On Topologically Massive Gravity with Extended Supersymmetry

TL;DR

This paper constructs extended supersymmetric topologically massive gravity in 2+1 dimensions using superspace methods, revealing unique features for different supersymmetry levels and explicitly formulating the $ ext{N}=4$ case.

Contribution

It introduces a superspace construction of extended supergravity with topological mass, detailing the scalar multiplet constraints and off-shell actions for various supersymmetries.

Findings

For $ ext{N} extgreater=3$, scalar multiplets are on-shell with geometry-determined potentials.

For $ ext{N} extgreater=4$, the theory has no free parameters, indicating a fixed structure.

At $ ext{N}=4$, the model reduces to topologically massive gravity at the chiral point with an explicit off-shell action.

Abstract

We describe the construction of $2+1$-dimensional toplogically massive adS gravity with ${\mathcal{N}}$-extended supersymmetry in superspace by means of introducing a compensating hypermultiplet for the super-Weyl invariance. For $\mathcal{N}\geq 3$ the scalar multiplet must be on shell and the potential for the scalar compensator is completely determined by the geometry. As a consequence the resulting massive theory has no free parameter for $\mathcal{N}\geq 4$. For $\mathcal{N}= 4$ we show that this leads to topologically massive gravity at the chiral point and construct the corresponding off-shell component action.