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Duality in two-dimensional $$(2,2)$$ supersymmetric non-abelian gauge theories. (English) Zbl 1342.81635
Summary: We study the low energy behaviour of $$N=(2, 2)$$ supersymmetric gauge theories in $$1+1$$ dimensions, with orthogonal and symplectic gauge groups and matters in the fundamental representation. We observe supersymmetry breaking in super-Yang-Mills theory and in theories with small numbers of flavors. For larger numbers of flavors, we discover duality between regular theories with different gauge groups and matter contents, where regularity refers to absence of quantum Coulomb branch. The result is applied to study families of superconformal field theories that can be used for superstring compactifications, with corners corresponding to three-dimensional Calabi-Yau manifolds. This work is motivated by recent development in mathematics concerning equivalences of derived categories.

##### MSC:
 81T75 Noncommutative geometry methods in quantum field theory 81T60 Supersymmetric field theories in quantum mechanics 81T13 Yang-Mills and other gauge theories in quantum field theory
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