The ABCDEFG of Little Strings

Abstract

Starting from type IIB string theory on an $ADE$ singularity, the $(2,0)$ little string arises when one takes the string coupling $g_s$ to 0. In this setup, we give a unified description of the codimension-two defects of the little string, labeled by a simple Lie algebra $\mathfrak{g}$. Geometrically, these are D5 branes wrapping 2-cycles of the singularity, subject to a certain folding operation when the algebra is non simply-laced. Equivalently, the defects are specified by a certain set of weights of ${}^L\mathfrak{g}$, the Langlands dual of $\mathfrak{g}$. As a first application, we show that the instanton partition function of the $\mathfrak{g}$-type quiver gauge theory on the defect is equal to a 3-point conformal block of the $\mathfrak{g}$-type deformed Toda theory in the Coulomb gas formalism. As a second application, we argue that in the $(2,0)$ CFT limit, the Coulomb branch of the defects flows to a nilpotent orbit of $\mathfrak{g}$.

63 pages + 12 figures; v2: corrected typos and added references

References in corpus (6)

• Tinkertoys for Gaiotto Duality
• Correlation functions in conformal Toda field theory I
• Generalized Superconformal Index for Three Dimensional Field Theories
• Triality in Little String Theories
• Dual Little Strings and their Partition Functions
• Little String Defects and Bala-Carter Theory

Cited by in corpus (7)

• Revisiting the classifications of 6d SCFTs and LSTs
• A slow review of the AGT correspondence
• Folding Orthosymplectic Quivers
• From Little String Free Energies Towards Modular Graph Functions
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Symmetries in A-Type Little String Theories, Part I
• Non-Perturbative Schwinger-Dyson Equations for 3d $\mathcal{N}=4$ Gauge Theories