Bose-Fermi Degeneracies in Large $N$ Adjoint QCD

Abstract

We analyze the large $N$ limit of adjoint QCD, an $SU(N)$ gauge theory with $N_f$ flavors of massless adjoint Majorana fermions, compactified on $S^3\times S^1$. We focus on the weakly-coupled confining small-$S^3$ regime. If the fermions are given periodic boundary conditions on $S^1$, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any $S^1$ size $L$, even though the bosonic and fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in the confining phase for any $L\sim N^0$, explaining how it is able to enjoy large $N$ volume independence for any $L$. The large $N$ boson-fermion cancellations take place in a setting where adjoint QCD is manifestly non-supersymmetric at any finite $N$, and are consistent with the recent conjecture that adjoint QCD has emergent fermionic symmetries in the large $N$ limit.

35 pages, 5 figures. v3: further minor corrections

References in corpus (12)

• Counting Gauge Invariants: the Plethystic Program
• Volume independence in large Nc QCD-like gauge theories
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Finite size phase transitions in QCD with adjoint fermions
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Large N Volume Independence and an Emergent Fermionic Symmetry
• Finite Volume Phases of Large N Gauge Theories with Massive Adjoint 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
• Remarks on Adjoint QCD with k Flavors, k>= 2

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• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• Emergent Dimensions and Braneworlds from Large-N Confinement
• Bose-Fermi cancellations without supersymmetry
• Emergent gravity from Eguchi-Kawai reduction
• Twisted superspace: Non-renormalization and fermionic symmetries in certain (heterotic string inspired) non-supersymmetric field theories
• Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter
• A 4D-2D equivalence for large-N Yang-Mills theory
• Quantum distillation in QCD
• Spectral sum rules for confining large-N theories
• L-functions for Meromorphic Modular Forms and Sum Rules in Conformal Field Theory
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories