# Zero-mode product expansions and higher order couplings in gauge backgrounds

## TL;DR

This paper investigates how zero-mode products in gauge backgrounds lead to a structured operator product expansion, simplifying higher-order couplings into three-point interactions in a four-dimensional effective field theory.

## Contribution

It reveals a selection rule that decomposes higher-order couplings into three-point couplings based on the structure of Dirac operators, connecting to conformal field theory.

## Key findings

- Higher-order couplings are expanded into three-point couplings.
- Selection rule derived from Dirac operator structure.
- Connection to operator product expansion in conformal field theory.

## Abstract

We study a four-dimensional low-energy effective field theory derived from extra dimensional field theories with general gauge backgrounds. We find that products among fermionic zero-modes and lightest scalar modes are expanded by other fermionic zero-modes and lightest scalar modes. Using this aspect, we show that higher-order couplings among the fermionic zero-modes and the lightest scalar mode can be decomposed into three-point couplings. This selection rule originating from a structure of the Dirac-type operators indicates the operator product expansion the underlying conformal field theory.