Abstract
We revisit the computation of the shear viscosity to entropy ratio in a holographic p-wave superfluid model, focusing on the role of rotational symmetry breaking. We study the interplay between explicit and spontaneous symmetry breaking and derive a simple horizon formula for η/s, which is valid also in the presence of explicit breaking of rotations and is in perfect agreement with the numerical data. We observe that a source which explicitly breaks rotational invariance suppresses the value of η/s in the broken phase, competing against the effects of spontaneous symmetry breaking. However, η/s always reaches a constant value in the limit of zero temperature, which is never smaller than the Kovtun-Son-Starinets (KSS) bound, 1/4π. This behavior appears to be in contrast with previous holographic anisotropic models which found a power-law vanishing of η/s at small temperature. This difference is shown to arise from the properties of the near-horizon geometry in the extremal limit. Thus, our construction shows that the breaking of rotations itself does not necessarily imply a violation of the KSS bound.
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Acknowledgments
We thank Alex Buchel and Blaise Gouteraux for discussion and comments on our results. M.B. acknowledges the support of the Shanghai Municipal Science and Technology Major Project (Grant No.2019SHZDZX01) and the sponsorship from the Yangyang Development Fund. S.C. acknowledges the support and hospitality of KITP and the Harvard University Physics Department, where parts of this work were carried on. This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. The work of S.C. was supported in part by the National Science Foundation under Grant No. PHY-2210271. The work of L.E. was supported in part by the NSF grant PHY-1915038. L.L. was partially supported by the National Natural Science Foundation of China Grants No.12122513, No.12075298 and No.12047503, and by the Chinese Academy of Sciences Project for Young Scientists in Basic Research YSBR-006.
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Baggioli, M., Cremonini, S., Early, L. et al. Breaking rotations without violating the KSS viscosity bound. J. High Energ. Phys. 2023, 16 (2023). https://doi.org/10.1007/JHEP07(2023)016
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DOI: https://doi.org/10.1007/JHEP07(2023)016