Composite Operators and Topological Contributions in Gauge Theory

TL;DR

This paper introduces a gauge invariant operator in higher-dimensional gauge theories that captures topological effects similar to those in theories with Chern-Simons BF terms, revealing new insights into topological contributions.

Contribution

It presents a novel gauge invariant operator associated with electric and magnetic branes in higher-dimensional gauge theories, linking it to topological effects akin to Chern-Simons BF terms.

Findings

Expectation value of the operator encodes topological contributions.

Operator reproduces effects similar to Chern-Simons BF terms.

Provides a new perspective on topological aspects in higher-dimensional gauge theories.

Abstract

In $D$-dimensional gauge theory with a kinetic term based on the p-form tensor gauge field, we introduce a gauge invariant operator associated with the composite formed from a electric $(p-1)$-brane and a magnetic $(q-1)$-brane in $D=p+q+1$ spacetime dimensions. By evaluating the partition function for this operator, we show that the expectation value of this operator gives rise to the topological contributions identical to those in gauge theory with a topological Chern-Simons BF term.