Akshay Yelleshpur Srikant

A bstract: Carrollian holography is a framework for flat space holography, suggesting that gravity in asymptotically flat spacetime in D dimensions is dual to a conformal Carrollian field theory in D – 1 dimensions living at null infinity. In this work, we elaborate on the definition of Carrollian amplitudes for massless scalar fields in general dimensions and provide explicit expressions for the two-, three-, and four-point functions. We show that these amplitudes naturally arise from Lorentzian holographic correlators in AdS/CFT through a correspondence between the flat space limit in the bulk and the Carrollian limit at the boundary. Finally, we use the relation between Carrollian and celestial holography to derive explicit expressions for celestial amplitudes in D dimensions, which are reinterpreted as correlators of the celestial CFT in D − 2 dimensions.

Finding a concrete example holography in four dimensional asymptotically flat space is an important open problem. A natural strategy is to take the flat space limit of the celebrated AdS₄/CFT₃ correspondence, which relates M-theory in AdS₄×S⁷ to a certain superconformal Chern-Simons-matter theory known as the ABJM theory. In this limit, the boundary of AdS₄ becomes null infinity and the ABJM theory should exhibit an emergent superconformal Carrollian symmetry. We investigate this possibility by matching the Carrollian limit of ABJM correlators with four-dimensional supergravity amplitudes that arise from taking the flat space limit of AdS₄×S⁷ and reducing along the S⁷. We also present a general analysis of three-dimensional superconformal Carrollian symmetry.

Carrollian amplitudes are flat space amplitudes written in position space at null infinity which can be re-interpreted as correlators in a putative dual Carrollian CFT. We argue that these amplitudes are the natural objects obtained in the flat space limit of AdS Lorentzian boundary correlators. The flat limit is taken entirely in position space by introducing Bondi coordinates in the bulk. From the bulk perspective, this procedure makes it manifest that the flat limit of any Witten diagram is the corresponding flat space Feynman diagram. It also makes explicit the fact that the flat limit in the bulk is implemented by a Carrollian limit at the boundary. We systematically analyse tree-level two, three and four-point correlators. Familiar features such as the distributional nature of Carrollian amplitudes and the presence of a bulk point singularity arise naturally as a consequence of requiring a finite and non-trivial Carrollian limit.

Conformally soft operators and their associated soft theorems on the celestial sphere encode the low energy behaviour of bulk scattering amplitudes. They lead to an infinite dimensional symmetry algebra of the celestial CFT at tree-level. In this paper, focusing our attention to Yang-Mills theory, we introduce new operators in the boundary celestial CFT in order to extend the definition of conformally soft currents to include one-loop effects. We then compute their OPEs with other operators in the theory. We also examine new subtleties that arise in defining OPEs of two conformally soft operators. We elucidate the connection between the new operators and loop corrected soft theorems in the bulk. Finally, we conclude by demonstrating how these operators fit into the framework of a logarithmic CFT.

In this paper we study the simplifying effects of supersymmetry on celestial OPEs at both tree and loop level. We find at tree level that theories with unbroken supersymmetry around a stable vacuum have celestial soft current algebras satisfying the Jacobi identity, and we show at one loop that celestial OPEs in these theories have no double poles.

Conformally soft operators and their associated soft theorems on the celestial sphere encode the low energy behaviour of bulk scattering amplitudes. They lead to an infinite dimensional symmetry algebra of the celestial CFT at tree-level. In this paper, we introduce new operators in the celestial CFT in order to extend the definition of conformally soft currents to include one-loop effects. We then compute their OPEs with other operators in the theory. We also examine new subtleties that arise in defining OPEs of two conformally soft operators. We elucidate the connection between the new operators and loop corrected soft theorems in the bulk. Finally, we conclude by demonstrating how these operators fit into the framework of a logarithmic CFT.

We compute scattering amplitudes involving one massive scalar and two, three, or four gravitons. We show that when the conformal dimension of the massive scalar is set to zero, the resulting celestial correlators depend only on the coordinates of the gravitons. Such correlators of gravitons are well-defined and do not suffer from divergences associated with the Mellin transform of usual graviton amplitudes. Moreover, they are non-distributional and take the form of standard CFT correlators. We show that they are consistent with the usual OPEs but the statement of the soft theorem is modified.