Surface defects in E-string compactifications and the van Diejen model

Abstract

We study the supersymmetric index of four dimensional theories obtained by compactifications of the six dimensional E string theory on a Riemann surface. In particular we derive the difference operator introducing certain class of surface defects to the index computation. The difference operator turns out to be, up to a constant shift, an analytic difference operator discussed by van Diejen.

arXiv comment20 pages, three figures; v.2 minor clarifications

References in corpus (18)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• An Index for 4 dimensional Super Conformal Theories
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Gauge Theories and Macdonald Polynomials
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• S-duality and 2d Topological QFT
• Bootstrapping the superconformal index with surface defects
• Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory
• Classifying bases for 6D F-theory models
• Holography for (1,0) theories in six dimensions
• Surface defects and elliptic quantum groups
• Yang-Baxter equation, parameter permutations, and the elliptic beta integral
• Elliptic hypergeometric functions
• Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type IV. The Relativistic Heun (van Diejen) Case
• Superconformal index with surface defects for class ${\mathcal{S}}_k$

Cited by in corpus (15)

• 5d Partition Functions with A Twist
• Revisiting the classifications of 6d SCFTs and LSTs
• On matrix models and their $q$-deformations
• A slow review of the AGT correspondence
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• E-string Quantum Curve
• Elliptic Quantum Curves of 6d SO(N) theories
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Surface defects on E-string from 5-brane webs
• Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
• An infrared bootstrap of the Schur index with surface defects
• $C_2$ generalization of the van Diejen model from the minimal $(D_5,D_5)$ conformal matter
• On Razamat's $A_2$ and $A_3$ kernel identities
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• Aspects of 4d supersymmetric dynamics and geometry