Transmutation of Pure 2-D Supergravity Into Topological 2-D Gravity and Other Conformal Theories

TL;DR

This paper demonstrates how 2-D supergravity can be transformed into topological 2-D gravity and other conformal theories through canonical field transformations, revealing a classical interpretation of twisting conformal models.

Contribution

It introduces a method to relate different conformal models via field transformations, using the gravitino and its ghost as fundamental building blocks.

Findings

Transformation of 2-D supergravity into topological gravity

Representation change as a classical twist of conformal models

Connection between gauge variation and conformal anomalies

Abstract

We consider the BRST and superconformal properties of the ghost action of 2-D supergravity. Using the background spin structure on the worldsheet, we show that this action can be transformed by canonical field transformations to reach other conformal models such as the 2-D topological gravity or the chiral models for which the gauge variation of the action reproduces the left or right conformal anomaly. Our method consists in using the gravitino and its ghost as fundamental blocks to build fields with different conformal weights and statistics. This indicates in particular that the twisting of a conformal model into another one can be classically interpreted as a change of "field representation" of the superconformal symmetry.