Little String Defects and Bala-Carter Theory

Abstract

We give a physical realization of the Bala-Carter labels that classify nilpotent orbits of semi-simple Lie algebras, for the case $\mathfrak{g}=A,D,E$. We start from type IIB string theory compactified on an $ADE$ singularity and study the six-dimensional (2,0) $\mathfrak{g}$-type little string on a Riemann surface with punctures. The defects are introduced as D-branes wrapping the 2-cycles of the singularity. At low energies, the little string becomes the (2,0) conformal field theory of type $\mathfrak{g}$. As an application, we derive the full list of $E_n$ little string defects, and their Bala-Carter label in the CFT limit. Furthermore, we investigate new relations between the quiver gauge theory describing the D-brane defects at low energies, and the weighted Dynkin diagrams of $\mathfrak{g}$. We also give a physical version of the dimension formula of a nilpotent orbit based on its weighted Dynkin diagram.

51 pages, 9 figures, 3 longtables. v2: Added proof of dimension formula, minor changes

References in corpus (22)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• D-branes, Quivers, and ALE Instantons
• Matrix Description of M-theory on $T^5$ and $T^5/Z_2$
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• A brief review of "little string theories"
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• Tinkertoys for the D_N series
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• Tinkertoys for the Twisted D-Series
• F-theory and the Classification of Little Strings
• McKay correspondence
• Gauge Theory, Ramification, And The Geometric Langlands Program
• Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes)
• N=2 gauge theories and degenerate fields of Toda theory
• Gauge/Liouville Triality
• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• Little strings and T-duality
• Instanton-Monopole Correspondence from M-Branes on ${\mathbb{S}}^1$ and Little String Theory
• Parameter counting for singular monopoles on R^3
• ADE Little String Theory on a Riemann Surface (and Triality)
• Interpolating the Coulomb Phase of Little String Theory

Cited by in corpus (5)

• Revisiting the classifications of 6d SCFTs and LSTs
• A slow review of the AGT correspondence
• The ABCDEFG of Little Strings
• Masses, Sheets and Rigid SCFTs
• Non-Perturbative Schwinger-Dyson Equations for 3d $\mathcal{N}=4$ Gauge Theories