The holographic p + ip solution failed to win the competition in dRGT massive gravity
Zhang-Yu Nie, Ya-Peng Hu, Hui Zeng
Abstract
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 p-wave 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 $$c_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>c</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> . 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 $$m^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>m</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> .