Quasi BPS Wilson loops, localization of loop equation by homology and exact beta function in the large N limit of SU(N) Yang-Mills theory

Abstract

We localize the loop equation of large-N YM theory in the ASD variables on a critical equation for an effective action by means of homological methods as opposed to the cohomological localization of equivariantly closed forms in local field theory. Our localization occurs for some special simple quasi BPS Wilson loops, that have no perimeter divergence and no cusp anomaly for backtracking cusps, in a partial Eguchi-Kawai reduction from four to two dimensions of the non-commutative theory in the limit of infinite non-commutativity and in a lattice regularization in which the ASD integration variables live at the points of the lattice, thus implying an embedding of parabolic Higgs bundles in the YM functional integral. We find that the beta function of the effective action is saturated by the non-commutative ASD vortices of the EK reduction. An exact canonical beta function of NSVZ type that reproduces the universal first and second perturbative coefficients follows by the localization on vortices. Finally we argue that a scheme can be found in which the canonical coupling coincides with the physical charge between static quark sources in the large-N limit and we compare our theoretical calculation with some numerical lattice result.

arXiv comment52 pages, latex; a change of notation in the vortices equations; a footnote added

References in corpus (24)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Noncommutative Field Theory
• Wilson loops in large N field theories
• Two Dimensional Gauge Theories Revisited
• Wilson Loops and Minimal Surfaces
• A Perturbative Window into Non-Perturbative Physics
• Quark confinement and the bosonic string
• Mirror symmetry, Langlands duality, and the Hitchin system
• The wall of the cave
• Holomorphy, Rescaling Anomalies and Exact beta Functions in Supersymmetric Gauge Theories
• String excitation energies in SU(N) gauge theories beyond the free-string approximation
• Holomorphic matrix models
• Arc Operads and Arc Algebras
• Closed/open string diagrammatics
• (Anti)symmetric matter and superpotentials from IIB orientifolds
• The light-cone gauge and the calculation of the two-loop splitting functions
• Beta function and infrared renormalons in the exact Wilson renormalization group in Yang-Mills theory
• Wild nonabelian Hodge theory on curves
• Global anti-self-dual Yang-Mills fields in split signature and their scattering
• Decorated Teichmüller Theory of Bordered Surfaces
• The large-N limit of QCD and the collective field of the Hitchin fibration
• The First Thirty Years of Large-N Gauge Theory
• Exact beta function from the holographic loop equation of large-N QCD_4
• Joining-splitting interaction of non-critical string

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