B-branes and related stuff

Teacher :Mauricio Romo
Schedule: Tue & Thur 15:20-16:55, 2020-2-18 ~ 5-7
Venue:Conference Room 1, Jin Chun Yuan West Bldg.


In this course I will present some advanced topics related with gauged linear sigma models (GLSM). I will mainly focus on how to get derived equivalences and functors between triangulated categories related to CY geometries, mathematically, this  is a generalization of Orlov’s equivalence and in physics  terms this is about correspondences of B-brane categories as we move on the quantum Kahler moduli space.  I will also present extensions of these results to non-CY cases. As time allows I will also present other modern topics such as Seiberg-like dualities and the incorporation of B-type domain walls on GLSMs and their categorical interpretation.



Some knowledge of 2d (2,2) supersymmetric QFTs  is required as well as some basic algebraic geometry. No previous knowledge on categories will be assumed. 


For the basics:

- K. Hori et al. Mirror Symmetry vol. 1

Physics references:

-  P. Aspinwall ‘D-branes on Calabi-Yau Manifolds’ hep-th/0403166

- M. Herbst, K. Hori and D. Page ‘Phases of N=2 Theories in 1+1 Dimensions with Boundary’ hep-th/0803.2045

Math references:

- M. Ballard, D. Favero and L. Katzarkov ‘Variation of Geometric Invariant Theory quotients and derived categories’ 1203.6643 [math.AG]

- D. Halpern-Leistner ‘The Derived Category of a GIT Quotient’ 1203.0276 [math.AG]