Geometry and Dynamics of a Coupled 4D-2D Quantum Field Theory

TL;DR

This paper explores the geometric and dynamical properties of a coupled 4D-2D quantum field theory involving nonAbelian vortices, revealing how vortex fluctuations influence 4D gauge modes and topological effects.

Contribution

It provides a detailed analysis of the interplay between 2D vortex zero modes and 4D gauge fields, highlighting the nonnormalizability of certain modes and the role of topological effects in a specific gauge model.

Findings

2D vortex zero modes excite massless 4D gauge modes.

Certain vortex zero modes become nonnormalizable due to divergent energies.

Topological effects like the nonAbelian Aharonov-Bohm effect are significant.

Abstract

Geometric and dynamical aspects of a coupled 4D-2D interacting quantum field theory - the gauged nonAbelian vortex - are investigated. The fluctuations of the internal 2D nonAbelian vortex zeromodes excite the massless 4D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2D CP(N-1) zeromodes associated with a nonAbelian vortex become nonnormalizable. Moreover, all sorts of global, topological 4D effects such as the nonAbelian Aharonov-Bohm effect come into play. These topological global features and the dynamical properties associated with the fluctuation of the 2D vortex moduli modes are intimately correlated, as shown concretely here in a U(1) x SU(N) x SU(N) model with scalar fields in a bifundamental representation of the two SU(N) factor gauge groups.