$DE$-type little strings from glued brane webs

TL;DR

This paper develops new brane web configurations for D- and E-type little string theories using advanced gluing techniques, enabling the computation of their supersymmetric partition functions on Omega-deformed spaces.

Contribution

It introduces a novel gluing method for little string theories via brane webs, generalizing topological vertex techniques to compute partition functions for D- and E-type cases.

Findings

Computed refined partition functions for D4 and D5 little string theories.

Extended the gluing approach to E6 little string theory.

Demonstrated consistency with known results and discussed higher rank generalizations.

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 $\mathbb{R}^4\times T^2$. As concrete examples, we consider little string theories arising from Type IIB NS5-branes probing $D_4$ or $D_5$ singularity. Their effective gauge theory descriptions as the affine $D_4$ or $D_5$ 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 $E_6$ singularity based on a trivalent gluing. We also discuss the generalization to higher rank cases and the symmetries of the partition functions.