Instanton Number of Noncommutative U(n) gauge theory

TL;DR

This paper demonstrates that the instanton number in noncommutative U(n) gauge theory on R^4 is an integer, identified with the integral of the first Pontrjagin class, using operator formalism and ADHM construction.

Contribution

It establishes the integrality of the instanton number in noncommutative gauge theory and relates it to the first Pontrjagin class through a novel operator formalism approach.

Findings

Instanton number is an integer in noncommutative U(n) gauge theory.

The instanton number corresponds to the dimension of the vector space V in ADHM construction.

The calculation uses a convergent series in operator formalism.

Abstract

We show that the integral of the first Pontrjagin class is given by an integer and it is identified with instanton number of the U(n) gauge theory on noncommutative ${\bf R^4}$. Here the dimension of the vector space $V$ that appear in the ADHM construction is called Instanton number. The calculation is done in operator formalism and the first Pontrjagin class is defined by converge series. The origin of the instanton number is investigated closely, too.