Line defects and 5d instanton partition functions

TL;DR

This paper studies line defect operators in 5d SUSY gauge theories, calculating their partition functions, showing they are finite polynomials in the defect mass, and exploring their relation to qq-characters.

Contribution

It provides an explicit calculation of line defect partition functions in 5d theories and proves their polynomial nature, linking them to Wilson loops and qq-characters.

Findings

Partition functions are finite polynomials in defect mass parameter x.

Explicit calculation confirms the polynomial property of the defect operators.

Discussion of the relation between defect partition functions and qq-characters.

Abstract

We consider certain line defect operators in five-dimensional SUSY gauge theories, whose interaction with the self-dual instantons is described by 1d ADHM-like gauged quantum mechanics constructed by Tong and Wong. The partition function in the presence of these operators is known to be a generating function of BPS Wilson loops in skew symmetric tensor representations of the gauge group. We calculate the partition function and explicitly prove that it is a finite polynomial of the defect mass parameter $x$, which is an essential property of the defect operator and the Wilson loop generating function. The relation between the line defect partition function and the qq-character defined by N. Nekrasov is briefly discussed.