Large N Volume Independence and an Emergent Fermionic Symmetry

TL;DR

This paper explores how large-N QCD-like theories maintain volume independence despite a Hagedorn spectrum, suggesting an emergent fermionic symmetry at large N that resolves apparent conflicts without requiring supersymmetry.

Contribution

It proposes that spectral degeneracies imply an emergent fermionic symmetry in large-N theories, resolving the tension between volume independence and Hagedorn spectra without supersymmetry.

Findings

Spectral degeneracies between bosonic and fermionic states are demonstrated.

Large-N theories can have a Hagedorn spectrum without phase transitions.

An example of spectral degeneracy in a non-supersymmetric toy model is provided.

Abstract

Large-N volume independence in circle-compactified QCD with N_f \geq 1 adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories are believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically implies a phase transition at some finite radius. This tension is resolved if there are degeneracies between the spectra of bosonic and fermionic states, as happens in the N_f=1 supersymmetric case. Resolution of the tension for N_f>1 then suggests the emergence of a fermionic symmetry at large N, where there is no supersymmetry. We can escape the Coleman-Mandula theorem since the N=\infty theory is free, with a trivial S-matrix. We show an example of such a spectral degeneracy in a non-supersymmetric toy example which has a Hagedorn spectrum.