学术报告(李晓斌 9.21)
Mirror symmetry and boundary conditions
What is mirror symmetry ? Mirror symmetry is a relation between generating function of Gromov-Witten invariants (A-model) and period integrals (B-model). From viewpoint of gauge theory and instanton counting, it is a duality between Nekrasov partition function and Seiberg-Witten prepotential. In this talk, I will discuss new dualities appearing in 5d N = 1 Sp(N) gauge theory with N_f (≤2N + 3) flavors and explain the computations about Nekrasov partition function based on topological vertex algorithm of 5-brane web with O5-plane which corresponds to non-toric geometry. With the help of random partition technique, Nekrasov partition function can be rewritten in terms of profile function, after taking thermodynamic limit and functional derivatives, the saddle point equation can be derived for the profile function. By introducing the resolvent, the corresponding Seiberg-Witten geometry and boundary conditions are derived and the relations with the prepotential in terms of the cycle integrals are discussed. They coincide with those directly obtained from the dual graph of the 5-brane web with O5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-type singularities. This is joint work with Futoshi Yagi.