Chiral effective potential in $4D$, $\mathcal{N}=4$ SYM theory

TL;DR

This work analyzes the chiral effective potential in 4D, N=4 SYM formulated with N=1 superfields using a background-field approach. It demonstrates that chiral corrections are finite and proportional to the classical chiral potential $W_{tree}$, with explicit one- and two-loop coefficients captured by Upsilon^{(1)} and Upsilon^{(2)}. In the ladder (large-N) limit, the authors sum leading-color triangle diagrams to obtain an all-orders coefficient Upsilon^{tot} multiplying $W_{tree}$, confirming a remarkably simple structure where quantum dynamics are encoded in a single factor. The results underscore the finiteness and highly constrained nature of chiral corrections in this finite theory, and they provide exact perturbative sums and large-N insights that may hint at deeper symmetries or integrability structures.

Abstract

We consider $4D$, $\mathcal{N}=4$, $SU(N)$ super Yang-Mills theory formulated in terms of $\mathcal{N}=1$ superfields where the leading low-energy contributions to effective action are given by chiral effective potential. This effective potential is calculated in one- and higher-loop approximations. It is shown that this potential is automatically finite and proportional to the classical chiral potential. All quantum corrections are found explicitly and factored into a coefficient at the classical potential.

Figures (6)

• Figure 1: Feynman rules necessary for calculating chiral contributions in the models considered in the main text. External thick lines denote classical background fields, thin lines denote quantum lines. Straight lines are chiral superpropagators, curved line is a vector superpropagator. Black dots denote vertices $g$.
• Figure 2: Feynman one-loop supergraph contributing to the chiral superpotential.
• Figure 3: Feynman two-loop chiral supergraph contributing to the non-holomorphic superpotential.
• Figure 4: Feynman two-loop finite diagrams that can contribute to the chiral superpotential.
• Figure 5: Feynman two-loop finite diagrams that can contribute to the chiral superpotential.