Supersymmetric localization in two dimensions

Abstract

This is an introductory review to localization techniques in supersymmetric two-dimensional gauge theories. In particular we describe how to construct Lagrangians of N=(2,2) theories on curved spaces, and how to compute their partition functions and certain correlators on the sphere, the hemisphere and other curved backgrounds. We also describe how to evaluate the partition function of N=(0,2) theories on the torus, known as the elliptic genus. Finally we summarize some of the applications, in particular to probe mirror symmetry and other non-perturbative dualities.

This is a contribution to the review volume `Localization techniques in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17 Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf

References in corpus (16)

• Witten Index and Wall Crossing
• Exact two-dimensional superconformal R-symmetry and c-extremization
• Sphere Partition Functions and the Zamolodchikov Metric
• Defects and Quantum Seiberg-Witten Geometry
• Comments on N=(2,2) Supersymmetry on Two-Manifolds
• Localization on three-dimensional manifolds
• Elliptic genera of ALE and ALF manifolds from gauged linear sigma models
• The long flow to freedom
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• An introduction to supersymmetric field theories in curved space
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• Self-dual Strings and 2D SYM
• New N = (2, 2) vector multiplets
• A brief review of the 2d/4d correspondences
• N=2 SUSY gauge theories on S^4
• Gromov-Witten invariants and localization

Cited by in corpus (22)

• Localization techniques in quantum field theories
• Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
• Top Down Approach to 6D SCFTs
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Localization on three-dimensional manifolds
• Localization and AdS/CFT Correspondence
• The grin of Cheshire cat resurgence from supersymmetric localization
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Holomorphic blocks and the 5d AGT correspondence
• New 2d $\mathcal{N}=(0,2)$ dualities from four dimensions
• Introduction to localization in quantum field theory
• More on Homological Supersymmetric Quantum Mechanics
• Gromov-Witten invariants and localization
• Remarks on Berry Connection in QFT, Anomalies, and Applications
• On exact correlation functions of chiral ring operators in $2d$ $\mathcal{N}=(2,2)$ SCFTs via localization
• Remarks on 2d Unframed Quiver Gauge Theories
• Quantum Sheaf Cohomology and Duality of Flag Manifolds
• 2d dualities from 4d
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Supersymmetric localisation of $\mathcal{N}=(2,2)$ theories on a spindle
• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• Localizing non-linear $\mathcal{N}=(2,2)$ sigma model on $S^2$