$DE$-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 ${\mathbb{R}}^4\times T^2$. 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.

v2: 97 pages, 32 figures, typos corrected and clarifications added

References in corpus (15)

• The Refined Topological Vertex
• 6d Conformal Matter
• Fiber-Base Duality and Global Symmetry Enhancement
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Rank-3 antisymmetric matter on 5-brane webs
• Complete prepotential for 5d $\mathcal{N}=1$ superconformal field theories
• Bootstrapping BPS spectra of 5d/6d field theories
• Discrete theta angle from an O5-plane
• Flop invariance of the topological vertex
• 5d/6d Wilson loops from blowups
• Instanton counting and O-vertex
• More on topological vertex formalism for 5-brane webs with O5-plane
• Topological vertex for 6d SCFTs with ${\mathbb{Z}}_2$-twist
• Refined topological vertex with ON-planes
• 6d/5d exceptional gauge theories from web diagrams

Cited by in corpus (1)

• Quantum toroidal algebras and solvable structures in gauge/string theory