Renormalized holographic subregion complexity under relevant perturbations

Dongmin Jang (Department of Physics, BK21 Physics Research Division, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon, 440-746, South Korea) ; Yoonbai Kim (Department of Physics, BK21 Physics Research Division, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon, 440-746, South Korea) ; O-Kab Kwon (Department of Physics, BK21 Physics Research Division, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon, 440-746, South Korea) ; D. Tolla (Department of Physics, BK21 Physics Research Division, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon, 440-746, South Korea; University College, Sungkyunkwan University, Suwon, 440-746, South Korea)

We construct renormalized holographic entanglement entropy (HEE) and subregion complexity (HSC) in the CV conjecture for asymptotically AdS4 and AdS5 geometries under relevant perturbations. Using the holographic renormalization method developed in the gauge/gravity duality, we obtain counter terms which are invariant under coordinate choices. We explicitly define different forms of renormalized HEE and HSC, according to conformal dimensions of relevant operators in the d = 3 and d = 4 dual field theories. We use a general embedding for arbitrary entangling subregions and showed that any choice of the coordinate system gives the same form of the counter terms, since they are written in terms of curvature invariants and scalar fields on the boundaries. We show an explicit example of our general procedure. Intriguingly, we find that a divergent term of the HSC in the asymptotically AdS5 geometry under relevant perturbations with operators of conformal dimensions in the range 0 < ∆ < 1 2 $$ \frac{1}{2} $$ and 7 2 $$ \frac{7}{2} $$ < ∆ < 4 cannot be cancelled out by adding any coordinate invariant counter term. This implies that the HSCs in these ranges of the conformal dimensions are not renormalizable covariantly. We also write the plot of the renormalization procedure in the case of asymptotically AdS d+1 geometries, with d > 4.

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      "surname": "Kim", 
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      "surname": "Tolla", 
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  "abstracts": [
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      "source": "Springer", 
      "value": "We construct renormalized holographic entanglement entropy (HEE) and subregion complexity (HSC) in the CV conjecture for asymptotically AdS4 and AdS5 geometries under relevant perturbations. Using the holographic renormalization method developed in the gauge/gravity duality, we obtain counter terms which are invariant under coordinate choices. We explicitly define different forms of renormalized HEE and HSC, according to conformal dimensions of relevant operators in the d = 3 and d = 4 dual field theories. We use a general embedding for arbitrary entangling subregions and showed that any choice of the coordinate system gives the same form of the counter terms, since they are written in terms of curvature invariants and scalar fields on the boundaries. We show an explicit example of our general procedure. Intriguingly, we find that a divergent term of the HSC in the asymptotically AdS5 geometry under relevant perturbations with operators of conformal dimensions in the range 0 &lt; \u2206 &lt;   <math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math>  $$ \\frac{1}{2} $$  and   <math> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </math>  $$ \\frac{7}{2} $$  &lt; \u2206 &lt; 4 cannot be cancelled out by adding any coordinate invariant counter term. This implies that the HSCs in these ranges of the conformal dimensions are not renormalizable covariantly. We also write the plot of the renormalization procedure in the case of asymptotically AdS d+1 geometries, with d &gt; 4."
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Published on:
21 July 2020
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2020 (2020)
Issue 7
Pages 1-37
DOI:
https://doi.org/10.1007/JHEP07(2020)137
arXiv:
2001.10937
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: