Critical N=(1,1) General Massive Supergravity

TL;DR

This paper analyzes the supermultiplet structure of $ =(1,1)$ General Massive Supergravity in AdS$_3$, identifying how modes organize into multiplets at generic and critical points, including the emergence of logarithmic modes.

Contribution

It provides a detailed linearized analysis of the supermultiplet structure of $ =(1,1)$ supergravity, revealing the behavior at critical points and the nature of supersymmetry transformations in logarithmic multiplets.

Findings

Modes form two massless and two massive multiplets at generic points.

Logarithmic modes appear at critical points, affecting supersymmetry transformations.

One critical point features a massive logarithmic multiplet with invertible supersymmetry.

Abstract

In this paper we study the supermultiplet structure of $\mathcal{N}=(1,1)$ General Massive Supergravity at non-critical and critical points of its parameter space. To do this, we first linearize the theory around its maximally supersymmetric AdS$_3$ vacuum and obtain the full linearized Lagrangian including fermionic terms. At generic values, linearized modes can be organized as two massless and 2 massive multiplets where supersymmetry relates them in the standard way. At critical points logarithmic modes appear and we find that in three of such points some of the supersymmetry transformations are non-invertible in logarithmic multiplets. However, in the fourth critical point, there is a massive logarithmic multiplet with invertible supersymmetry transformations.