Gross-Ooguri Phase Transition at Zero and Finite Temperature: Two Circular Wilson Loop Case

TL;DR

This paper analytically investigates the Gross-Ooguri phase transition for two circular Wilson loops in the AdS/CFT framework at zero and finite temperatures, revealing a key relation between Euclidean action and loop separation.

Contribution

It introduces an analytical method to relate Euclidean action and loop separation for Wilson loops, providing new insights into the phase transition at finite temperature.

Findings

Derived a functional relation between Euclidean action and loop separation.

Explored the physical implications for the Gross-Ooguri phase transition.

Analyzed the correlator at both zero and finite temperatures.

Abstract

In the context of $AdS/CFT$ correspondence the two Wilson loop correlator is examined at both zero and finite temperatures. On the basis of an entirely analytical approach we have found for Nambu-Goto strings the functional relation $d S_c^{(Reg)} / dL = 2 \pi k$ between Euclidean action $S_c$ and loop separation $L$ with integration constant $k$, which corresponds to the analogous formula for point-particles. The physical implications of this relation are explored in particular for the Gross-Ooguri phase transition at finite temperature.