Asymptotic Freedom in the BV formalism

Chris Elliott, Brian R Williams, Philsang Yoo

Research output: Contribution to journalArticlepeer-review


We define the beta-function of a perturbative quantum field theory in the mathematical framework introduced by Costello -- combining perturbative renormalization and the BV formalism -- as the cohomology class of a certain element in the obstruction-deformation complex. We show that the one-loop beta-function is a well-defined element of the local deformation complex for translation-invariant and classically scale-invariant theories, and furthermore that it is locally constant as a function on the space of classical interactions and computable as a rescaling anomaly, or as the logarithmic one-loop counterterm. We compute the one-loop beta-function in first-order Yang--Mills theory, recovering the famous asymptotic freedom for Yang--Mills in a mathematical context.
Original languageEnglish
Pages (from-to) 246-283
Number of pages49
JournalJournal of geometry and physics
Early online date19 Sep 2017
Publication statusPublished - 31 Jan 2018


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