Volume independence for Yang-Mills fields on the twisted torus

Abstract

We review some recent results related to the notion of volume independence in SU(N) Yang-Mills theories. The topic is discussed in the context of gauge theories living on a d-dimensional torus with twisted boundary conditions. After a brief introduction reviewing the formalism for introducing gauge fields on a torus, we discuss how volume independence arises in perturbation theory. We show how, for appropriately chosen twist tensors, perturbative results to all orders in the 't Hooft coupling depend on a specific combination of the rank of the gauge group (N) and the periods of the torus (l) given by l N^{2/d}, for d even.We discuss the well-known relation to non-commutative field theories and address certain threats to volume independence associated to the occurrence of tachyonic instabilities at one-loop order. We end by presenting some numerical results in 2+1 dimensions that extend these ideas to the non-perturbative domain.

arXiv comment31 pages. Review paper. Dedicated to the memory of Pierre van Baal

References in corpus (53)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• SU(N) gauge theories in 2+1 dimensions
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
• Volume independence in large Nc QCD-like gauge theories
• Finite N Matrix Models of Noncommutative Gauge Theory
• String excitation energies in SU(N) gauge theories beyond the free-string approximation
• Nonperturbative Dynamics of Noncommutative Gauge Theory
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• Large N reduction in the continuum three dimensional Yang-Mills theory
• On the effective action of confining strings
• Closed flux tubes and their string description in D=2+1 SU(N) gauge theories
• Large $N$ reduction with the Twisted Eguchi-Kawai model
• SU(N) gauge theories in 2+1 dimensions -- further results
• A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane
• The string tension from smeared Wilson loops at large N
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• A precise calculation of the fundamental string tension in SU(N) gauge theories in 2+1 dimensions
• Large-N volume independence in conformal and confining gauge theories
• Symmetry Breaking In Twisted Eguchi-Kawai Models
• Closed k-strings in SU(N) gauge theories : 2+1 dimensions
• Quantum Field Theories With Compact Noncommutative Extra Dimensions
• The closed string spectrum of SU(N) gauge theories in 2+1 dimensions
• Large-N reduction in QCD-like theories with massive adjoint fermions
• Investigating Yang-Mills theory and Confinement as a function of the spatial volume
• Phase structure of twisted Eguchi-Kawai model
• Proposal for the numerical solution of planar QCD
• Large N Volume Independence and an Emergent Fermionic Symmetry
• Excitations in Hot Non-Commutative Theories
• Gauge invariant structures and Confinement
• Closed Strings Tachyons and Non-Commutative Instabilities
• Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions
• Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1)
• On the unitarity of quantum gauge theories on non-commutative spaces
• Universality of large N phase transitions in Wilson loop operators in two and three dimensions
• Large-N reduction in QCD with two adjoint Dirac fermions
• Non-Relativistic Non-Commutative Field Theory and UV/IR Mixing
• Twisted space-time reduced model of large N QCD with two adjoint Wilson fermions
• Morita Duality and Large-N Limits
• Instanton-like Contributions to the Dynamics of Yang-Mills Fields on the Twisted Torus
• Aspects of Gauge Theory on Commutative and Noncommutative Tori
• Deconfinement in Yang-Mills theory through toroidal compactification with deformation
• On the spectrum of closed k=2 flux tubes in D=2+1 SU(N) gauge theories
• Computation of the one-loop Symanzik coefficients for the square action
• Phases of three dimensional large N QCD on a continuum torus
• From Perturbation Theory to Confinement: How the String Tension is built up
• Weak-coupling analysis of the single-site large-N gauge theory coupled to adjoint fermions
• Numerical computation of the beta function of large N SU(N) gauge theory coupled to an adjoint Dirac fermion
• Computation of the string tension in three dimensional Yang-Mills theory using large N reduction
• Square Symanzik action to one-loop order
• Strings and Discrete Fluxes of QCD

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• Emergent Dimensions and Braneworlds from Large-N Confinement
• Bose-Fermi cancellations without supersymmetry
• Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to Number Theory
• Exponential reduction of finite volume effects with twisted boundary conditions
• The twisted gradient flow coupling at one loop
• Quantum distillation in QCD
• The two-dimensional twisted reduced principal chiral model revisited
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• Topological order and the vacuum of Yang-Mills theories
• Feynman Amplitudes in Periodically Compactified Spaces -- Spin 0
• Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence