Abstract
In this work, we continue our study of string theory in the background that interpolates between AdS3 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.
Highlights
When the cutoff UV scale is much smaller than the non-locality (Hagedorn) scale, we find exotic quadratic and logarithmic divergences which are not expected in a local quantum field theory
Codes various phenomena on the gravity side, such as emergence of a quasilocal bulk spacetime local observables propagating on it, spatial connectivity of the bulk geometry, event horizons and gravitational singularities etc, has led to the recognition and importance of various concepts from the quantum information and computation (QIC) literature which capture aspects of quantum field theories not captured by traditional observables such as correlation functions of local operators or Wilson loops
The full geometry interpolates between AdS3 in the IR to flat spacetime with a linear dilaton in the UV
Summary
The aim of this section to compute the computational complexity of the LST dual to the background M3 (2.6) using holographic methods, namely the Complexity-Volume (CV) [33] and Complexity-Action (CA) [54, 55] prescriptions. We reveal the UV-divergences which arise in a nonlocal field theory such as two-dimensional LST, and compare and contrast them with those arising in a local quantum field theory (e.g. a CFT2)
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