Asymptotic freedom in the BV formalism

Elliott, Chris; Williams, Brian R.; Yoo, Philsang

doi:10.1016/j.geomphys.2017.08.009

Cited by 10 publications

(19 citation statements)

References 19 publications

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“…As a peculiar corollary of our main result, and our work in developing the one-loop β-function for QFT in the BV formalism [EWY18], we have the following.…”

Section: One-loop Regularization For Theories On C Dmentioning

confidence: 64%

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Renormalization for Holomorphic Field Theories

Williams

2020

Commun. Math. Phys.

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We introduce the concept of a holomorphic field theory on any complex manifold in the language of the Batalin-Vilkovisky formalism. When the complex dimension is one, this setting agrees with that of chiral conformal field theory. Our main result concerns the behavior of holomorphic theories under renormalization group flow. Namely, we show that holomorphic theories are one-loop finite. We use this to completely characterize holomorphic anomalies in any dimension.Throughout, we compare our approach to holomorphic field theories to more familiar approaches including that of supersymmetric field theories. 7

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“…As a peculiar corollary of our main result, and our work in developing the one-loop β-function for QFT in the BV formalism [EWY18], we have the following.…”

Section: One-loop Regularization For Theories On C Dmentioning

confidence: 64%

“…, w k−1 ). For a reference similar to the notation used here see the Appendix of our work in [EWY18]. The inequality in (21) becomes |W k,(n)…”

Section: A Simplification For One-loop Weightsmentioning

confidence: 99%

Renormalization for Holomorphic Field Theories

Williams

2020

Commun. Math. Phys.

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“…The theory of RG flow and effective action (EA) has been studied in a BV framework both from a physical [9,10] and a mathematical [11][12][13][14][15] point of view and in a variety of guises. Recent mathematical studies close in spirit to our contribution are [16][17][18].…”

Section: Introductionmentioning

confidence: 94%

Exact renormalization group in Batalin-Vilkovisky theory

Zucchini

2018

J. High Energ. Phys.

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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 r1sR. The extra odd direction in scale spaceallows 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.MSC: 81T13 81T20 81T45

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“…(See refs. [17][18][19] for three recent mathematical studies similar in spirit to ours). The rest of this section will be devoted to introducing the reader to the subject and to motivate our approach to it.…”

Section: Introductionmentioning

confidence: 97%

Exact renormalization group and effective action: A Batalin–Vilkovisky algebraic formulation

Zucchini

2019

Journal of Mathematical Physics

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In the present paper, which is a mathematical follow-up of [16] taking inspiration from [11], we present an abstract formulation of exact renormalization group (RG) in the framework of Batalin-Vilkovisky (BV) algebra theory.In the first part, we work out a general algebraic and geometrical theory of BV algebras, canonical maps, flows and flow stabilizers. In the second part, relying on this formalism, we build a BV algebraic theory of the RG. In line with the graded geometric outlook of our approach, we adjoin the RG scale with an odd parameter and analyse in depth the implications of the resulting RG supersymmetry and find that the RG equation (RGE) takes Polchinski's form [3]. Finally, we study abstract purely algebraic odd symplectic free models of RG flow and effective action (EA) and the perturbation theory thereof to illustrate and exemplify the general theory.MSC: 81T13 81T20 81T45

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Asymptotic freedom in the BV formalism

Cited by 10 publications

References 19 publications

Renormalization for Holomorphic Field Theories

Renormalization for Holomorphic Field Theories

Exact renormalization group in Batalin-Vilkovisky theory

Exact renormalization group and effective action: A Batalin–Vilkovisky algebraic formulation

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