A Carroll Limit of AdS/CFT: A Triality with Flat Space Holography?

TL;DR

This work proposes a Carrollian limit of the AdS/CFT correspondence, positing a duality between string theory in a Carroll bulk and Carroll $\mathcal{N}=4$ SYM, and suggests a unifying triality linking Carroll string theory, flat-space string theory, and Carroll gauge theory. By implementing Carroll contractions on both gravity and gauge sectors and enforcing consistency with the decoupling limit, the authors obtain a Carroll $AdS_5\times S^5$ background and a magnetic Carroll $\mathcal{N}=4$ SYM on the Penrose boundary, aligning with flat space holography intuitions. They analyze the Carroll SYM symmetries, uncovering an infinite-dimensional Conformal Carroll Algebra and revealing non-closure of certain internal symmetries under ordinary brackets, which points to deeper algebraic structures or potential gauge redundancies. The results open a new avenue for flat space holography and outline future directions, including spectrum matching, fermion inclusion, and a robust Carroll supergravity framework to solidify the Carroll bulk/boundary dictionary.

Abstract

We construct a novel holographic duality by taking a Carrollian limit of the AdS/CFT correspondence, relating string theory in a Carroll bulk geometry to a Carroll $\mathcal{N}=4$ Super Yang-Mills theory. We further propose the existence of an underlying triality connecting Carroll string theory, relativistic string theory in flat spacetime, and Carroll gauge theory. Finally, we analyse the symmetries of the Carroll gauge theory, showing that they are non-linearly realised and do not close under ordinary Lie brackets.

Figures (1)

• Figure 1: The red double arrow indicates Maldacena's holography. The blue double arrows represent the proposed triality. The acronyms ST and SYM stand, respectively, for String Theory and Super Yang-Mills.