Covariant quantisation of tensor multiplet models

TL;DR

This paper applies advanced quantisation formalisms to supersymmetric tensor multiplet models, demonstrating quantum equivalence and extending the quantisation techniques to supergravity backgrounds and harmonic superspace.

Contribution

It introduces a covariant quantisation approach for supersymmetric tensor multiplet models using the BV formalism and extends the analysis to supergravity backgrounds and harmonic superspace.

Findings

Quantum supercurrents coincide in classically equivalent models.

Quantisation in supergravity backgrounds is successfully achieved.

Results align with previous harmonic superspace quantisation methods.

Abstract

The Batalin-Vilkovisky formalism is applied to quantise the ${\cal N}=1$ supersymmetric generalisation of the Freedman-Townsend (FT) model, which was proposed by Lindstr\"om and Ro\v{c}ek in 1983 in Minkowski superspace and is lifted to a supergravity background in this paper. This super FT theory describes a non-Abelian tensor multiplet and is known to be classically equivalent to a supersymmetric nonlinear sigma model. Using path integral considerations, we demonstrate that this equivalence holds at the quantum level in the sense that the quantum supercurrents in the two theories coincide. A modified Faddeev-Popov procedure is employed to quantise models for the ${\cal N}=2$ tensor multiplet in harmonic superspace. The obtained results agree with those derived by applying the Batalin-Vilkovisky scheme within the harmonic superspace setting.