On First Order Formalism in String Theory

TL;DR

This paper develops a new off-shell first order formalism in string theory, deriving Einstein-like equations with B-field and dilaton, and finds novel solutions including plane waves, enhancing understanding of string backgrounds.

Contribution

It introduces a novel off-shell formalism in string theory that yields new solutions and insights into background equations involving Einstein gravity, B-field, and dilaton.

Findings

Derived quadratic equations for background fields equivalent to Einstein equations with B-field and dilaton.

Discovered a new class of solutions including plane wave backgrounds.

Analyzed properties of the BRST operator in the new formalism.

Abstract

We consider the first order formalism in string theory, providing a new off-shell description of the nontrivial backgrounds around an "infinite metric". The OPE of the vertex operators, corresponding to the background fields in some "twistor representation", and conditions of conformal invariance results in the quadratic equation for the background fields, which appears to be equivalent to the Einstein equations with a Kalb-Ramond B-field and a dilaton. Using a new representation for the Einstein equations with B-field and dilaton we find a new class of solutions including the plane waves for metric (graviton) and the B-field. We discuss the properties of these background equations and main features of the BRST operator in this approach.