Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary

Understand

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.