On the Underlying Nonrelativistic Nature of Relativistic Holography

TL;DR

This paper reveals that relativistic holography can be understood as a nonrelativistic brane theory, showing deep connections between Newton-Cartan geometry, nonrelativistic string theories, and the AdS/CFT correspondence.

Contribution

It demonstrates that standard relativistic holography is fundamentally a statement within a nonrelativistic brane framework, unifying various recent developments in nonrelativistic string and brane theories.

Findings

N=4 SYM is the worldvolume theory of D3-branes in NR D3-brane theory

AdS_5*S^5 corresponds to an RR black 3-brane with Newton-Cartan structure

AdS/CFT duality is equivalent to brane duality within NR D3-brane theory

Abstract

Over the past quarter century, considerable effort has been invested in the study of nonrelativistic (NR) string theory, its U-dual NR brane theories, and their geometric foundations in (generalized) Newton-Cartan geometry. Many interesting results have been obtained, both for their intrinsic value and in the hope that they hold useful lessons for relativistic string/M theory. By synthesizing two strands of recent developments (especially, arXiv:2312.13243 and arXiv:2410.03591), we argue that this hope has already come to fruition, because standard, relativistic holography can now be recognized as a statement within a corresponding nonrelativistic brane theory. Our main conclusions are general, but in the familiar example of D3-brane based holography, they read as follows: (i) N=4 SYM is exactly the worldvolume theory of D3-branes within `NR D3-brane theory'; (ii) AdS_5*S^5 is exactly the corresponding RR black 3-brane, and includes an asymptotically flat-Newton-Cartan region; (iii) AdS/CFT duality is precisely synonymous with black-brane/D-brane (i.e., closed-string/open-string) duality within NR D3-brane theory; (iv) Newton-Cartan geometry is the underlying structure upon which entanglement of the D3-brane degrees of freedom builds relativistic spacetime.