Breaking rotations without violating the KSS viscosity bound

• Published in: The journal of high energy physics Vol. 2023; no. 7; pp. 16 - 33
• Main Authors: Baggioli, Matteo, Cremonini, Sera, Early, Laura, Li, Li, Sun, Hao-Tian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 03.07.2023; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Broken symmetry; Classical and Quantum Gravitation; Elementary Particles; Fluids; Gauge-Gravity Correspondence; High energy physics; Holography; Holography and Hydrodynamics; Horizon; P waves; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Shear viscosity; String Theory; Superfluidity; Symmetry; Viscosity; AdS-CFT Correspondence; Gauge-Gravity Correspondence; Holography and Hydrodynamics
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2023)016

A bstract 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 / 4 π . 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.