TY - JOUR

T1 - Aspects of subregion holographic complexity

AU - Al-Ajmi, Mudhahir

N1 - Publisher Copyright:
© 2019 World Scientific Publishing Company.

PY - 2019

Y1 - 2019

N2 - This is a mini-review about the rapidly growing subject of dual holographic complexity (HC) for subsystems in conformal field theory (CFT) using a subregion volume enclosed by the entangled area in the dual bulk theory. This proposal is named as HC = volume. We use this proposal to compute the HC for different geometries in bulk theory. Because this HC quantity diverges as a result of the existence of the UV cutoff in the CFT, we proposed a suitable regularization scheme by subtracting the contribution of the background (pure) AdS spacetime from the deformation of the AdS geometry. Furthermore, the time-dependent geometries are investigated using the AdS/CFT proposal and hence, we proposed a time-dependent copy for HC in such nonstatic geometries. As an attempt to make a relation between HC and holographic entanglement entropy (HEE), inspired from the pure geometrical origins, we showed that HC and HEE which are duals to different volumes/areas in the bulk theory would be connected in a universal form for a general deformation AdS geometry (called holographic Cavalieri principle). As a pioneering idea we build a holographic model for P-V critically in black holes via regularized HC as the dual thermodynamic volume. The second-order phase transitions in two-dimensional holographic superconductors is explained by using the regularized HC as an order parameter. All the results presented in this mini-review are collected from the list of published works of the first author of this paper. In several cases, we gave further explanation and clarification to make the ideas more understandable to the community. Other proposals for complexity like complexity as on shell action are not included in this review paper.

AB - This is a mini-review about the rapidly growing subject of dual holographic complexity (HC) for subsystems in conformal field theory (CFT) using a subregion volume enclosed by the entangled area in the dual bulk theory. This proposal is named as HC = volume. We use this proposal to compute the HC for different geometries in bulk theory. Because this HC quantity diverges as a result of the existence of the UV cutoff in the CFT, we proposed a suitable regularization scheme by subtracting the contribution of the background (pure) AdS spacetime from the deformation of the AdS geometry. Furthermore, the time-dependent geometries are investigated using the AdS/CFT proposal and hence, we proposed a time-dependent copy for HC in such nonstatic geometries. As an attempt to make a relation between HC and holographic entanglement entropy (HEE), inspired from the pure geometrical origins, we showed that HC and HEE which are duals to different volumes/areas in the bulk theory would be connected in a universal form for a general deformation AdS geometry (called holographic Cavalieri principle). As a pioneering idea we build a holographic model for P-V critically in black holes via regularized HC as the dual thermodynamic volume. The second-order phase transitions in two-dimensional holographic superconductors is explained by using the regularized HC as an order parameter. All the results presented in this mini-review are collected from the list of published works of the first author of this paper. In several cases, we gave further explanation and clarification to make the ideas more understandable to the community. Other proposals for complexity like complexity as on shell action are not included in this review paper.

KW - AdS/CFT

KW - black holes in AdS spacetime

KW - conformal symmetry

KW - holographic complexity

KW - holographic entanglement entropy

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U2 - 10.1142/S0218271819300234

DO - 10.1142/S0218271819300234

M3 - Article

SN - 0218-2718

VL - 28

JO - International Journal of Modern Physics D

JF - International Journal of Modern Physics D

IS - 15

M1 - 1930023

ER -