Stability of Wilson Loops and Other Observables in Various Type IIB Backgrounds

This work involves the stability study of various observables (Wilson loop, 't Hooft loop and Entanglement Entropy) under linear fluctuations of the coordinates for certain ten-dimensional solutions of type IIB Supergravity that have appeared in the literature recently. These backgrounds are defined using intersecting and wrapped D5 branes, their holographically dual field theories are speculated to confine and they have a non-local UV completion that is governed by Little String Theory. The present study confirms previous claims on the stability of the solutions made using the concavity condition for the energy of the probe strings, by studying the eigenvalue problem for each case and also providing a numerical analysis.