An introduction to supersymmetric field theories in curved space

Abstract

In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background fields. We present the general principles, which broadly apply to theories with different amounts of supersymmetry in diverse dimensions, as well as specific applications to N=1 theories in four dimensions and their three-dimensional cousins with N=2 supersymmetry.

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 (18)

• Towards a derivation of holographic entanglement entropy
• Notes on SUSY Gauge Theories on Three-Sphere
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Sphere Partition Functions and the Zamolodchikov Metric
• Localization on Hopf surfaces
• Comments on the Fayet-Iliopoulos Term in Field Theory and Supergravity
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• The supersymmetric index in four dimensions
• Localization on three-dimensional manifolds
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• The F-Theorem and F-Maximization
• Supersymmetric counterterms from new minimal supergravity
• Global Symmetries and D-Terms in Supersymmetric Field Theories
• Introduction to localization in quantum field theory
• 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 (24)

• Localization techniques in quantum field theories
• Entanglement entropy: holography and renormalization group
• The supersymmetric index in four dimensions
• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Localization on three-dimensional manifolds
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• The F-Theorem and F-Maximization
• Holomorphic blocks and the 5d AGT correspondence
• A slow review of the AGT correspondence
• Twisting with a Flip (the Art of Pestunization)
• Teichmuller TQFT vs Chern-Simons Theory
• Supersymmetric localization in two dimensions
• Introduction to localization in quantum field theory
• 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
• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
• Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae
• The $\mathcal{N}=2$ Prepotential and the Sphere Free Energy
• Quantum theory, thermal gradients and the curved Euclidean space
• Compactifying 5d superconformal field theories to 3d
• A String Dual for Partially Topological Chern-Simons-Matter Theories
• Boundary Conditions in Topological AdS${}_4$/CFT${}_3$
• Loop Corrected Supercharges from Holomorphic Anomalies