Closed String Tachyons on AdS Orbifolds and Dual Yang-Mills Instantons

TL;DR

This paper investigates the decay of AdS orbifolds via closed string tachyon condensation, analyzing bulk gravity solutions and dual gauge theory vacua, revealing exact matches in energies and describing instanton-mediated transitions.

Contribution

It extends the analysis of AdS orbifold decay from AdS_5/Z_k to AdS_3/Z_k and constructs explicit instanton solutions for gauge theory vacua transitions.

Findings

Bulk gravity solutions describe AdS orbifold decay.

Casimir energies match dual geometry masses.

Instanton solutions characterize gauge theory transitions.

Abstract

We study the condensation of localized closed string tachyons on AdS orbifolds both from the bulk and boundary theory viewpoints. We first extend the known results for AdS_5/Z_k to AdS_3/Z_k case, and we proposed that the AdS_3/Z_k decays into AdS_3/Z_k' with k' < k. From the bulk viewpoint, we obtain a time-dependent gravity solution describing the decay of AdS orbifold numerically. From the dual gauge theory viewpoint, we calculated the Casimir energies of gauge theory vacua and it is found that their values are exactly the same as the masses of dual geometries, even though they are in different parameter regimes of 't Hooft coupling. We also consider AdS_5 orbifold. The decay of AdS_5/Z_k is dual to the transition between the dual gauge theory vacua on R_t x S^3/Z_k, parametrized by different holonomies along the orbifolded spatial cycle. We constructed the instanton solutions describing the transitions by making use of instanton solutions on R_t x S^2.