generalization of the van Diejen model from the minimal conformal matter

Area of Science:

• Theoretical Physics
• String Theory
• Conformal Field Theory

Background:

• Investigates 4-dimensional (4D) compactifications of 6-dimensional (6D) minimal conformal matter theories.
• Focuses on theories defined on punctured Riemann surfaces, a key area in modern theoretical physics.
• Introduces supersymmetric surface defects as a novel approach to studying these complex systems.

Purpose of the Study:

• To analyze superconformal indices in 4D compactifications of 6D conformal matter theories.
• To develop and characterize finite difference operators representing supersymmetric surface defects.
• To generalize existing models, specifically the van Diejen model, for these defect operators.

Main Methods:

• Employs finite difference operators acting on superconformal indices to model supersymmetric surface defects.
• Derives explicit expressions for an infinite tower of difference operators, focusing on the $$ case.
• Analyzes properties of these operators stemming from the geometry of compactifications and provides kernel function expressions.

Main Results:

• Successfully derived an infinite tower of difference operators for the $$ symmetry case, generalizing the van Diejen model.
• Provided explicit expressions for the kernel function of both the new $$ operator and a previously studied $$ generalization.
• Extended the analysis to $$-type punctures, deriving a full tower of commuting difference operators.

Conclusions:

• The study establishes a new framework for incorporating supersymmetric surface defects into superconformal index calculations.
• The derived operators and their properties offer significant insights into the structure of compactified conformal field theories.
• Results generalize existing mathematical models and pave the way for further investigations into related physical systems.