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We review the properties of orbifold operations on two-dimensional quantum field theories, either bosonic or fermionic, and describe the Orbifold groupoids which control the composition of orbifold operations. Three-dimensional TQFTs of Dijkgraaf-Witten type will play an important role in the analysis. We briefly discuss the extension to generalized symmetries and applications to constrain RG flows.
We study (4+2n)-dimensional N=1 super Yang-Mills theory on the orbifold background with non-vanishing magnetic flux. In particular, we study zero-modes of spinor fields. The flavor structure of our models is different from one in magnetized torus mod
We analyse topological orbifold conformal field theories on the symmetric product of a complex surface M. By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by Hurwitz numbers
We study three generation models in the four-dimensional spacetime, which can be derived from the ten-dimensional N=1 super Yang-Mills theory on the orbifold background with a non-vanishing magnetic flux. We classify the flavor structures and show po
Boundary states for D-branes at orbifold fixed points are constructed in close analogy with Cardys derivation of consistent boundary states in RCFT. Comments are made on the interpretation of the various coefficients in the explicit expressions, and
Following on from earlier work relating modules of meromorphic bosonic conformal field theories to states representing solutions of certain simple equations inside the theories, we show, in the context of orbifold theories, that the intertwiners betw