Hidden Symmetries of Large N QCD

TL;DR

The paper uncovers a hidden local supersymmetry in large N QCD loop dynamics, leading to a topological supergravity interpretation and new insights into meson, glueball sectors, and chiral symmetry breaking.

Contribution

It introduces a novel local SUSY symmetry in large N QCD loop equations, revealing a 1D topological supergravity structure without an einbein-gravitino.

Findings

Derivation of large N_c loop equation in superloop space

Identification of a 1D topological supergravity structure

Discussion of implications for meson, glueball sectors, and chiral symmetry breaking

Abstract

The local SUSY symmetry of the loop dynamics of QCD is found. The remarkable thing is, there is no einbein-gravitino on this theory, which makes it a 1D topological supergravity, or locally SUSY quantum mechanics. Using this symmetry, we derive the large $N_c$ loop equation in momentum superloop space. Introducing as before the position operator $\X{\mu}$ we argue that the superloop equation is equivalent to invariance of correlation functions of products of these operators with respect to certain quadrilinear transformation. The applications to meson and glueball sectors as well as the chiral symmetry breaking are discussed. The 1D field theory with Quark propagating around the loop in superspace is constructed.