DE-type little strings from glued brane webs

Abstract

We propose brane web configurations for D-type and E-type mathcal{N} =(1,0) little string theories based on a trivalent or quadrivalent gluing of 5-brane web diagrams. Tri-/quadri-valent gluing is a powerful way of computing 5d/6d partition functions for supersymmetric gauge theories based on the topological vertex. We generalize the gluing techniques to little string theories by introducing a new compact direction and compute their supersymmetric partition functions on Omega-deformed ℝ4×T2. As concrete examples, we consider little string theories arising from Type IIB NS5-branes probing D4 or D5 singularity. Their effective gauge theory descriptions as the affine D4 or D5 quiver gauge theory can be realized with quadrivalent or trivalent gluing, respectively. Based on these gluings of 5-brane webs, we compute their refined partition functions and compare them with the known results. We extend the computation of the partition function to little string theory engineered from IIB NS5-branes probing E6 singularity based on a trivalent gluing. We also discuss the generalization to higher rank cases and the symmetries of the partition functions.