+1 dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.     

Spontaneous supersymmetry breaking in string theory

We present a construction of string theories, with spontaneously broken supersymmetry and chiral fermion families, obtained by a suitable choice of boundary conditions in toroidal compactifications of ten-dimensional (1,1) or heterotic models. The crystallographic groups in four-dimensions determine the possible values of the supersymmetry-breaking parameters, which therefore are discrete.     

Spontaneous breaking of supersymmetry through dimensional reduction

A general technique for deriving consistent theories with spontaneously broken supersymmetry and massive gravitinos is illustrated by exploiting the chiral invariance of N = 1 supergravity in four dimensions to construct a theory with broken N = 2 supersymmetry in three dimensions.     

Spontaneous supersymmetry breaking in supersymmetric string theories

A generalization of the dimensional reduction of supersymmetric string theories is introduced which leads to spontaneous breaking of supersymmetry. This supersymmetry breaking has non-trivial consequences for the quantization and dynamics of the theory. The lowest quantum correction to the cosmological constant is calculated and found to be unacceptably large.     

Spontaneous supersymmetry breaking induced by vacuum condensates

We propose a novel mechanism of spontaneous supersymmetry breaking which relies upon a ubiquitous feature of Quantum Field Theory, vacuum condensates. Such condensates play a crucial role in many phenomena. Examples include Unruh effect, superconductors, particle mixing, and quantum dissipative systems. We argue that in all these phenomena supersymmetry, when present, is spontaneously broken. Evidence for our conjecture is given for the Wess–Zumino model, that can be considered as an approximation to the supersymmetric extensions of the above mentioned systems. The magnitude of the effect is estimated for a recently proposed experimental setup based on an optical lattice.     

Spontaneous breaking of local supersymmetry by gravitational instantons

We study the gravitino condensate 〈(D_μΨ_ν − D_μΨ_ν)(D^μΨ^ν − D^νΨ^μ)〉 in the one-loop approximation around a nontrivial background metric. It turns out that, among the known regular solutions of the euclidean Einstein equations, the Eguchi-Hanson metric is the unique relevant configuration. The standard functional integration gives a finite answer for the gravitino condensate. Due to the presence of an anomalous supersymmetry transformation law, this implies that local supersymmetry is broken spontaneously in all supergravity models with scalar multiplets.     

Taste symmetry breaking at finite temperature

The breaking of the taste symmetry is studied in the temperature range between 140 MeV to 550 MeV. In order to investigate this violation we have calculated the screening masses of the various taste states fitting the exponential decay of the spatial correlators. The computation has been performed using dynamical N _f =2+1 gauge field configurations generated with the p4 staggered action along the Line of Constant Physics (LCP) defined by a pion mass m _π of approximately 220 MeV and the kaon mass m _K equals 500 MeV. For temperatures below the transition an agreement with the predictions of the staggered chiral perturbation theory has been found and no temperature effect can be observed on the taste violation. Above the transition the taste splitting still shows an $\mathcal{O}(a^{2})$ behavior but with a temperature-dependent slope. In addition to the analysis done for the pion multiplet we have performed an analogous computation for the light–strange and strange mesons and also looked at the scalar, vector and axial-vector channels to understand how the multiplets split at finite temperature. Finally the temperature dependence of the pion decay constant f _π is investigated to get further information regarding the chiral symmetry restoration.     

Spontaneous supersymmetry breaking by large-N matrices

Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity. In our models, the large value of N gives a natural explanation for the origin of small parameters appearing in the field theories which trigger the supersymmetry breaking.     

Goldstone realization of Lorentz-symmetry and supersymmetry at finite temperature

The Ward-Takahashi identities of Lorentz symmetry are examined at finite temperature. It is shown that the Lorentz symmetry is broken with the Goldstone realization. The analogy with finite-temperature supersymmetry-breaking in an R-invariant model is explained.     

Spontaneous breaking of supersymmetry and gauge invariance in supergravity

Using the new minimal auxiliary fields of N = 1 supergravity it is found possible to construct a model of local supersymmetry which spontaneously breaks both supersymmetry and gauge invariance. The status of the cosmological constant resulting from this breaking is discussed.     

Mean field at finite temperature and symmetry breaking

For an infinite system of nucleons interacting through a central spin-isospin schematic force we discuss how the Hartree-Fock theory at finite temperature T yields back, in the T=0 limit, the standard zero-temperature Feynman theory when there is no symmetry breaking. The attention is focused on the mechanism of cancellation of the higher order Hartree-Fock diagrams and on the dependence of this cancellation upon the range of the interaction. When a symmetry breaking takes place it turns out that more iterations are required to reach the self-consistent Hartree-Fock solution, because the cancellation of the Hartree-Fock diagrams of order higher than one no longer occurs. We explore in particular the case of an explicit symmetry breaking induced by a constant, uniform magnetic field B acting on a system of neutrons. Here we compare calculations performed using either the single-particle Matsubara propagator or the zero-temperature polarization propagator, discussing under which perturbative scheme they lead to identical results (if B is not too large). We finally address the issue of the spontaneous symmetry breaking for a system of neutrons using the technique of the anomalous propagator: in this framework we recover the Stoner equation and the critical values of the interaction corresponding to a transition to a ferromagnetic phase.