Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary
Kentaro Hori, Mauricio Romo
TL;DR
This work provides an exact hemisphere partition function for a broad class of 2D (2,2) supersymmetric gauge theories with boundary, reveals that the result computes D-brane central charges and depends holomorphically on twisted chiral parameters. The authors derive a Mellin–Barnes integral form, analyze contour choices, and reveal a grade-restriction mechanism that governs brane transport across phase boundaries. In the large-volume (geometric) limit, the central charge expression naturally involves the Gamma class, aligning with mirror-symmetric expectations and providing explicit maps between branes and their CFT/ LG counterparts. The study also demonstrates a factorization of the S^2 partition function into two hemispheres connected by an annulus, clarifying how boundary data encode open-string indices and RR overlaps. Overall, the results offer calculable bridges between GLSMs, boundary branes, and mirror-symmetric descriptions, with broad implications for D-brane dynamics in 2DQFTs and beyond.
Abstract
We compute the partition function on the hemisphere of a class of two-dimensional (2,2) supersymmetric field theories including gauged linear sigma models. The result provides a general exact formula for the central charge of the D-brane placed at the boundary. It takes the form of Mellin-Barnes integral and the question of its convergence leads to the grade restriction rule concerning branes near the phase boundaries. We find expressions in various phases including the large volume formula in which a characteristic class called the Gamma class shows up. The two sphere partition function factorizes into two hemispheres glued by inverse to the annulus. The result can also be written in a form familiar in mirror symmetry, and suggests a way to find explicit mirror correspondence between branes.