A note on the boundary contribution with bad deformation in gauge theory

TL;DR

This paper investigates boundary contributions in gauge theory with bad deformations, proposing a new method based on ${ m extbf{N=4}}$ SYM theory to compute these contributions and demonstrate gauge theory's cut-constructibility.

Contribution

It introduces a novel approach using ${ m extbf{N=4}}$ SYM theory to calculate boundary contributions in gauge theories with bad deformations, extending the understanding of their structure.

Findings

Developed an on-shell recursion relation for boundary contributions.

Showed gauge theory remains cut-constructible under certain bad deformations.

Provided a practical method to analyze boundary effects without Feynman diagrams.

Abstract

Motivated by recently progresses in the study of BCFW recursion relation with nonzero boundary contributions for theories with scalars and fermions\cite{Bofeng}, in this short note we continue the study of boundary contributions of gauge theory with the bad deformation. Unlike cases with scalars or fermions, it is hard to use Feynman diagrams directly to obtain boundary contributions, thus we propose another method based on the ${\cal N}=4$ SYM theory. Using this method, we are able to write down a useful on-shell recursion relation to calculate boundary contributions from related theories. Our result shows the cut-constructibility of gauge theory even with the bad deformation in some generalized sense.