On volume subregion complexity in non-conformal theories
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Regular Article - Theoretical Physics
On volume subregion complexity in non-conformal theories M. Asadia School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
Received: 15 June 2020 / Accepted: 17 July 2020 © The Author(s) 2020
Abstract We study the volume prescription of the holographic subregion complexity in a holographic 5-dimensional model consisting of Einstein gravity coupled to a scalar field with a non-trivial potential. The dual 4-dimensional gauge theory is not conformal and exhibits a RG flow between two different fixed points. In both zero and finite temperature we show that the holographic subregion complexity can be used as a measure of non-conformality of the model. This quantity exhibits also a monotonic behaviour in terms of the size of the entangling region, like the behaviour of the entanglement entropy in this setup. There is also a finite jump due to the disentangling transition between connected and disconnected minimal surfaces for holographic renormalized subregion complexity at zero temperature.
Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . 2 Review on the background . . . . . . . . . . . . . . 3 Review on the entanglement entropy, complexity and subregion complexity . . . . . . . . . . . . . . . . 4 Analytical prescription . . . . . . . . . . . . . . . . 5 Numerical results . . . . . . . . . . . . . . . . . . . 5.1 Zero temperature . . . . . . . . . . . . . . . . 5.2 Finite temperature . . . . . . . . . . . . . . . . 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .
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1 Introduction The gauge/gravity duality is a conjectured relationship between quantum field theory and gravity. The underlying duality provides an important framework to study key properties of the boundary field theory dual to some gravitational a e-mail:
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theory on the bulk side [1–4]. The most significant example of gauge/gravity duality is the AdS/CFT correspondence which proposes a duality between asymptotically AdS spacetimes in d + 1 dimensions and d-dimensional conformal field theories. This correspondence also indicates that there could be a deep relation between quantum gravity and quantum information theory, in the sense that there could be a holographic dual for some quantum information theory objects. Therefore, one could expect that the nature of spacetime geometry could be understood from quantum information theory. This framework has been applied to study quantities such as entanglement entropy, n-partite information and recently extended to the quantum computational complexity in field theory. The generalization of gauge/gravity duality to field theories which are not conformal seems to be important. It is then interesting to develop our understanding of this duality for more general cases. There are many different families of non-conformal theories which one can study the effect of the n
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