Heavy Quarkonium Melting in Large N Thermal QCD

TL;DR

This paper provides a formal proof of heavy quarkonium melting in large N thermal QCD theories with well-behaved UV completions, analyzing melting temperatures and implications for deconfinement transitions.

Contribution

It offers a general proof of quarkonium melting in large N theories with specific UV conditions, extending previous models and clarifying subtleties involved.

Findings

Melting temperatures of heavy quarkonium states are determined.

UV completions without Landau poles are crucial for melting.

Evidence suggests deconfinement phase transitions at certain temperatures.

Abstract

Large N QCD is mostly governed by planar diagrams and should show linear confinement when these diagrams are suitably summed. The linear confinement of quarks in a class of these theories using gravity duals that capture the logarithmic runnings of the coupling constants in the IR and strongly coupled asymptotic conformal behavior in the UV was studied in our previous work. We also extended the theories to high temperatures and argued the possibilities of meltings and suppressions of heavy quarkonium states. In this paper we give a formal proof of melting using very generic choices of UV completions, and point out some subtleties associated with meltings in generic large N theories. Our proof requires only the existence of well defined UV behaviors that are devoid of Landau poles and UV divergences of the Wilson loops, allowing degrees of freedom to increase monotonously with energy scale. We determine the melting temperatures of heavy quarkonium states, which could suggest the presence of deconfinement phase transitions in these theories.