Osp(1|2) Chern-Simons gauge theory as 2D N=1 Induced Supergravity

TL;DR

This paper establishes a connection between Osp(1|2) Chern-Simons gauge theory and two-dimensional N=1 supergravity, showing how the gauge theory's physical states relate to supergravity partition functions and moduli spaces.

Contribution

It reveals a novel relationship between Osp(1|2) Chern-Simons theory and 2D N=1 supergravity, linking gauge theory states to supergravity partition functions and super Teichmüller space.

Findings

Inner product of physical states yields supergravity partition function.

Moduli space of flat connections includes super Teichmüller space.

Establishes a gauge theory-supergravity correspondence.

Abstract

We demonstrate the close relationship between Chern-Simons gauge theory with gauge group Osp(1|2) and N=1 induced supergravity in two dimensions. More precisely, the inner product of the physical states in the former yields the partition function of the latter evaluated in the Wess-Zumino supergauge. It is also shown that the moduli space of flat Osp(1|2) connections naturally includes super Teichm\"uller space of super Riemann surfaces.