Exact renormalization group in Batalin-Vilkovisky theory

Abstract In this paper, inspired by the Costello’s seminal work [11], we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In the spirit of effective field theory, the BV bracket and Laplacian structure as well as the BV effecti...

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Main Author:	Roberto Zucchini
Format:	Article
Language:	English
Published:	Springer 2018-03-01
Series:	Journal of High Energy Physics
Subjects:	BRST Quantization Differential and Algebraic Geometry Renormalization Group Topological Field Theories
Online Access:	http://link.springer.com/article/10.1007/JHEP03(2018)132

id	doaj-art-44e259e1409946fda2a61109fa44b037
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spelling	doaj-art-44e259e1409946fda2a61109fa44b0372018-08-15T21:56:50ZengSpringerJournal of High Energy Physics1029-84792018-03-012018313510.1007/JHEP03(2018)132Exact renormalization group in Batalin-Vilkovisky theoryRoberto Zucchini0Dipartimento di Fisica ed Astronomia, Università di Bologna, I.N.F.N., sezione di BolognaAbstract In this paper, inspired by the Costello’s seminal work [11], we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In the spirit of effective field theory, the BV bracket and Laplacian structure as well as the BV effective action (EA) depend on an effective energy scale. The BV EA at a certain scale satisfies the BV quantum master equation at that scale. The RG flow of the EA is implemented by BV canonical maps intertwining the BV structures at different scales. Infinitesimally, this generates the BV exact renormalization group equation (RGE). We show that BV RG theory can be extended by augmenting the scale parameter space R to its shifted tangent bundle T [1]ℝ. The extra odd direction in scale space allows for a BV RG supersymmetry that constrains the structure of the BV RGE bringing it to Polchinski’s form [6]. We investigate the implications of BV RG supersymmetry in perturbation theory. Finally, we illustrate our findings by constructing free models of BV RG flow and EA exhibiting RG supersymmetry in the degree −1 symplectic framework and studying the perturbation theory thereof. We find in particular that the odd partner of effective action describes perturbatively the deviation of the interacting RG flow from its free counterpart.http://link.springer.com/article/10.1007/JHEP03(2018)132BRST QuantizationDifferential and Algebraic GeometryRenormalization GroupTopological Field Theories
institution	Open Data Bank
collection	Open Access Journals
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language	English
format	Article
author	Roberto Zucchini
spellingShingle	Roberto Zucchini Exact renormalization group in Batalin-Vilkovisky theory Journal of High Energy Physics BRST Quantization Differential and Algebraic Geometry Renormalization Group Topological Field Theories
author_facet	Roberto Zucchini
author_sort	Roberto Zucchini
title	Exact renormalization group in Batalin-Vilkovisky theory
title_short	Exact renormalization group in Batalin-Vilkovisky theory
title_full	Exact renormalization group in Batalin-Vilkovisky theory
title_fullStr	Exact renormalization group in Batalin-Vilkovisky theory
title_full_unstemmed	Exact renormalization group in Batalin-Vilkovisky theory
title_sort	exact renormalization group in batalin-vilkovisky theory
publisher	Springer
series	Journal of High Energy Physics
issn	1029-8479
publishDate	2018-03-01
description	Abstract In this paper, inspired by the Costello’s seminal work [11], we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In the spirit of effective field theory, the BV bracket and Laplacian structure as well as the BV effective action (EA) depend on an effective energy scale. The BV EA at a certain scale satisfies the BV quantum master equation at that scale. The RG flow of the EA is implemented by BV canonical maps intertwining the BV structures at different scales. Infinitesimally, this generates the BV exact renormalization group equation (RGE). We show that BV RG theory can be extended by augmenting the scale parameter space R to its shifted tangent bundle T [1]ℝ. The extra odd direction in scale space allows for a BV RG supersymmetry that constrains the structure of the BV RGE bringing it to Polchinski’s form [6]. We investigate the implications of BV RG supersymmetry in perturbation theory. Finally, we illustrate our findings by constructing free models of BV RG flow and EA exhibiting RG supersymmetry in the degree −1 symplectic framework and studying the perturbation theory thereof. We find in particular that the odd partner of effective action describes perturbatively the deviation of the interacting RG flow from its free counterpart.
topic	BRST Quantization Differential and Algebraic Geometry Renormalization Group Topological Field Theories
url	http://link.springer.com/article/10.1007/JHEP03(2018)132
_version_	1612704839230291968

Exact renormalization group in Batalin-Vilkovisky theory

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