Heavy quark potential at finite temperature in a dual gravity closer to large $N$ QCD

In gauge-gravity duality, heavy quark potential at finite temperature is usually calculated with the pure AdS background, which does not capture the renormalisation group (RG) running in the gauge theory part and the potential also does not contain any confining term in the deconfined phase. Following the developments on the Klebanov-Strassler geometry, we employ a geometry which captures the RG flow similar to QCD, to obtain the heavy quark potential by analytically continuing the string configurations into the complex plane. In addition to the attractive terms, the obtained potential has confining terms both at $T=0$ and $T\ne 0$, compared to the calculations usually done in the literature, where only Coulomb like term is present in the deconfined phase. The potential also develops an (negative) imaginary part above a critical separation, $r_c(=0.53z_h)$. Moreover our potential exhibits a behaviour, different from the usual Debye screening obtained from the perturbation theory.

Figure 1

Variations of the real and imaginary part of the potential with the separation $r$, where the value of both coefficients $A_2$ and $B_2$ are taken as 0.24.