Yang-Mills, Gravity, and 2D String Symmetries

TL;DR

This paper explores the relationship between string theory, 2D geometric field theories, and gravity-Yang-Mills couplings, revealing new insights into anomalies, gauge invariance, and the structure of gravity in lower dimensions.

Contribution

It introduces a novel connection between higher-dimensional theories and 2D field theories, identifying gravitational and gauge anomalies with symmetry orbits and coupling gravity to Yang-Mills with torsion-like terms.

Findings

Gravity can couple to Yang-Mills via a torsion-like term while maintaining gauge invariance.

The work recovers higher-dimensional theories from 2D reductions and identifies their anomaly structures.

It suggests a distinction between cosmological and local gravitational phenomena.

Abstract

It is well known that by using the infinite dimensional symmetries that issue from string theories, one can build 2D geometric field theories. These 2D field theories can be identified with gravitational and gauge anomalies that arise in the presence of background gauge and gravitational anomalies. In this work we consider the background fields as residuum from reducing higher dimensional field theories to two dimensions. This implies a new relationship between string theory and field theories. We identify the isotropy equations of the distinct orbits as the Gau\ss 's law constraints of a Yang-Mills theory coupled to a gravitational theory that has been evaluated on a two-dimensional manifold. We show explicitly how one may recover the higher dimensional theories and extract this new theory of gravity and its coupling to Yang-Mills theory. This gravitational theory is able to couple to Yang-Mills via a torsion-like term and yet maintain gauge invariance. Also this new theory of gravity suggest a natural distinction between cosmology and local gravitation. We comment on the analogue of Chern-Simons theory for diffeomorphism, the vacuum structure of gravity, and also the possibility of extracting explicit realizations of distinct differentiable structures in four dimensions.