Browsing by Subject "Class S"
Now showing 1 - 1 of 1
- Results Per Page
- Sort Options
Item Towards a self-dual geometric Langlands program(2018-06-15) Derryberry, Richard Thomas; Ben-Zvi, David, 1974-; Neitzke, Andrew; Blumberg, Andrew; Keel, Sean; Nadler, DavidThis thesis is comprised of two logically separate but conjecturally related parts. In the first part of the thesis I study theories of class S [32] via the formalism of relative quantum field theories [30]. From this physical formalism, and by analogy to the physical derivation of usual geometric Langlands [45, 86], I conjecture the existence of a self-dual version of the geometric Langlands program. In the second part of the thesis I study shifted Cartier duality for the moduli of Higgs bundles. The main results are: (1) a criteria for ramification of L-valued cameral covers, (2) a generalisation of the Langlands duality/mirror symmetry results for the moduli of Higgs bundles of [24, 37], and (3) the existence of a self-dual version of the moduli of Higgs bundles. This self-dual space is conjecturally the target space for a theory of class S compactified on a torus, and provides positive evidence for the self-dual geometric Langlands program.