Yang-Mills theory a la string

TL;DR

This paper explores a surface-based Yang-Mills theory linked to the rotational connection of higher codimension surfaces, analyzing its equations and relation to traditional Yang-Mills theory.

Contribution

It introduces a novel surface-centric Yang-Mills framework and clarifies the connection between its Euler-Lagrange equations and classical Yang-Mills equations.

Findings

Derived Euler-Lagrange equations for the surface Yang-Mills functional

Established relationships between surface equations and standard Yang-Mills equations

Provided a new geometric perspective on Yang-Mills theory for embedded surfaces

Abstract

A surface of codimension higher than one embedded in an ambient space possesses a connection associated with the rotational freedom of its normal vector fields. We examine the Yang-Mills functional associated with this connection. The theory it defines differs from Yang-Mills theory in that it is a theory of surfaces. We focus, in particular, on the Euler-Lagrange equations describing this surface, introducing a framework which throws light on their relationship to the Yang-Mills equations.