Holographic chiral algebra: supersymmetry, infinite Ward identities, and EFTs

Abstract

Celestial holography promisingly reformulates the scattering amplitude holographically in terms of celestial conformal field theory living at null infinity. Recently, an infinite-dimensional symmetry algebra was discovered in Einstein-Yang-Mills theory. The starting point in the derivation is the celestial OPE of two soft currents, and the key ingredient is the summation of $$ \overline{\mathrm{SL}\left(2,\mathbb{R}\right)} $$ SL 2 ℝ ¯ descendants in OPE. In this paper, we consider the supersymmetric Einstein-Yang-Mills theory and obtain the supersymmetric extension of the holographic symmetry algebra. Furthermore, we derive infinitely many Ward identities associated with the infinite soft currents which generate the holographic symmetry algebra. This is realized by considering the OPE between a soft symmetry current and a hard operator, and then summing over its $$ \overline{\mathrm{SL}\left(2,\mathbb{R}\right)} $$ SL 2 ℝ ¯ descendants. These Ward identities reproduce the known Ward identities corresponding to the leading, sub-leading, and sub-sub-leading soft graviton theorems as well as the leading and sub-leading soft gluon theorems. By performing shadow transformations, we also obtain infinitely many shadow Ward identities, including the stress tensor Ward identities for sub-leading soft graviton. Finally, we use our procedure to discuss the corrections to Ward identities in effective field theory (EFT), and reproduce the corrections to soft theorems at sub-sub-leading order for graviton and sub-leading order for photon. For this aim, we derive general formulae for the celestial OPE and its corresponding Ward identities arising from a cubic interaction of three spinning massless particles. Our formalism thus provides a unified framework for understanding the Ward identities in celestial conformal field theory, or equivalently the soft theorems in scattering amplitude.

Goldilocks Modes and the Three Scattering Bases

“…from the tree-level expansion (3.1). For gravity, these conformally soft gravitons with ∆ = −n with n = −2, −1, 0, 1, ... generate the w 1+∞ algebra of the single helicity sector that has become a very active topic as of late [26,27,[59][60][61]. The implications of this infinite-dimensional celestial symmetry algebra for gravity in asymptotically flat spacetimes is an interesting problem.…”

Black Holes in Klein Space

“…The conformal boundary of Euclidean space is a point, whereas that of Klein space includes a Lorentzian torus [15]. This "celestial torus" both provides a natural home for and constrains the nature of the sought-for holographic dual of 4D quantum gravity [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Higher spin dynamics in gravity and $w_{1 + \infty}$ celestial symmetries

“…As such, the celestial OPE (87) suggests that (9) receives corrections beyond s = 3. These corrections can be interpreted as arising from higher dimension operators in the low-energy effective action [97,114,115]. We leave a complete understanding of this, as well issues arising when mixing helicity sectors [28,29,32,34,36,112] to future work.…”

“…In Section 4.3 we review the celestial diamond structure pointed out in [37,76,77] and we extend this structure to a general (sub) s -leading soft graviton. In Section 4.4 we clarify the definition of the light transform of the soft graviton, as well as its relation to the w-currents identified with the generators of the wedge subalgebra of w 1+∞ symmetry in [96,97] and the canonical soft charges. The OPEs of the latter two quantities are compared in Section 4.5, revealing an intriguing connection between the two sets of global and canonical charges.…”