Marginal Operators from Celestial Diamonds

TL;DR

This paper explores marginal operators in celestial conformal field theories, providing a geometric framework for understanding boundary theory deformations and their bulk duals in asymptotically flat spacetimes.

Contribution

It introduces a new definition of marginal operators in celestial CFTs as composite operators linked to celestial memory and Goldstone diamonds, enhancing the understanding of boundary deformations.

Findings

Marginal operators correspond to vacuum transitions in the bulk.

A geometric interpretation of boundary deformations in celestial CFTs.

New framework for defining marginal operators in celestial holography.

Abstract

For a given conformal field theory (CFT), one can deform it via the addition of a marginal operator to the spectrum. In two dimensions, when the added operator has conformal weights $h=\bar{h}=1$, conformal symmetry is not broken and the resulting theory is a distinct CFT. Studying such marginal operators for celestial CFTs allows for a geometric understanding of the space of allowed boundary theories dual to quantum field theories (QFT) in bulk asymptotically flat spacetimes. In traditional holographic examples, a marginal deformation on the boundary corresponds to a vacuum transition in the bulk theory. We affirm this in celestial CFTs which requires a general definition of marginal operators as composite celestial operators via pairs that live at distinct corners of celestial memory and Goldstone diamonds.