Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations

TL;DR

This paper explores how Lorentz-violating deformations in Little String Theory affect holographic complexity, revealing intertwined effects of nonlocality and Lorentz violation on divergence structures and phase transitions.

Contribution

It extends previous holographic complexity studies of LST by incorporating Lorentz-violating JT and TJ deformations, analyzing their impact on divergence structures and phase transitions.

Findings

Nonlocality and Lorentz violation are intertwined in UV divergence structure.

Coefficients of divergences encode Lorentz boost violation signatures.

Subregion complexity exhibits a Hagedorn phase transition.

Abstract

This work is an extension of our previous work [1] where we exploited holography to compute the complexity characteristics of Little String Theory (LST), a nonlocal, nongravitational field theory which flows to a local 2d CFT in the IR under RG via an integrable irrelevant (TT) deformation. Here we look at the more general LST obtained by UV deforming the 2d CFT by incorporating Lorentz violating irrelevant JT and TJ deformations on top of TT deformation, in an effort to capture the novel signatures of Lorentz violation (on top of nonlocality) on quantum complexity. In anticipation of the fact that the dual field theory is Lorentz violating, we compute the volume complexity in two different Lorentz frames and the comparison is drawn between the results. It turns out that for this system the nonlocality and Lorentz violation effects are inextricably intertwined in the UV divergence structure of the quantum complexity. The coefficients of the divergences carry the signature of Lorentz boost violation. We also compute the subregion complexity which displays a (Hagedorn) phase transition with the transition point being the same as that for the phase transition of entanglement entropy [2]. These new results are consistent with our previous work [1]. Null warped AdS3 is treated as an interesting special case.