Finite Deformations of CFT and Spacetime Geometry

TL;DR

This paper explores how the space of 2D quantum field theories can be described using off-shell states of a free closed string, linking conformal invariance conditions to a gravity theory with additional fields.

Contribution

It provides an explicit method to parametrize QFTs via string states and derives the low-energy limit as a Brans-Dicke type gravity theory.

Findings

Parametrization of 2D QFTs using string off-shell states

Explicit calculation procedure for higher order conformal invariance terms

Low-energy limit corresponds to Brans-Dicke gravity with a tensor field

Abstract

We demonstrate in detail how the space of two-dimensional quantum field theories can be parametrized by off-shell states of a free closed string moving in a flat background. The dynamic equation corresponding to the condition of conformal invariance includes an infinite number of higher order terms, and we give an explicit procedure for their calculation. The symmetries corresponding to equivalence relations of theories are described. In this framework we show how to perform nonperturbative analysis in the low-energy limit and prove that it corresponds to the Brans-Dicke theory of gravity interacting with a skew symmetric tensor field.