Ground state wavefunctions of elliptic relativistic integrable Hamiltonians

Abstract

We derive ground state eigenfunctions and eigenvalues of various relativistic elliptic integrable models. The models we discuss appear in computations of superconformal indices of four-dimensional theories obtained by compactifying six-dimensional models on Riemann surfaces. These include, among others, the Ruijsenaars-Schneider model and the van Diejen model. The derivation of the eigenfunctions builds on physical inputs, such as conjectured Lagrangian across dimensions IR dualities and assumptions about the behavior of the indices in the limit of compactifications on surfaces with large genus/number of punctures/flux.

arXiv comment14 pages, 1 figure, supplementary Wolfram Mathematica file; v2: minor typos fixed, references added; v3: minor changes, published version

References in corpus (33)

• An Index for 4 dimensional Super Conformal Theories
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Integrability and Seiberg-Witten Exact Solution
• Gauge Theories and Macdonald Polynomials
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Non-trivial Fixed Points of The Renormalization Group in Six Dimensions
• On Geometric Classification of 5d SCFTs
• Defects and Quantum Seiberg-Witten Geometry
• Gauge Theory and Integrability, II
• Gauge Theory and Integrability, I
• E-String Theory on Riemann Surfaces
• Compactification of 6d minimal SCFTs on Riemann surfaces
• Rank $Q$ E-string on a torus with flux
• S-duality and the N=2 Lens Space Index
• Duality walls and defects in 5d N=1 theories
• Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
• Surface defects and elliptic quantum groups
• Unification of integrability in supersymmetric gauge theories
• The Quantum DELL System
• Flavored surface defects in 4d N=1 SCFTs
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Surface defects in E-string compactifications and the van Diejen model
• Duality in elliptic Ruijsenaars system and elliptic symmetric functions
• Shiraishi functor and non-Kerov deformation of Macdonald polynomials
• Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type IV. The Relativistic Heun (van Diejen) Case
• On the N=2 superconformal index and eigenfunctions of the elliptic RS model
• Elliptic Quantum Curves of 6d SO(N) theories
• A-type Quiver Varieties and ADHM Moduli Spaces
• Superconformal index with surface defects for class ${\mathcal{S}}_k$
• Construction of eigenfunctions for the elliptic Ruijsenaars difference operators
• On Razamat's $A_2$ and $A_3$ kernel identities