Search

Quantum complexity has already shed light on CFT states dual to bulk geometries containing spacelike singularities [1–3]. In this work, we turn our attention to the quantum complexity of CFT/quantum gravity states which are dual to bulk geometries containing a naked timelike singularity. The appearance of naked timelike singularities in semiclassical gravity is allowed in string theory, particularly in the context of holography, so long as they satisfy the Gubser criterion [4-5] — those naked timelike singularities which arise as the extremal limits of geometries containing cloaked singularities are admissible. In this work, we use holographic complexity as a probe on geometries containing naked timelike singularities and explore potential relation to the Gubser criterion for detecting allowable naked timelike singularities. We study three specific cases of naked timelike singularities, namely the negative mass Schwarzschild-AdS spacetime, the timelike Kasner-AdS [6] and Einstein-dilaton system [7]. The first two cases are outright ruled out by the Gubser criterion while the third case is more subtle — according to the Gubser criterion the singularity switches from forbidden to admissible as the parameter α is dialed in the range [0, 1] across the transition point at α = 1 / 3 . We probe all three geometries using two holographic complexity prescriptions, namely CA and CV. For the case of the negative mass SAdS and timelike Kasner-AdS4 the complexities display no sign of pathology (both receive finite contribution from the naked singularity). For the Einstein-Dilaton case, action-complexity does display a sharp transition from physical positive values to patholgical negative divergent values (arising from the singularity) as one transcends the Gubser bound. Our study suggests that neither action-complexity (CA) nor volume-complexity (CV) can serve as a sensitive tool to investigate (naked) timelike singularities. [ABSTRACT FROM AUTHOR]

Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro–Kac–Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS 3 spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT 2 s using circuit complexity as a tool. First we compute the holographic volume complexity (CV) which displays a linear UV divergence structure, more akin to that of a local CFT 2 and has a very complicated dependence on the Virasoro central charge c and the U(1) Kac–Moody level parameter k. Next we consider circuit complexity based on Virasoro–Kac–Moody symmetry gates where the complexity functional is the geometric (group) action on coadjoint orbits of the Virasoro–Kac–Moody group. We consider a special solution to extremization equations for which complexity scales linearly with "time". In the semiclassical limit (large c, k, while c/k remains finite and small) both the holographic volume complexity and circuit complexity scales with k. [ABSTRACT FROM AUTHOR]

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 T T ¯ deformation. Here we look at the more general LST obtained by UV deforming the 2d CFT by incorporating Lorentz violating irrelevant J T ¯ and T J ¯ deformations on top of T T ¯ 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 special case of interest. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We perform a comparative study of the time dependence of the holographic quantum complexity of some space like singular bulk gravitational backgrounds. This is done by considering the two available notions of complexity, one that relates it to the maximal spatial volume and the other that relates it to the classical action of the Wheeler-de Witt patch. We calculate and compare the leading and the next to leading terms and find some universal features. The complexity decreases towards the singularity for both definitions, for all types of singularities studied. In addition the leading terms have the same quantitative behavior for both definitions in restricted number of cases and the behaviour itself is different for different singular backgrounds. The quantitative details of the next to leading terms, such as their specific form of time dependence, are found not to be universal. They vary between the different cases and between the different bulk definitions of complexity. We also address some technical points inherent to the calculation. [ABSTRACT FROM AUTHOR]