Koszul duality in quantum field theory

Paquette, Natalie M.; Williams, Brian R.

doi:10.48550/arxiv.2110.10257

Cited by 3 publications

(5 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here we will write down the generators of the chiral algebra and their OPEs explicitly. They are derived in the bulk of the paper by starting with the twistor space description of the theory and using the method of Koszul duality [11,12]. We work in Euclidean signature here, although since our integrand is an entire analytic function, we can readily move to other signatures.…”

Section: The Chiral Algebramentioning

confidence: 99%

“…As explained in [11,43], the algebras resulting from these constraints can be encapsulated mathematically by the notion of Koszul duality. We refer to [12] for a recent exposition and more details on this point of view.…”

Section: The Chiral Algebra By Koszul Dualitymentioning

confidence: 99%

“…This is a consequence of conservation of momentum, which in spinor-helicity notation takes the formj ij [jk] = 0.With four particles, this means[12] 13 = [42] 43 , so that[12][34] 13 24 = [13][24] 12 34 .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Celestial holography meets twisted holography: 4d amplitudes from chiral correlators

Costello¹,

Paquette²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We propose a new program for computing a certain integrand of scattering amplitudes of four-dimensional gauge theories which we call the form factor integrand, starting from 6d holomorphic theories on twistor space. We show that the form factor integrands can be expressed as sums of products of 1.) correlators of a 2d chiral algebra, related to the algebra of asymptotic symmetries uncovered recently in the celestial holography program, and 2.) OPE coefficients of a 4d non-unitary CFT. We prove that conformal blocks of the chiral algebras are in one-to-one correspondence with local operators in 4d. We use this bijection to recover the Parke-Taylor formula, the CSW formula, and certain one-loop scattering amplitudes. Along the way, we explain and derive various aspects of celestial holography, incorporating techniques from the twisted holography program such as Koszul duality. This perspective allows us to easily and efficiently recover the infinite-dimensional chiral algebras of asymptotic symmetries recently extracted from scattering amplitudes of massless gluons and gravitons in the celestial basis. We also compute some simple one-loop corrections to the chiral algebras and derive the three-dimensional bulk theories for which these 2d algebras furnish an algebra of boundary local operators.

show abstract

Section: The Chiral Algebramentioning

confidence: 99%

Section: The Chiral Algebra By Koszul Dualitymentioning

confidence: 99%

See 1 more Smart Citation

Celestial holography meets twisted holography: 4d amplitudes from chiral correlators

Costello¹,

Paquette²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In fact, there's a second conjectural relation between the chiral algebras at 𝑟 = 0 and 𝑟 = ∞. They are expected to be 'Koszul dual' to each other; see [72,77,78] for reviews of this fact. Physically, this means that the chiral algebra at 𝑟 = ∞ is isomorphic to the most general chiral algebra that can be gauge invariantly coupled to the chiral algebra at 𝑟 = 0.…”

Section: Jhep02(2024)228mentioning

confidence: 99%

Equating extrapolate dictionaries for massless scattering

Jørstad,

Pasterski,

Sharma

2024

J. High Energ. Phys.

View full text Add to dashboard Cite

We study features of celestial CFT correlation functions when the bulk theory is itself a CFT. We show that conformal inversions in the bulk map boost eigenstates to shadow transformed boost eigenstates. This is demonstrated explicitly for the wavefunctions of free massless scalars, and finds interesting applications to building extrapolate dictionaries. Because inversions exchange null infinity and the light cone of the origin, one finds a relation between the massless extrapolate dictionary — involving correlators of operators inserted along null infinity — and the slice-by-slice extrapolate dictionary recently studied by Sleight and Taronna starting from the hyperbolic foliation of de Boer and Solodukhin. Namely, boundary correlators of Sleight and Taronna coincide with celestial amplitudes of shadow transformed boost eigenstates. These considerations are unified by lifting celestial correlators to the Einstein cylinder. This also sheds new light on the extraction of the 𝑆-matrix from the flat limit of AdS/CFT.

show abstract

“…Mathematically, the chiral algebra U is Koszul dual to the algebra of local operators in classical Poisson-BF theory on PT. For more details on the role of Koszul duality in quantum field theory we refer the reader to [50].…”

Section: Jhep01(2023)018mentioning

confidence: 99%

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

Roland

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

Koszul duality in quantum field theory

Cited by 3 publications

References 39 publications

Celestial holography meets twisted holography: 4d amplitudes from chiral correlators

Celestial holography meets twisted holography: 4d amplitudes from chiral correlators

Equating extrapolate dictionaries for massless scattering

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

Contact Info

Product

Resources

About