From String Backgrounds to Topological Field Theories

TL;DR

This paper explores the connections between string backgrounds, topological field theories, and Calabi-Yau varieties through the lens of BRST formalism, revealing new links between these mathematical physics concepts.

Contribution

It provides new evidence for a relationship connecting bosonic and W-string backgrounds to B-model topological conformal field theories on noncompact Calabi-Yau varieties.

Findings

Identifies common features of BRST cohomology in string backgrounds and topological theories.

Establishes a link between string backgrounds and B-model topological theories.

Suggests a unified framework for understanding string and topological field theories.

Abstract

The BRST formalism has played a fundamental role in the construction of bosonic closed string backgrounds, ie. the stringy analogs of classical solutions to the field equations of general relativity. The concept of a string background has been extended to the notion of $W$-strings, where the BRST symmetry is still largely conjectural. More recently, the BRST formalism has entered the construction of two dimensional topological conformal quantum field theories, such as those that arise from Calabi-Yau varieties. In this lecture, we focus on common features of the BRST cohomology algebras of string backgrounds and topological field theories. In this context, we present some new evidence for a remarkable relationship that transports us from bosonic and $W$-string backgrounds to the B-model topological conformal field theories associated to certain noncompact Calabi-Yau varieties. This paper will appear in the proceedings of the {\it Symposium on BRS Symmetry} held at RIMS, September 18-22, 1995.