Non-Hermitian Structure and Exceptional Points in Yang-Mills Theory from Analytic Continuation of Nc

TL;DR

This paper explores how analytically continuing the number of colors in Yang-Mills theory introduces non-Hermitian features, revealing exceptional points, topological defects, and connections to PT symmetry, with implications for conformal field theories.

Contribution

It uncovers a non-Hermitian structure in Yang-Mills theory via complex Nc analysis, identifying exceptional points and topological effects that influence operator spectra and symmetries.

Findings

Identification of exceptional points in complex Nc space.

Demonstration of topological defects and geometric phases.

Logarithmic scaling behavior near exceptional points.

Abstract

We show that analytic continuation of the number of colors, Nc, naturally endows Yang-Mills theory with a non-Hermitian structure. By examining the spectrum of the dilatation operator as a function of complex Nc, we identify a network of Exceptional Points (EPs) -- non-Hermitian degeneracies where anomalous dimensions degenerate and operator eigenstates coalesce. We demonstrate that these EPs act as topological defects in complex Nc-space, generating non-Abelian geometric phases and enforcing nontrivial monodromies among gauge-invariant operators. Moreover, we establish a correspondence between the spontaneous breaking of an emergent PT symmetry of the dilatation operator and the fundamental spacetime PT symmetry of the underlying gauge theory. In the vicinity of EPs, the resulting non-Hermitian dynamics produces logarithmic scaling behavior in correlation functions, characteristic of logarithmic conformal field theories. Our results place conventional unitary Yang-Mills theory within a broader complexified parameter space possessing rich topological structure, suggesting a new interface between non-Hermitian physics and quantum field theory.