A few recent developments in 2d (2,2) and (0,2) theories
arXiv:1501.01628
Abstract
In this note we summarize a few of the many recent developments in two-dimensional quantum field theories. We begin with a review of the current state of quantum sheaf cohomology, a heterotic analogue of quantum cohomology. We then turn to dualities: we outline the current status of (0,2) mirror symmetry, and then outline recent work on two-dimensional gauge dualities. In particular, we describe how many two-dimensional gauge dualities in both (2,2) and (0,2) supersymmetric gauge theories can be understood simply as different presentations of the same infrared (IR) geometry. We then discuss (not necessarily supersymmetric) two-dimensional nonabelian gauge theories in which a subgroup of the gauge group acts trivially on massless matter. We describe how these theories 'decompose' into disjoint unions of other theories indexed by discrete theta angles, a fact which in other contexts has proven to have implications for interpretations of certain gauged linear sigma models (GLSMs) and for Gromov-Witten invariants of stacks. We conclude with a discussion of recent developments in infinitesimal moduli of heterotic compactifications.
arXiv comment20 pages, LaTeX, contribution to proceedings of String-Math 2014; v2: typos fixed
References in corpus (33)
- Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
- Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
- Reading between the lines of four-dimensional gauge theories
- Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
- Partition functions of N=(2,2) gauge theories on S^2 and vortices
- Elliptic genera of 2d N=2 gauge theories
- Exact Results in D=2 Supersymmetric Gauge Theories
- Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N=(2,2) Theories
- Residues and World-Sheet Instantons
- Cluster decomposition, T-duality, and gerby CFT's
- D-Branes, Derived Categories, and Grothendieck Groups
- Dual Cones and Mirror Symmetry for Generalized Calabi-Yau Manifolds
- Homological projective duality for Grassmannians of lines
- Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications
- Notes on gauging noneffective group actions
- World-sheet Stability of (0,2) Linear Sigma Models
- Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
- GLSM's for partial flag manifolds
- The Revival of (0,2) Linear Sigma Models
- Half-Twisted Correlators from the Coulomb Branch
- New Methods for Characterizing Phases of 2D Supersymmetric Gauge Theories
- Recent Developments in (0,2) Mirror Symmetry
- Quantization of Fayet-Iliopoulos Parameters in Supergravity
- Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties
- Worldsheet Instantons, Torsion Curves, and Non-Perturbative Superpotentials
- On marginal deformations of (0,2) non-linear sigma models
- Notes on nonabelian (0,2) theories and dualities
- On Orbifolds of (0,2) Models
- The Coulomb Branch in Gauged Linear Sigma Models
- N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions
- On Gromov-Witten theory of root gerbes
- Chiral operators in two-dimensional (0,2) theories and a test of triality
- Analogues of Mathai-Quillen forms in sheaf cohomology and applications to topological field theory
Cited by in corpus (6)
- Notes on generalized global symmetries in QFT
- Quantum periods of Calabi-Yau fourfolds
- Quantum sheaf cohomology on Grassmannians
- Geometric Constructions of Two Dimensional (0,2) SUSY Theories
- Calabi-Yau generalized complete intersections and aspects of cohomology of sheaves
- On supermatrix models, Poisson geometry and noncommutative supersymmetric gauge theories