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Paper   IPM / Physic / 17171
School of Physics
  Title:   Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
  Author(s):  F. Omidi
  Status:   Preprint
  Year:  2023
  Supported by:  IPM
In this paper, we investigate generalized volume-complexity $\mathcal{C}_{\rm gen}$ for a two-sided uncharged HV black brane in $d+2$ dimensions. This quantity which was recently introduced in [arXiv:2111.02429 [hep-th]], 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 $\mathcal{C}_{\rm gen}$ for different values of the hyperscaling violating exponent $\theta$ and dynamical exponent $z$. It is observed that $\mathcal{C}_{\rm gen}$ always grows linearly at late times provided that we choose $\lambda$ properly. Moreover, it reaches to its late time value from below. %Furthermore, it is an increasing function of $d$, $\theta$ and $\lambda$. For the case $\lambda=0$, we find an analytic expression for the late time growth rate for arbitrary values of $\theta$ and $z$. %In this case, $\mathcal{C}_{\rm gen}$ is a decreasing function of $z$. However, for $\lambda \neq 0$, 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.

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