Generalized volume-complexity for two-sided hyperscaling violating black branes

In this paper, we investigate generalized volume-complexity C-gen for a two-sided uncharged HV black brane in d+ 2 dimensions. This quantity which was recently introduced in [48], is an extension of volume in the Complexity=Volume (CV) proposal, by adding higher curvature corrections with a coupling constant lambda to the volume functional. We numerically calculate the growth rate of C-gen for different values of the hyperscaling violation exponent 0 and dynamical exponent z. It is observed that C-gen always grows linearly at late times provided that we choose lambda properly. Moreover, it approaches its late time value from below. For the case lambda = 0, we find an analytic expression for the late time growth rate for arbitrary values of theta and z. However, for lambda &NOTEQUexpressionL; 0, the late time growth rate can only be calculated analytically for some specific values of theta and z. We also examine the dependence of the growth rate on d, theta, z and lambda. Furthermore, we calculate the complexity of formation obtained from volume-complexity and show that it is not UV divergent. We also examine its dependence on the thermal entropy and temperature of the black brane. At the end, we also numerically calculate the growth rate of C-gen for the case where the higher curvature corrections are a linear combination of the Ricci scalar, square of the Ricci tensor and square of the Riemann tensor. We show that for appropriate values of the coupling constants, the late time growth rate is again linear.

Automated summary

In this paper, the authors investigate the generalized volume-complexity C-gen for a two-sided uncharged HV black brane in d+ 2 dimensions. They numerically calculate the growth rate of C-gen for different values of the hyperscaling violation exponent 0 and dynamical exponent z, and find that C-gen always grows linearly at late times with properly chosen lambda. The authors also examine the dependence of the growth rate on d, theta, z, and lambda, and calculate the complexity of formation obtained from volume-complexity. They show that it is not UV divergent and examine its dependence on the thermal entropy and temperature of the black brane. Furthermore, they numerically calculate the growth rate of C-gen for a linear combination of higher curvature corrections and show that the late time growth rate is again linear for appropriate values of the coupling constants.