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

TL;DR

This paper explores holographic complexity in a string theory background interpolating between AdS and flat spacetime, revealing non-locality signatures through unusual divergences in complexity measures, and extends analysis to finite temperature effects.

Contribution

It introduces a holographic complexity analysis for a background interpolating between AdS and LST, highlighting non-locality effects and divergence structures not seen in local theories.

Findings

Discovery of quadratic and logarithmic divergences in complexity measures

Non-locality signatures evident at short distances in the holographic setup

Finite temperature corrections do not introduce new exotic divergences

Abstract

In this work, we continue our study of string theory in the background that interpolates between $AdS_3$ in the IR to flat spacetime with a linear dilaton in the UV. The boundary dual theory interpolates between a CFT$_2$ in the IR to a certain two-dimensional Little String Theory (LST) in the UV. In particular, we study \emph{computational complexity} of such a theory through the lens of holography and investigate the signature of non-locality in the short distance behavior of complexity. When the cutoff UV scale is much smaller than the non-locality (Hagedorn) scale, we find exotic quadratic and logarithmic divergences (for both volume and action complexity) which are not expected in a local quantum field theory. We also generalize our computation to include the effects of finite temperature. Up to second order in finite temperature correction, we do not any find newer exotic UV-divergences compared to the zero temperature case.