An infinite family of w1+∞ invariant theories on the celestial sphere

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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.

Section: Introductionmentioning

confidence: 99%

“…Please see[46,47] for the derivation of the differential equations in the pure YM case using BCFW shift 3. For a similar story in the case of gravitons please see[6,44,45].…”

mentioning

confidence: 99%

MHV gluon scattering in the massive scalar background and celestial OPE

Banerjee,

Mandal,

Manu

et al. 2023

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Celestial self-dual Yang-Mills theory: a new formula and the OPE limit

Chattopadhyay,

Tao

2024

Celestial holography is a new way to understand flat-space amplitudes. Self-dual theories, due to their nice properties, are good subjects to study celestial holography. In this paper, we developed a new formula to calculate the celestial color-ordered self-dual Yang-Mills amplitudes based on celestial Berends-Giele currents, which makes the leading OPE limit manifest. In addition, we explore some higher-order terms of OPE in the celestial self-dual Yang-Mills theory.

w1+∞ and Carrollian holography

Saha

2024

In a 1 + 2D Carrollian conformal field theory, the Ward identities of the two local fields $$ {S}_0^{+} $$ S 0 + and $$ {S}_1^{+} $$ S 1 + , entirely built out of the Carrollian conformal stress-tensor, contain respectively up to the leading and the subleading positive helicity soft graviton theorems in the 1 + 3D asymptotically flat space-time. This work investigates how the subsubleading soft graviton theorem can be encoded into the Ward identity of a Carrollian conformal field $$ {S}_2^{+} $$ S 2 + . The operator product expansion (OPE) $$ {S}_2^{+}{S}_2^{+} $$ S 2 + S 2 + is constructed using general Carrollian conformal symmetry principles and the OPE commutativity property, under the assumption that any time-independent, non-Identity field that is mutually local with $$ {S}_0^{+} $$ S 0 + , $$ {S}_1^{+} $$ S 1 + , $$ {S}_2^{+} $$ S 2 + has positive Carrollian scaling dimension. It is found that, for this OPE to be consistent, another local field $$ {S}_3^{+} $$ S 3 + must automatically exist in the theory. The presence of an infinite tower of local fields $$ {S}_{k\ge 3}^{+} $$ S k ≥ 3 + is then revealed iteratively as a consistency condition for the $$ {S}_2^{+}{S}_{k-1}^{+} $$ S 2 + S k − 1 + OPE. The general $$ {S}_k^{+}{S}_l^{+} $$ S k + S l + OPE is similarly obtained and the symmetry algebra manifest in this OPE is found to be the Kac-Moody algebra of the wedge sub-algebra of w1+∞. The Carrollian time-coordinate plays the central role in this purely holographic construction. The 2D Celestial conformally soft graviton primary $$ {H}^k\left(z,\overline{z}\right) $$ H k z z ¯ is realized to be contained in the Carrollian conformal primary $$ {S}_{1-k}^{+}\left(t,z,\overline{z}\right) $$ S 1 − k + t z z ¯ . Finally, the existence of the infinite tower of fields $$ {S}_k^{+} $$ S k + is shown to be directly related to an infinity of positive helicity soft graviton theorems.