String junctions in curved backgrounds, their stability and dyon interactions in SYM

TL;DR

This paper systematically constructs and analyzes string junctions in curved backgrounds relevant to gauge/gravity duality, examining their stability and interactions of dyons in strongly coupled SYM theories.

Contribution

It introduces a method to construct and analyze string junctions in curved backgrounds, including stability analysis and examples in various D3-brane geometries.

Findings

String junctions can be perturbatively stable even if not energetically minimal.

Stability under small fluctuations is established for various configurations.

Examples include non-extremal, multicenter D3-brane backgrounds, and Rindler space.

Abstract

We provide a systematic construction of string junctions in curved backgrounds which are relevant in computing, within the gauge/gravity correspondence, the interaction energy of heavy dyons, notably of quark-monopole pairs, in strongly coupled SYM theories. To isolate the configurations of physical interest we examine their stability under small fluctuations and prove several general statements. We present all details, in several examples, involving non-extremal and multicenter D3-brane backgrounds as well as the Rindler space. We show that a string junction could be perturbatively stable even in branches that are not energetically the most favorable ones. We present a mechanical analog of this phenomenon.