Non-Lorentzian Kač-Moody algebras

Self Cite

The isomorphism between the (extended) BMS4 algebra and the 1 + 2D Carrollian conformal algebra hints towards a co-dimension one formalism of flat holography with the field theory residing on the null-boundary of the asymptotically flat space-time enjoying a 1 + 2D Carrollian conformal symmetry. Motivated by this fact, we study the general symmetry properties of a source-less 1 + 2D Carrollian CFT, adopting a purely field-theoretic approach. After deriving the position-space Ward identities, we show how the 1 + 3D bulk super-translation and the super-rotation memory effects emerge from them, manifested by the presence of a temporal step-function factor in the same. Temporal-Fourier transforming these memory effect equations, we directly reach the bulk null-momentum-space leading and sub-leading soft graviton theorems. Along the way, we construct six Carrollian fields $$ {S}_0^{\pm } $$ S 0 ± , $$ {S}_1^{\pm } $$ S 1 ± , T and $$ \overline{T} $$ T ¯ corresponding to these soft graviton fields and the Celestial stress-tensors, purely in terms of the Carrollian stress-tensor components. The 2D Celestial shadow-relations and the null-state conditions arise as two natural byproducts of these constructions. We then show that those six fields consist of the modes that implement the super-rotations and a subset of the super-translations on the quantum fields. The temporal step-function allows us to relate the operator product expansions (OPEs) with the operator commutation relations via a complex contour integral prescription. We deduce that not all of those six fields can be taken together to form consistent OPEs. So choosing $$ {S}_0^{+} $$ S 0 + , $$ {S}_1^{+} $$ S 1 + and T as the local fields, we form their mutual OPEs using only the OPE-commutativity property, under two general assumptions. The symmetry algebra manifest in these holomorphic-sector OPEs is then shown to be Vir $$ \overset{\wedge }{\ltimes \overline{\textrm{sl}\left(2,{\mathbb{R}}\right)}} $$ ⋉ sl 2 ℝ ¯ ∧ with an abelian ideal.

Section: Jhep06(2023)051mentioning

confidence: 99%

Section: Symmetry Algebra From the Opementioning

confidence: 99%

Carrollian approach to 1 + 3D flat holography

Saha

2023

Self Cite

Irrelevant and marginal deformed BMS field theories

He,

Mao

2024

In this study, we investigate various deformations within the framework of Bondi-van der Burg-Metzner-Sachs invariant field theory (BMSFT). Specifically, we explore the impact of Bondi-van der Burg-Metzner-Sachs (BMS) symmetry on the theory by introducing key deformations, namely, $$ T\overline{T} $$ T T ¯ , JTμ, and $$ \sqrt{T\overline{T}} $$ T T ¯ deformations. In the context of generic seed theories possessing BMS symmetry, we derive the first-order correction of correlation functions using the systematic application of BMS symmetry ward identities. However, it is worth noting that higher-order corrections are intricately dependent on the specific characteristics of the seed theories. To illustrate our findings, we select the BMS free scalar and free fermion as representative seed theories. We then proceed to analytically determine the deformed action by solving the nontrivial flow equations. Additionally, we extend our analysis to include second-order deformations within these deformed theories.

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.