Duality In Two-Dimensional (2,2) Supersymmetric Non-Abelian Gauge Theories

Abstract

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.

90 pages, 2 figures; typos and simple errors corrected, references corrected and added

References in corpus (7)

• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• FJRW rings and Landau-Ginzburg Mirror Symmetry
• Homological projective duality for Grassmannians of lines
• Seiberg-like duality in three dimensions for orthogonal gauge groups
• Mirror symmetry and projective geometry of Reye congruences I
• The Pfaffian-Grassmannian derived equivalence
• Homological Projective Duality

Cited by in corpus (10)

• Elliptic genera of 2d N=2 gauge theories
• 3d dualities from 4d dualities
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• The long flow to freedom
• Homological Projective Duality via Variation of Geometric Invariant Theory Quotients
• 2d SCFTs from M2-branes
• Mixed braid group actions from deformations of surface singularities
• Determinantal Quintics and Mirror Symmetry of Reye Congruences