Are all TCFTs obtained by twisting N=2 SCFTs?

TL;DR

This paper investigates whether all two-dimensional topological conformal field theories (TCFTs) can be derived from twisting N=2 superconformal field theories (SCFTs), proposing a unifying perspective and providing evidence through string theory embeddings.

Contribution

It demonstrates that TCFTs from various string theories, including critical bosonic strings, can be obtained by twisting N=2 SCFTs, suggesting a universal description of TCFTs.

Findings

Embedding the critical bosonic string into the NSR string yields a TCFT from twisting N=2 SCFT.

The construction of the N=2 superconformal algebra is flexible, allowing generalizations to other string theories.

Conjecture that all TCFTs can be described as topologically twisted N=2 SCFTs.

Abstract

A large class of two-dimensional topological conformal field theories (TCFTs) are obtained by the twisting construction of Witten and Eguchi-Yang. However there seem to exist TCFTs which are not obtained in this way; for instance, TCFTs obtained from the Kazama algebra and critical string theories with generic background. We will show that by embedding the critical bosonic string into the NSR string, its TCFT can indeed be obtained by twisting a N=2 SCFT. A closer look at the construction of the N=2 superconformal algebra will show that the embedding is not essential, and this will tell us how to generalise this to other string theories. We thus conclude with the natural conjecture that _all_ TCFTs have a description as topologically twisted N=2 SCFTs. (Talk given at the Workshop on Strings, Gravity and Related Topics, held at the ICTP (Trieste, Italy) on 29-30 June, 1995.)