Renormalization for Holomorphic Field Theories

Williams, Brian R.

doi:10.1007/s00220-020-03693-5

Cited by 22 publications

(30 citation statements)

References 34 publications

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“…where κ g is the Chevalley-Eilenberg differential for g and [−, −] h is the Lie bracket on h. (Further terms would appear if h were an L ∞ algebra rather than simply Lie.) Thus, another way to encode N = 1 supersymmetry is to prescribe a Maurer-Cartan element in 14) or equivalently a BRST-type differential acting in the space…”

Section: Supersymmetric Field Theoriesmentioning

confidence: 99%

“…In this section, we set up notations and conventions for holomorphic field theories. We mostly follow the approach to this subject presented in [14].…”

Section: Holomorphic Field Theorymentioning

confidence: 99%

“…For related work, including supporting evidence of some conjectures of Costello and Li, see [2,13]. In addition, a foundational mathematical treatment of holomorphic field theory is given in [14]. In this paper, we will most closely borrow notations and conventions from the cited works [2,14].…”

Section: Introductionmentioning

confidence: 99%

“…In addition, a foundational mathematical treatment of holomorphic field theory is given in [14]. In this paper, we will most closely borrow notations and conventions from the cited works [2,14].…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, facets of these theories, such as their anomalies, can be cast in a more algebraic framework. While we do not delve deeply into a utilization of such features in this paper, we refer the reader to [14] for work on the renormalization of holomorphic field theories.…”

Section: Introductionmentioning

confidence: 99%

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Twisted characters and holomorphic symmetries

Saberi

Williams

2020

Lett Math Phys

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We consider holomorphic twists of arbitrary supersymmetric theories in four dimensions. Working in the BV formalism, we rederive classical results characterizing the holomorphic twist of chiral and vector supermultiplets, computing the twist explicitly as a family over the space of nilpotent supercharges in minimal supersymmetry. The BV formalism allows one to work with or without auxiliary fields, according to preference; for chiral superfields, we show that the result of the twist is an identical BV theory, the holomorphic $$\beta \gamma $$ β γ system with superpotential, independent of whether or not auxiliary fields are included. We compute the character of local operators in this holomorphic theory, demonstrating agreement of the free local operators with the usual index of free fields. The local operators with superpotential are computed via a spectral sequence and are shown to agree with functions on a formal mapping space into the derived critical locus of the superpotential. We consider the holomorphic theory on various geometries, including Hopf manifolds and products of arbitrary pairs of Riemann surfaces, and offer some general remarks on dimensional reductions of holomorphic theories along the $$(n-1)$$ ( n - 1 ) -sphere to topological quantum mechanics. We also study an infinite-dimensional enhancement of the flavor symmetry in this example, to a recently studied central extension of the derived holomorphic functions with values in the original Lie algebra, that generalizes the familiar Kac–Moody enhancement in two-dimensional chiral theories.

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Section: Supersymmetric Field Theoriesmentioning

confidence: 99%

“…In this section, we set up notations and conventions for holomorphic field theories. We mostly follow the approach to this subject presented in [14].…”

Section: Holomorphic Field Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Twisted characters and holomorphic symmetries

Saberi

Williams

2020

Lett Math Phys

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On the associativity of 1-loop corrections to the celestial operator product in gravity

Roland

2023

J. High Energ. Phys.

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The question of whether the holomorphic collinear singularities of graviton amplitudes define a consistent chiral algebra has garnered much recent attention. We analyse a version of this question for infinitesimal perturbations around the self-dual sector of 4d Einstein gravity. The singularities of tree amplitudes in such perturbations do form a consistent chiral algebra, however at 1-loop its operator products are corrected by the effective graviton vertex. We argue that the chiral algebra can be interpreted as the universal holomorphic surface defect in the twistor uplift of self-dual gravity, and show that the same correction is induced by an anomalous diagram in the bulk-defect system. The 1-loop holomorphic collinear singularities do not form a consistent chiral algebra. The failure of associativity can be traced to the existence of a recently discovered gravitational anomaly on twistor space. It can be restored by coupling to an unusual 4th-order gravitational axion, which cancels the anomaly by a Green-Schwarz mechanism. Alternatively, the anomaly vanishes in certain theories of self-dual gravity coupled to matter, including in self-dual supergravity.

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One-loop corrections to the celestial chiral algebra from Koszul Duality

Fernández

2023

J. High Energ. Phys.

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We consider self-dual Yang-Mills theory (SDYM) in four dimensions and its lift to holomorphic BF theory on twistor space. Following the work of Costello and Paquette, we couple SDYM to a quartic axion field, which guarantees associativity of the (extended) celestial chiral algebra at the quantum level. We demonstrate how to reproduce their one-loop quantum deformation to the chiral algebra using Koszul duality.

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Renormalization for Holomorphic Field Theories

Cited by 22 publications

References 34 publications

Twisted characters and holomorphic symmetries

Twisted characters and holomorphic symmetries

On the associativity of 1-loop corrections to the celestial operator product in gravity

One-loop corrections to the celestial chiral algebra from Koszul Duality

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