The ABCDEFG of little strings

Abstract

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 g $$ \mathfrak{g} $$ . 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 g $$ {}^L\mathfrak{g} $$ , the Langlands dual of g $$ \mathfrak{g} $$ . As a first application, we show that the instanton partition function of the g $$ \mathfrak{g} $$ -type quiver gauge theory on the defect is equal to a 3-point conformal block of the g $$ \mathfrak{g} $$ -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 g $$ \mathfrak{g} $$ .

Keywords

• Brane Dynamics in Gauge Theories
• Conformal and W Symmetry
• Nonperturbative Effects
• Supersymmetry and Duality