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Mirror Symmetry
• Space translation. If I have some apparatus, and move it to a different place it will work the same. The laws governing its behavior are the same under space translation. • Time translation. TheExpand
D-Branes And Mirror Symmetry
We study (2,2) supersymmetric field theories on two-dimensional worldsheet with boundaries. We determine D-branes (boundary conditions and boundary interactions) that preserve half of the bulkExpand
Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$N=2 Gauge Theories with Rank-One Gauge Groups
We compute the elliptic genera of two-dimensional $${\mathcal{N} = (2, 2)}$$N=(2,2) and $${\mathcal{N} = (0, 2)}$$N=(0,2) -gauged linear sigma models via supersymmetric localization, for rank-oneExpand
Duality of the Fermionic 2d Black Hole and N = 2 Liouville Theory as Mirror Symmetry
We prove the equivalence of the SL(2, R)/U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2d Black Hole, and N = 2 Liouville theory. We show that this duality is an example ofExpand
Phases Of N=2 Theories In 1+1 Dimensions With Boundary
We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-PatonExpand
Elliptic Genera of 2d $${\mathcal{N}}$$N = 2 Gauge Theories
We compute the elliptic genera of general two-dimensional $${\mathcal{N} = (2, 2)}$$N=(2,2) and $${\mathcal{N} = (0, 2)}$$N=(0,2) gauge theories. We find that the elliptic genus is given by the sumExpand
Orientifolds and mirror symmetry
We study parity symmetries and crosscap states in classes ofN =2 supersymmetric quantum eld theories in 1 + 1 dimensions, including non-linear sigma models, gauged WZW models, Landau-Ginzburg models,Expand
Branes and N=2 theories in two dimensions
Type IIA brane configurations are used to construct N = 2 supersymmetric gauge theories in two dimensions. Using localization of chiral multiplets in ten-dimensional space-time, supersymmetricExpand
Dynamics of N=2 supersymmetric gauge theories in three-dimensions
We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exactExpand
Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-Branes
We construct and analyze dual N = 4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded inExpand