Abstract
The holographic complexity has been studied in a background which includes a critical point in the dual field theory. We have examined how the complexity rate and the saturation time of dynamical variables in the theory behave as one moves towards the critical point. Two significant results of our analysis are that (i) it takes more time for the complexity in field theory dual to become time dependent as one moves away from the critical point and (ii) near the critical point the complexity starts evolving linearly in time sooner than the other points away from it. We also observe different behaviour for complexity rate in action and volume prescriptions. In action prescription we have used the time scales in theory to obtain the dynamical critical exponent and interestingly have observed that different time scales produce the same value up to very small error.
Highlights
The holographic complexity has been studied in a background which includes a critical point in the dual field theory
We have examined how the complexity rate and the saturation time of dynamical variables in the theory behave as one moves towards the critical point
This proposal has been introduced in two different recipes: characterizing the size of black hole interior with its spatial volume or its action are known as volume [8] or action [9, 10] conjectures, CV or CA, in the literature
Summary
Where G5 is the five dimensional Newton’s constant. This action is the gravitational action of 1RCBH model [28,29,30,31,32,33] with dilaton potential as. We set AdS radius equal to one throughout the paper AdS solution is located at r → ∞ and rH is the black hole horizon and is obtained from h(rH ) = 0, rH =. Q rH in the bulk solution with respect to μ T in the boundary we will see that the background considered responding to each value of here contains two different It indicates the existence of branches of variables cora first order phase transition in field theory. In the dual holographic plasma to this background the bulk viscosity and baryon conductivity have been computed in [34] and the dynamical critical exponent could be obtained. The value of the dynamical critical exponent was confirmed in [35] and [36] by studying quasi-normal modes and quantum quench in this background, respectively
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