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Holographic complexity of LST and single trace \(T\overline{T}\). (English) Zbl 1461.83054

Summary: In this work, we continue our study of string theory in the background that interpolates between \(\mathrm{AdS}_3\) in the IR to flat spacetime with a linear dilaton in the UV. The boundary dual theory interpolates between a \(\mathrm{CFT}_2\) 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.

MSC:

83E05 Geometrodynamics and the holographic principle
83E30 String and superstring theories in gravitational theory
81T28 Thermal quantum field theory
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