The holographic p + ip solution failed to win the competition in dRGT massive gravity
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Regular Article - Theoretical Physics
The holographic p + ip solution failed to win the competition in dRGT massive gravity Zhang-Yu Nie1,a , Ya-Peng Hu2,b , Hui Zeng1,c 1 2
Kunming University of Science and Technology, Kunming 650500, China College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Received: 1 May 2020 / Accepted: 21 October 2020 © The Author(s) 2020
Abstract In this paper, the holographic p-wave superfluid model with charged complex vector field is studied in dRGT massive gravity beyond the probe limit. The stability of pwave and p + ip solutions are compared in the grand canonical ensemble. The p-wave solution always get lower value of grand potential than the p + ip solution, showing that the holographic system still favors an anisotropic (p-wave) solution even with considering a massive gravity theory in bulk. In the holographic superconductor models with dRGT massive gravity in bulk, a key scaling symmetry is found to be violated by fixing the reference metric parameter c0 . Therefore, in order to get the dependence of condensate and grand potential on temperature, different values of horizon radius should be considered in numerical work. With a special choice of model parameters, we further study the dependence of critical back-reaction strength on the graviton mass parameter, beyond which the superfluid phase transition become first order. We also give the dependence of critical temperature on the back reaction strength b and graviton mass parameter m2.
1 Introduction The AdS/CFT correspondence [1–3] provides a novel way to study the strongly coupled systems. One successful application is the so called holographic superconductor [4,5], which mimic the superconductor phase transition with a spontaneously emerged charged hair in the bulk black hole spacetime. Various different matter fields as well as gravitational theories are considered to build different holographic superconductor and superfluid models [6], in order to realize vara e-mail:
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ious superconducting phenomenons and to check some universal laws [7]. Superfluid with p-wave pairing has also been realized holographically. In the early study [8], an SU(2) gauge field is introduced and the three generators are used to realize the electro-magnetic vector potential and the condensed vector orders respectively, with the non-Abelian coupling between the generators act as the U(1) charged coupling. The quasi normal modes are also calculated and it turns out that the p-wave solution is stable while p + ip solution is unstable. When back reaction is turned on and becomes large enough, the p-wave phase transition becomes first order [9]. Later in Ref. [10], the p-wave phases are realized in holographic mode with five-dimensional gauged supergravities in bulk. Analytical methods are also applied to study the critical behavior of the holographic p-wave model [11]. Recent studies [
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