Equation (3.18) and the Hawking temperature (2.4) show that (3.19) can be rewritten as According to the AdS / CFT dictionary, we obtain the relation Thus, from Eqs. (3.17) and (3.21) we find that the expectationvalue 〈O + 〉 is In the study of (2 + 1) and (3 + 1)-dimensional superconductors, Horowitz et al. [8] got a univer- sal relation connecting the gap frequency in conductivity with the critical temperature T$_{c}$ , which is 9 IV. ELECTRICAL CONDUCTIVITY IN HO ˇ RAVA-LIFSHITZ BLACK-HOLE BACKGROUND TABLE I: The critical temperature T$_{c}$ obtained by the analytical method (left column) and the numerical method (right column). The matching point is set as z$_{m}$ = 10 / 15. We have used ρ = 1 in the calculation. T$_{c}$ = 3 8 π L √ ρ ˜ b . (3.22) 〈O + 〉 ≡ LC$_{+}$r λ$_{+}$ + $_{L}$− 2 λ$_{+}$ = LC$_{+}$ ( 8 π T 3 ) λ$_{+}$ . (3.23) where Υ is a constant which is given by ϵ 0.0 0.1 0.2 0.5 0.9 m $^{2}$L2 AdS = 0 0 . 0492 0 . 0499 0 . 0504 0 . 0502 0 . 0515 0 . 0510 0 . 0544 0 . 0545 0 . 0577 0 . 0599 m $^{2}$L2 AdS = − 1 0 . 0566 0 . 0563 0 . 0573 0 . 0589 0 . 0580 0 . 0622 0 . 0602 0 . 0740 0 . 0631 0 . 0914 m $^{2}$L2 AdS = − 2 0 . 0779 0 . 0763 0 . 0749 0 . 0757 0 . 0734 0 . 0785 0 . 0725 0 . 0919 0 . 0741 0 . 1130