Aspects of compactification on a linear dilaton background

We consider the most general Kaluza-Klein (KK) compactification on S1/ℤ2 of a five dimensional (5D) graviton-dilaton system, with a non-vanishing dilaton background varying linearly along the fifth dimension. We show that this background produces a Higgs mechanism for the KK vector coming from the 5D metric, which becomes massive by absorbing the string frame radion. The $$ \mathcal{N} $$ N = 2 minimal supersymmetric extension of this model, recently built as the holographic dual of Little String Theory, is then reinvestigated. An analogous mechanism can be considered for the 4D vector coming from the (universal) 5D Kalb-Ramond two-form. Packaging the two massive vectors into a spin-3/2 massive multiplet, it is shown that the massless spectrum arranges into a $$ \mathcal{N} $$ N = 1, D = 4 supersymmetric theory. This projection is compatible with an orbifold which preserves half of the original supersymmetries already preserved by the background. The description of the partial breaking $$ \mathcal{N} $$ N = 2 → $$ \mathcal{N} $$ N = 1 in this framework, with only vector multiplets and no hypermultiplets, remains an interesting open question which deserves further investigation.

S-duality and supersymmetry on curved manifolds

We perform a systematic study of S-duality for $$ \mathcal{N} $$ N = 2 supersymmetric non-linear abelian theories on a curved manifold. Localization can be used to compute certain supersymmetric observables in these theories. We point out that localization and S-duality acting as a Legendre transform are not compatible. For these theories S-duality should be interpreted as Fourier transform and we provide some evidence for this. We also suggest the notion of a coholomological prepotential for an abelian theory that gives the same partition function as a given non-abelian supersymmetric theory.

Interacting Fermions and Supersymmetric Models

Chapter 24 discusses interacting fermions and supersymmetry (SUSY) models. The chapter addresses the semi-classical formalism relative to a fermion field in a bosonic background. It covers topics that include bosonic and fermionic bound states (both Dirac and Majorana), symmetric wells, supersymmetric theory, general results in SUSY theories, integrable SUSY models, non-integrable multi-frequency super Sine–Gordon models, phase transition and meta-stable states. It also discusses the conditions under which the overall theory presents supersymmetry and the consequences thereof. It also covers how semi-classical formulae can help to identify the particle excitations and estimate one of their most important characteristics, i.e. their mass.