Ultraviolet and Infrared Finiteness in Two Dimensional Curved Space-Time

TL;DR

This paper demonstrates that certain two-dimensional field theories in curved space-time are free of anomalies and are ultraviolet and infrared finite at all perturbation orders, using cohomological analysis and supersymmetry-like transformations.

Contribution

It introduces a local supersymmetry-like invariance in curved backgrounds and proves the theory's finiteness and anomaly absence to all orders.

Findings

The theory is anomaly-free in curved space-time.

Ultraviolet and infrared divergences are absent at all perturbation orders.

The model maintains invariance under new supersymmetry-like transformations.

Abstract

Different models of field theories in two dimensions can be described by the action $Tr\int \vf F$. In the presence of a curved background, we construct a local supersymmetry-like transformations under which the action is invariant. Furthermore, by analysing the cohomology of the theory we show the absence of anomalies. Also the ultraviolet as well as the infrared finiteness of the theory are proven to all orders of perturbation theory.