Holographic complexity of LST and single trace TT

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 CFT2 in the IR to a certain two-dimensional Little String Theory (LST) in the UV. In particular, we study 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.

Automated summary

The work investigates string theory in backgrounds interpolating between AdS(3) in the IR and flat spacetime with a linear dilaton in the UV. Through holography, it studies computational complexity and the signature of non-locality in complexity's short distance behavior. Exotic divergences in complexity (quadratic and logarithmic) are found when the UV scale is significantly smaller than the non-locality scale.