Quantum Complexity of Nonlocal Field Theories

TL;DR

This paper investigates whether complexity in nonlocal field theories exhibits universal scaling laws similar to entanglement entropy, revealing phase transitions and nonlocality effects through holographic duals with running dilaton and B-field backgrounds.

Contribution

It introduces a holographic analysis of complexity in nonlocal field theories, showing nonlocality influences hyperscaling and reveals phase transitions in subregion complexity.

Findings

Complexity shows nonlocality-induced hyperscaling behavior.

Subregion complexity exhibits phase transitions aligned with entanglement entropy.

Results extend understanding of nonlocality effects in holographic complexity.

Abstract

Entanglement entropy for nonlocal field theories displays a universal ``volume law" scaling \cite{Barbon:2008ut, Karczmarek:2013xxa, Shiba:2013jja, Pang:2014tpa} as opposed to the ``area law" scaling for local field theories. The aim of this work is to determine whether complexity displays any such an universal scaling laws. The field theories considered here are obtained by deforming $\mathcal{N}=4$ SYM theory by higher dimension operators introducing nonlocality, namely a dipole deformation and noncommutativity (NCSYM) by turning on world volume Kalb-Ramond $B$ field. The dual gravity backgrounds have a running dilaton, in addition to the $B$-field background, which alter AdS asymptotics. Our results capture nonlocality in the hyperscaling behavior for complexity. We also compute the subregion complexity which display phase transitions in the nonlocal field theories with the transition point being the same as that for the phase transition of entanglement entropy \cite{Karczmarek:2013xxa}. These new results dovetail nicely with our findings from our previous works \cite{Chakraborty:2020fpt, Katoch:2022hdf, Bhattacharyya:2022ren} on other lower dimensional nonlocal field theories such as little string theories (LSTs) and warped conformal field theories (WCFTs).