Large-N volume independence in conformal and confining gauge theories

Abstract

Consequences of large $N$ volume independence are examined in conformal and confining gauge theories. In the large $N$ limit, gauge theories compactified on ${\mathbb{R}}^{d-k}\times (S^1{)}^k$ are independent of the $S^1$ radii, provided the theory has unbroken center symmetry. In particular, this implies that a large $N$ gauge theory which, on ${\mathbb{R}}^d$, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on ${\mathbb{R}}^{d-k}\times (S^1{)}^k$. In other words, finite volume effects are $1/N$ suppressed. In lattice formulations of vector-like theories, this implies that numerical studies to determine the boundary between confined and conformal phases may be performed on one-site lattice models. In $N=4$ supersymmetric Yang-Mills theory, the center symmetry realization is a matter of choice: the theory on ${\mathbb{R}}^{4-k}\times (S^1{)}^k$ has a moduli space which contains points with all possible realizations of center symmetry. Large $N$ QCD with massive adjoint fermions and one or two compactified dimensions has a rich phase structure with an infinite number of phase transitions coalescing in the zero radius limit.

24 pages, added ref

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• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Microscopic Structure of Magnetic Bions
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• Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
• Deconfinement in N=1 super Yang-Mills theory on R^3 x S^1 via dual-Coulomb gas and "affine" XY-model
• Resurgence in $\eta$-deformed Principal Chiral Models
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• $\theta$ dependence in trace deformed $SU(3)$ Yang-Mills theory: a lattice study
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• Phases of a two dimensional large N gauge theory on a torus
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• Partial-Symmetry-Breaking Phase Transitions
• From 3d dualities to hadron physics
• Spectral form factor for free large $N$ gauge theory and strings
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• $\theta$-dependence and center symmetry in Yang-Mills theories
• Bose-Fermi Degeneracies in Large $N$ Adjoint QCD
• Bose-Fermi cancellations without supersymmetry
• Emergent gravity from Eguchi-Kawai reduction
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• Volume independence for Yang-Mills fields on the twisted torus
• Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
• Dihedral symmetry in $SU(N)$ Yang-Mills theory
• 1-form symmetry versus large N QCD
• Renormalon structure in compactified spacetime
• Exponential reduction of finite volume effects with twisted boundary conditions
• The twisted gradient flow coupling at one loop
• Chern-Simons diffusion rate in a holographic Yang-Mills theory
• Generating new dualities through the orbifold equivalence: a demonstration in ABJM and four-dimensional quivers
• New States of Gauge Theories on a Circle
• Dimensionally reduced SYM${}_4$ at large-$N$: an intriguing Coulomb approximation
• Phases of circle-compactified QCD with adjoint fermions at finite density
• QCD in magnetic field, Landau levels and double-life of unbroken center-symmetry
• Monte-Carlo simulations of overlap Majorana fermions
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• Lattice simulations of adjoint QCD with one Dirac overlap fermion
• Holographic Dual of the Eguchi-Kawai Mechanism
• ${\mathbb{Z}}_N$ stability and continuity in twisted Eguchi-Kawai model with two-flavor adjoint fermions
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• Novel first-order phase transition and critical points in SU(3) Yang-Mills theory with spatial compactification
• On the perturbative aspects of deformed Yang-Mills theory