Derives a distributional real-line integral formula for abelian observables in A-twisted N=(2,2) theories on S², verifies it on the CP^{N-1} GLSM correlator, and uses hyperfunctions to equate it with contour integrals matching the Jeffrey-Kirwan prescription.
Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary
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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.
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Derives general formula for monodromy action on B-brane charge lattice via hemisphere partition functions in GLSMs and refines it for examples using quantum Kähler discriminant and torus link fundamental groups.
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Hyperfunctions in $A$-model Localization
Derives a distributional real-line integral formula for abelian observables in A-twisted N=(2,2) theories on S², verifies it on the CP^{N-1} GLSM correlator, and uses hyperfunctions to equate it with contour integrals matching the Jeffrey-Kirwan prescription.
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Monodromy of Calabi-Yau threefold flops via grade restriction rule and their quantum Kahler moduli
Derives general formula for monodromy action on B-brane charge lattice via hemisphere partition functions in GLSMs and refines it for examples using quantum Kähler discriminant and torus link fundamental groups.
- Localisation of $\mathcal{N} = (2,2)$ theories on spindles of both twists