Introduction to localization in quantum field theory

Abstract

This is the introductory chapter to the volume. We review the main idea of the localization technique and its brief history both in geometry and in QFT. We discuss localization in diverse dimensions and give an overview of the major applications of the localization calculations for supersymmetric theories. We explain the focus of the present volume.

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 (12)

• The supersymmetric index in four dimensions
• Localization on three-dimensional manifolds
• Localization and AdS/CFT Correspondence
• The F-Theorem and F-Maximization
• Holomorphic blocks and the 5d AGT correspondence
• Supersymmetric localization in two dimensions
• An introduction to supersymmetric field theories in curved space
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• A brief review of the 2d/4d correspondences
• N=2 SUSY gauge theories on S^4
• Supersymmetric backgrounds from 5d N=1 supergravity
• Gromov-Witten invariants and localization

Cited by in corpus (24)

• Localization techniques in quantum field theories
• Lectures on AdS Black Holes, Holography and Localization
• Localization and AdS/CFT Correspondence
• Equivariant localization and holography
• A slow review of the AGT correspondence
• Localization vs holography in $4d$ $\mathcal{N}=2$ quiver theories
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• An introduction to supersymmetric field theories in curved space
• Three-point functions in a $\mathcal{N}=2$ superconformal gauge theory and their strong-coupling limit
• Strong coupling expansions in $\mathcal{N}=2$ quiver gauge theories
• Review of localization in geometry
• Topological Correlators and Surface Defects from Equivariant Cohomology
• 7D supersymmetric Yang-Mills on curved manifolds
• Random matrices with row constraints and eigenvalue distributions of graph Laplacians
• Localization and Duality for ABJM Latitude Wilson Loops
• Phases of five-dimensional supersymmetric gauge theories
• APS $\eta$-invariant, path integrals, and mock modularity
• Linear Quivers at Large-$N$
• Exact WKB Analysis of ${\mathbb{CP}}^1$ Holomorphic Blocks
• Defect correlators in a $\mathcal{N}=2$ SCFT at strong coupling
• Integrated correlators with a Wilson line in a $\mathcal{N}=2$ quiver gauge theory at strong coupling
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography
• Localizing non-linear $\mathcal{N}=(2,2)$ sigma model on $S^2$