Review of localization in geometry

Abstract

Review of localization in geometry: equivariant cohomology, characteristic classes, Atiyah-Bott formula, Atiyah-Singer equivariant index formula, Mathai-Quillen formalism

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 (2)

• Introduction to localization in quantum field theory
• N=2 SUSY gauge theories on S^4

Cited by in corpus (14)

• Localization techniques in quantum field theories
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• N=2 SUSY gauge theories on S^4
• Blocks and Vortices in the 3d ADHM Quiver Gauge Theory
• A-branes, foliations and localization
• Factorisation of 3d $\mathcal{N}=4$ Twisted Indices and the Geometry of Vortex Moduli Space
• Localization and Duality for ABJM Latitude Wilson Loops
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• Algorithms for representations of quiver Yangian algebras
• Witten index for weak supersymmetric systems: invariance under deformations
• Oscillator Calculus on Coadjoint Orbits and Index Theorems
• Weak supersymmetric $su(N|1)$ quantum systems
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations