一类新的Stückelb erg全息超导模型∗

摘要

本文研究了含Stückelberg机理的黑洞全息超导模型。通过选取标量场新的高阶修正形式，建立了新的Stückelberg黑洞全息超导模型。通过研究模型参数对标量场凝聚的影响，发现了当模型参数大于临界值时，高阶修正可以引起一阶相变。同时本文还考查了反作用对临界值的影响。%The AdS/CFT correspondence has provided us a useful approach to describe strongly interacting systems holo-graphically through weakly coupled gravitational duals. One of the mostly studied gravity duals is the holographic superconductor, which is constructed by a scalar field coupled to a Maxwell field in an AdS black hole background. It is shown that when the Hawking temperature of a black hole drops below a critical value, the black hole becomes unstable and this instability in the (d+1) dimensional AdS black hole corresponds to a d-dimensional phase transition at the boundary, called holographic superconductor model. Generally speaking, the instability of the gravity systems belongs to the second-order phase transition. Lately, it was stated that the holographic superconductor with the spontaneous breaking of a global U(1) symmetry via the Stückelberg mechanism allows the first-order phase transition to occur. Some further studies are carried out by considering new forms of the Stückelberg mechanism. So it is very interesting to extend the discussion to other new forms of Stückelberg mechanism to explore the rich properties of holographic super-conductors. By considering new higher correction terms of the scalar fields, we investigate a general class of holographic superconductors via Stückelberg mechanism in the background of four-dimensional AdS black hole. We obtain richer structures in the metal/superconductor phase transitions. We study the condensation of the scalar operator and find that when the model parameter is above a threshold value, this new model allows first-order phase transition to occur. We also examine the effects of the backreaction on the threshold model parameter and find that backreaction makes the first-order phase transitions easier to happen (or smaller threshold parameters above which the phase transition changes from second to first order). We may conclude that the model parameter coupled with the backreaction can determine the order of phase transitions.