Today theoretical physicists are facing the difficulty that General Relativity is not (pertubatively) renormalizable, and find that it is very hard to construct the quantum theory of gravity with LI. A possible solution is to break the LI in the ultraviolet (UV) region, so that the theory is renormalizable and unitary. However, the invariance should be recovered in the infrared (IR), so that all of the gravitational experiments in the IR can be satisfied. According to this idea, Horava proposed a Horava-Lifshitz (HL) gravity without LI, and recently it was shown that LI can be broken at very high energy scale, without causing conflict with observations. Therefore, it would be very interesting to study effects due to the broken LI, and we find that it is possible to realize the holographic superconductor in HL gravity.
This work was a generalization of the AdS/CFT correspondence proposed by Hartnoll, Herzog and Horowitz. They used AdS/CFT correspondence to explain the phase change in black hole spacetime, and successfully obtained the holographic superconductor curve lines of a black hole. After considering the holographic superconductor in the Horava-Lifshitz gravity, we found the effect from the broken LI, which can influence the conductivity and condensate curve lines, but the holographic superconductor still can be realized in gravity without LI.
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