Hidden functional relation in Large-N Quark-Monopole system at finite temperature

TL;DR

This paper investigates the quark-monopole potential at finite temperature using AdS/CFT, revealing a hidden functional relation that links boundary quantities to bulk properties, with implications for extra dimensions.

Contribution

It uncovers a novel functional relation in the quark-monopole system at finite temperature, highlighting a connection between boundary physics and bulk geometry.

Findings

Potential invariant under g → 1/g and U_T → U_T / g

Existence of a maximum quark-monopole separation

Functional relation causing bifurcation in L-dependence of potential

Abstract

The quark-monopole potential is computed at finite temperature in the context of $AdS/CFT$ correspondence. It is found that the potential is invariant under $g \to 1/g$ and $U_T \to U_T / g$. As in the quark-quark case there exists a maximum separation between quark and monopole, and $L$-dependence of the potential exhibits a bifurcation behavior. We find a functional relation $dE_{QM}^{Reg} / dL = [(1/E_{(1,0)}^{Reg}(U_0))^2 + (1/E_{(0,1)}^{Reg}(U_0))^2]^{-1/2}$ which is responsible for the bifurcation. The remarkable property of this relation is that it makes a relation between physical quantities defined at the $AdS$ boundary through a quantity defined at the bulk. The physical implication of this relation for the existence of the extra dimension is speculated.