The Zamolodchikov C-Function, Classical Closed String Field Theory, The Duistermaat-Heckman Theorem, The Renormalization Group, and all that

TL;DR

This paper develops a topological field theory using a generalized Duistermaat-Heckman theorem to localize the path integral of a modified Zamolodchikov C-Function, connecting it to classical closed string field theory and renormalization group fixed points.

Contribution

It introduces a novel topological field theory framework that links the Zamolodchikov C-Function, the Duistermaat-Heckman theorem, and classical closed string field theory.

Findings

Localization of path integral over all 2D theories to RG fixed points

Interpretation of string field theory action via C-Function modification

Establishment of a topological field theory approach to string theory

Abstract

In this article we formulate a `topological' field theory by employing a generalization of the Duistermaat-Heckman Theorem to localize the path-integral of the `topological action' C^2 , where C is a slight modification of the Zamolodchikov C-Function, over the space of all two-dimensional field theories to the fixed points of the renormalization group's identity component. Also, we propose an interpretation of the background independent classical closed string field theory action S in terms of the Zamolodchikov C-Function's modification.