Revisiting the shadow stress tensor in celestial CFT

Banerjee, Sumilan; Pasterski, Sabrina

doi:10.1007/jhep04(2023)118

Cited by 12 publications

(10 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The ansatz for these OPEs are made from the corresponding Carrollian conformal Ward identities (themselves derived JHEP06(2023)051 from general symmetry principles) in the first place. Our results for the singular parts of these OPEs match with those obtained in the Celestial CFT [34,37,41,73,92] where the starting point was the (linearized) Einstein theory in the bulk AFS. Finally, we translate these OPEs into the language of the algebra of the modes, using the complex contour integral prescription developed in section 4.…”

Section: Symmetry Algebra From the Opesupporting

confidence: 81%

“…So, only one of T or S − 1 can be treated as a local field in a theory [73]. Obviously, there is an anti-holomorphic version of the super-rotation Ward identities derived above.…”

Section: Jhep06(2023)051mentioning

confidence: 97%

“…When choosing the two operators whose product is to be expanded, we need to remember that all the operators involved in an OPE are local (composite) operators and that OPEs are associative. Since a field and its shadow transformation both can not be treated as local operators in a theory [73], we have to choose one as a candidate local-field from each of the three following pairs: {T, S − 1 },{ T , S + 1 } and {S + 0 , S − 0 }, leaving the other as its non-local shadow. As will be explained, only the following two choices can respect the OPE associativity: {T, S + 1 , S + 0 } and { T , S − 1 , S − 0 }.…”

Section: Jhep06(2023)051mentioning

confidence: 99%

“…Since, a field and its shadow transformation can not both be local operators in a theory [73], we shall later choose to treat S + 0 as the local field in this work. Before moving on to the super-rotation Ward identities, a comment on the nature of the Carrollian energy-density T t t is in order.…”

Section: Jhep06(2023)051mentioning

confidence: 99%

See 3 more Smart Citations

Carrollian approach to 1 + 3D flat holography

Saha

2023

J. High Energ. Phys.

View full text Add to dashboard 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.

show abstract

Section: Symmetry Algebra From the Opesupporting

confidence: 81%

“…So, only one of T or S − 1 can be treated as a local field in a theory [73]. Obviously, there is an anti-holomorphic version of the super-rotation Ward identities derived above.…”

Section: Jhep06(2023)051mentioning

confidence: 97%

Section: Jhep06(2023)051mentioning

confidence: 99%

Section: Jhep06(2023)051mentioning

confidence: 99%

See 2 more Smart Citations

Carrollian approach to 1 + 3D flat holography

Saha

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…We start by revisiting the construction of [2] for the shadow scalar conformal primary wavefunctions. We use the following definition of the shadow transform (see [52,53] for early works and [2,[54][55][56][57] for a more recent literature)…”

Section: Scalar Shadowsmentioning

confidence: 99%

p-forms on the celestial sphere

Donnay,

Esmaeili,

Heissenberg

2023

SciPost Phys.

View full text Add to dashboard Cite

We construct a basis of conformal primary wavefunctions (CPWs) for pp-form fields in any dimension, calculating their scalar products and exhibiting the change of basis between conventional plane wave and CPW mode expansions. We also perform the analysis of the associated shadow transforms. For each family of pp-form CPWs, we observe the existence of pure gauge wavefunctions of conformal dimension \Delta=pΔ=p, while shadow pp-forms of this weight are only pure gauge in the critical spacetime dimension value D=2p+2D=2p+2. We then provide a systematic technique to obtain the large-rr asymptotic limit near \mathscr Iℐ based on the method of regions, which naturally takes into account the presence of both ordinary and contact terms on the celestial sphere. In D=4D=4, this allows us to reformulate in a conformal primary language the links between scalars and dual two-forms.

show abstract

Celestial gluon and graviton OPE at loop level

Krishna

2024

J. High Energ. Phys.

View full text Add to dashboard Cite

In this paper, we analyze the loop corrections to celestial OPE for gluons and gravitons. Even at the loop level, the soft gluons and gravitons have conformal dimensions ∆ = 1 −$${\mathbb{Z}}_{\ge 0}$$. The only novelty is the presence of higher poles. At one loop level, there are two types of conformal soft gluons with a single pole and a double pole in the ∆ plane. The celestial OPEs are obtained using the collinear splitting functions. In the case of gluons, the splitting functions receive loop corrections. After taking the holomorphic soft limit, we find the OPE of conformal soft gluons. We find a novel mixing of simple and double poles soft gluon operators in the OPE. In the case of gravitons, where splitting functions are known to be all loop exact, we still find a wedge algebra of w∞ which is in addition to the wedge algebra of w1+∞ already found by Strominger.

show abstract

Revisiting the shadow stress tensor in celestial CFT

Cited by 12 publications

References 49 publications

Carrollian approach to 1 + 3D flat holography

Carrollian approach to 1 + 3D flat holography

p-forms on the celestial sphere

Celestial gluon and graviton OPE at loop level

Contact Info

Product

Resources

About