Loop-level gluon OPEs in celestial holography

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.

“…In the case of SD Yang-Mills, this kind of associativity check was performed in [17]. Similar calculations also appear in [62,63].…”

Section: Failure Of Associativitymentioning

confidence: 82%

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

Roland

2023

“…Perturbative local operators in the HT twist can be realized by Q-cohomology classes of G-invariant operators built from the lowest components φ, ψ, ∂c, B of the fundamental fields and their ∂ derivatives. 4 In order to access the full, non-perturbative algebra of local operators it is useful to use a state-operator correspondence to relate these operators to states of the theory on a sphere P 1 . The space of such states can be obtained from the above twisted description via geometric quantization of the moduli space of solutions to the equations of motion on P 1 .…”

Section: Monopoles In Ht -Twisted N =mentioning

confidence: 99%

“…The space of such states can be obtained from the above twisted description via geometric quantization of the moduli space of solutions to the equations of motion on P 1 . 4 The fact that one should consider ∂c and not c itself is due to the fact that its covariant derivative Dzc is cohomologous to a gaugino λ−; local operators should not include an anti-derivative of this gaugino, cf. [26, section 3.2].…”

Section: Monopoles In Ht -Twisted N =mentioning

confidence: 99%

“…The impact of quantum corrections on these classical chiral algebras, and their fourdimensional origin, has been recently explored by several groups, e.g. [3][4][5][6][7][8][9]. It was observed in [7] that in a formulation of self-dual Yang Mills (SDYM) theory, the chiral algebra of asymptotic symmetries, when deformed to include the theory's one-loop collinear splitting amplitude, failed to be associative.…”

Section: Introductionmentioning

confidence: 99%

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Twistorial monopoles & chiral algebras

Garner,

Paquette

2023

We initiate the study of how the insertion of magnetically charged states in 4d self-dual gauge theories impacts the 2d chiral algebras supported on the celestial sphere at asymptotic null infinity, from the point of view of the 4d/2d twistorial correspondence introduced by Costello and the second author. By reducing the 6d twistorial theory to a 3d holomorphic-topological theory with suitable boundary conditions, we can motivate certain non-perturbative enhancements of the celestial chiral algebra corresponding to extensions by modules arising from 3d boundary monopole operators. We also identify the insertion of 4d (non-abelian) monopoles with families of spectral flow automorphisms of the celestial chiral algebra.

“…One gets these null states in case of gravitons as well as gluons by demanding consistency of the celestial OPE with the soft theorems [6,7,44,45]. For more discussions on celestial OPE please see [20,[36][37][38][39][40][41][42][43]. Now for gluons, the Mellin transform of tree level three and four point scattering amplitudes are distributional in nature due to the momentum conserving delta function and the conformal invariance of the tree level Yang-Mills theory.…”

Section: Introductionmentioning

confidence: 99%

MHV gluon scattering in the massive scalar background and celestial OPE

Banerjee,

Mandal,

Manu

et al. 2023

In this paper we study the tree-level OPE between two positive helicity outgoing gluons in the celestial CFT for the Yang-Mills theory chirally coupled to a massive scalar background. This theory breaks the translation as well as scale invariance. We compute the subleading terms in the OPE expansion and show that they are same as the subleading terms of the OPE expansions in the MHV sector. As a result the amplitudes of this theory also satisfy the set of differential equations obtained previously for MHV amplitudes in pure YM theory. This is not surprising because the symmetries coming from the leading and subleading soft gluon theorems do not change in the presence of a massive scalar background.