Wrapping interactions and the genus expansion of the 2-point function of composite operators

TL;DR

This paper systematically analyzes wrapping interactions in gauge theories like N=4 SYM, focusing on their role in the genus expansion of 2-point functions and introducing a method to isolate these effects using spectator fields.

Contribution

It presents a new strategy to identify wrapping contributions in the genus expansion, applicable to theories with color degrees of freedom, including N=4 SYM.

Findings

Developed a systematic approach to isolate wrapping interactions.

Demonstrated the method with explicit computations in a toy model.

Provided insights relevant for AdS/CFT correspondence checks.

Abstract

We perform a systematic analysis of wrapping interactions for a general class of theories with color degrees of freedom, including N=4 SYM. Wrapping interactions arise in the genus expansion of the 2-point function of composite operators as finite size effects that start to appear at a certain order in the coupling constant at which the range of the interaction is equal to the length of the operators. We analyze in detail the relevant genus expansions, and introduce a strategy to single out the wrapping contributions, based on adding spectator fields. We use a toy model to demonstrate our procedure, performing all computations explicitly. Although completely general, our treatment should be particularly useful for applications to the recent problem of wrapping contributions in some checks of the AdS/CFT correspondence.