# (21.04.) 2d (0,2) Theories and F-theory

Timo Weigand (Heidelberg)

21.04.2016 at 16:15

Geometric engineering via F-theory allows for the construction and investigation of interesting field theories in various dimensions. In this talk we report on the recent extension of this programme to the construction of 2-dimensional gauge theories from F-theory on torus-fibered Calabi-Yau five-folds. Such theories exhibit N=(0,2) supersymmetry and therefore have the structure of an N=(0,2) gauged linear sigma model. The defining data such as the abelian or non-abelian gauge algebra, the structure of the 2d (0,2) matter multiplets and their interactions are determined by performing a partial topological twist on the Super-Yang-Mills theory originating from a stack of 7-branes wrapping a Kahler three-cycle. This three-cycle is embedded into a complex four-fold, which forms the base of an F-theory torus-fibration. Depending on whether the base is compact or non- compact, the 2d effective theories are coupled to quantum gravity or not. Extra chiral sectors arise from D3- branes wrapping holomorphic curves on the base. Another route to studying such 2d F-theory compactifications, including background fluxes, is via the dual supersymmetric quantum mechanics obtained by compactifying M-theory on the same torus-fibration. Finally, by interpreting the 2d gauged linear sigma model as (part of) the worldsheet theory of a heterotic string, we are lead to considering a correspondence between the F-theory torus-fibered Calabi-Yau five-fold and the target space of the heterotic string.

Arnold Sommerfeld Center

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