Holographic Complexity in String and M Theory

TL;DR

This paper develops a framework for studying holographic complexity within the full string and M theory dualities, extending beyond the usual AdS context, and introduces new universal, gauge-invariant complexity functionals.

Contribution

It provides a higher-dimensional approach to holographic complexity, relating it to lower-dimensional theories and proposing new universal, gauge-invariant complexity functionals.

Findings

Established a relation between higher-dimensional and AdS holographic complexity functionals.

Demonstrated gauge invariance constrains boundary terms in complexity functionals.

Proposed new universal, gauge-invariant complexity functionals for string and M theory.

Abstract

Thus far, the literature regarding holographic complexity almost entirely focuses on the context of $(d+1)$-dimensional anti-de Sitter spacetime rather than the full higher-dimensional gauge/gravity duality in string or M theory. We provide a framework to study holographic complexity in the full duality, explaining the relation of complexity functionals in the higher-dimensional theory to those in anti-de Sitter spacetime and when complexity functionals can apply universally to gauge/gravity dualities rather than a specific dual pair. We also show that gauge invariance constrains boundary terms for complexity functionals, using the ten- and eleven-dimensional supergravity actions as key examples. Finally, we propose new universal complexity functionals following these considerations, including a revised gauge-invariant action complexity.