All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory

Abstract

We give a complete, self-contained, and mathematically rigorous proof that Euclidean Yang-Mills theories are perturbatively renormalisable, in the sense that all correlation functions of arbitrary composite local operators fulfil suitable Ward identities. Our proof treats rigorously both all ultraviolet and infrared problems of the theory and provides, in the end, detailed analytical bounds on the correlation functions of an arbitrary number of composite local operators. These bounds are formulated in terms of certain weighted spanning trees extending between the insertion points of these operators. Our proofs are obtained within the framework of the Wilson-Wegner-Polchinski-Wetterich renormalisation group flow equations, combined with estimation techniques based on tree structures. Compared with previous mathematical treatments of massless theories without local gauge invariance [R. Guida and Ch. Kopper, arXiv:1103.5692; J. Holland, S. Hollands, and Ch. Kopper, Commun. Math. Phys. 342 (2016) 385] our constructions require several technical advances; in particular, we need to fully control the BRST invariance of our correlation functions.

arXiv comment82 pages, includes comparison with other mathematically rigorous approaches, matches published version

References in corpus (23)

• Exact evolution equation for the effective potential
• Local BRST cohomology in gauge theories
• Local BRST cohomology in the antifield formalism: I. General theorems
• OPE Convergence in Conformal Field Theory
• Quantum fields in curved spacetime
• Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory
• Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
• Renormalized Quantum Yang-Mills Fields in Curved Spacetime
• QFT on curved spacetimes: axiomatic framework and examples
• The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory
• Full field algebras
• Removal of violations of the Master Ward Identity in perturbative QFT
• The Master Ward Identity
• Perturbative Renormalization by Flow Equations
• The operator product expansion converges in perturbative field theory
• Batalin-Vilkovisky formalism in locally covariant field theory
• Recursive construction of operator product expansion coefficients
• Renormalization of Spontaneaously Broken SU(2) Yang-Mills Theory with Flow Equations
• Large Momentum bounds from Flow Equations
• Renormalization Proof for Spontaneously broken Yang-Mills Theory with Flow Equations
• Renormalization Proof for Massive phi_4^4 Theory on Riemannian Manifolds
• The operator product expansion converges in massless ${\phi }_4^4$-theory
• Associativity of the operator product expansion

Cited by in corpus (9)

• BRST in the Exact RG
• Action principle for OPE
• Products of composite operators in the exact renormalization group formalism
• Quantum gravity, renormalizability and diffeomorphism invariance
• Renormalization of SU(2) Yang-Mills theory with Flow Equations
• Flow equation approach to singular stochastic PDEs
• Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges
• The gluon condensate in an effective SU(2) Yang-Mills theory
• Constructing CFTs from AdS flows