Lectures on Two-Dimensional Noncommutative Gauge Theory 2: Quantization

TL;DR

This paper explores the quantization of two-dimensional noncommutative gauge theory, analyzing symmetries, vacuum amplitudes, instantons, and presenting a new combinatorial solution on fuzzy tori.

Contribution

It provides the first exact quantum solutions and symmetry analysis for noncommutative gauge theory on a torus, including a novel combinatorial approach.

Findings

Derived exact vacuum amplitude expression

Classified instanton contributions

Introduced a new combinatorial solution on fuzzy tori

Abstract

These notes comprise the second part of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. Here we shall deal with the quantum field theory. Topics covered include an investigation of the symmetries of quantum gauge theory on the noncommutative torus within the path integral formalism, the derivation of the exact expression for the vacuum amplitude, and the classification of instanton contributions. A section dealing with a new, exact combinatorial solution of gauge theory on a two-dimensional fuzzy torus is also included.