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arXiv · 2309.07399

Geometric Derivation of the Finite $N$ Master Loop Equation

Omar Abdelghani·Ron Nissim
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Abstract

In this paper we provide a geometric derivation of the master loop equation for the lattice Yang-Mills model with structure group $G \in \{SO(N),SU(N), U(N)\}$. This approach is based on integration by parts on $G$. In the appendix we compare our approach to that of \cite{Ch19a} and \cite{J16} based on Schwinger-Dyson equations, and \cite{SheSmZh22} based on stochastic analysis. In particular these approaches are all easily seen to be equivalent. The novelty in our approach is the use of intrinsic geometry of $G$ which we believe simplifies the derivation.

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Omar Abdelghani, Ron Nissim. 2023-09-14. Geometric Derivation of the Finite $N$ Master Loop Equation. https://arxiv.org/abs/2309.07399

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