Asymptotic Freedom in the BV Formalism
| Autor: | Elliott, Chris, Williams, Brian, Yoo, Philsang |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.geomphys.2017.08.009 |
| Popis: | 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. Comment: Minor edits made |
| Databáze: | arXiv |
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