Wilson loops in warped resolved deformed conifolds

TL;DR

This paper investigates quark-antiquark potentials via Wilson loops in a warped resolved deformed conifold background, analyzing energy-separation relationships and the impact of IR singularities on probe string behavior.

Contribution

It provides a detailed analysis of Wilson loop behavior in a flavoured resolved deformed conifold, highlighting the effects of IR singularities on quark potential calculations.

Findings

Identification of conditions for minimum quark separation

Observation of unusual behavior linked to IR singularity

Analysis of energy dependence on quark separation

Abstract

We calculate quark-antiquark potentials using the relationship between the expectation value of the Wilson loop and the action of a probe string in the string dual. We review and categorize the possible forms of the dependence of the energy on the separation between the quarks. In particular, we examine the possibility of there being a minimum separation for probe strings which do not penetrate close to the origin of the bulk space, and derive a condition which determines whether this is the case. We then apply these considerations to the flavoured resolved deformed conifold background of Gaillard et al. We suggest that the unusual behaviour we observe in this solution is likely to be related to the IR singularity which is not present in the unflavoured case.