Large N Volume Independence and an Emergent Fermionic Symmetry

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.

5 pages, 1 figure. v3: corrected typos, and added an important set of references to the idea of misaligned supersymmetry

References in corpus (8)

• Volume independence in large Nc QCD-like gauge theories
• (In)validity of large N orientifold equivalence
• Finite size phase transitions in QCD with adjoint fermions
• Large-N reduction in QCD-like theories with massive adjoint fermions
• Twisted space-time reduced model of large N QCD with two adjoint Wilson fermions
• Large-N volume reduction of lattice QCD with adjoint Wilson fermions at weak-coupling
• Large-N reduction of SU(N) Yang-Mills theory with massive adjoint overlap fermions
• Baryons and Skyrmions in QCD with Quarks in Higher Representations

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