Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories

Abstract

In these lectures I give a pedagogical presentation of some of the recent progress in supersymmetric Chern-Simons-matter theories, coming from the use of localization and matrix model techniques. The goal is to provide a simple derivation of the exact interpolating function for the free energy of ABJM theory on the three-sphere, which implies in particular the N^{3/2} behavior at strong coupling. I explain in detail part of the background needed to understand this derivation, like holographic renormalization, localization of path integrals, and large N techniques in matrix models

73 pages, 7 figures. v2: references and clarifications added, misprints corrected. v3: more references, clarifications, and corrections. v4: more corrections and clarifications, final version to appear in J. Phys. A

References in corpus (4)

• Multi-Matrix Models and Tri-Sasaki Einstein Spaces
• Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
• The large N limit of quiver matrix models and Sasaki-Einstein manifolds
• Comments on F-maximization and R-symmetry in 3D SCFTs

Cited by in corpus (63)

• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• ABJM theory as a Fermi gas
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Generating Non-perturbative Physics from Perturbation Theory
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• Lectures on AdS Black Holes, Holography and Localization
• Multiple Membranes in M-theory
• Matrix models from operators and topological strings
• Newton-Cartan (super)gravity as a non-relativistic limit
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• The Partition Function of ABJ Theory
• Wilson Loops in 5d N=1 SCFTs and AdS/CFT
• Large-N correlation functions in $\mathcal{N}=2$ superconformal QCD
• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
• Stress Tensors from Trace Anomalies in Conformal Field Theories
• Localization and AdS/CFT Correspondence
• Super-Rényi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals
• The F-Theorem and F-Maximization
• Toroidal and Elliptic Quiver BPS Algebras and Beyond
• Localization at large N in Chern-Simons-matter theories
• Keeping matter in the loop in dS${}_3$ quantum gravity
• Airy Function and 4d Quantum Gravity
• Free energy and defect $C$-theorem in free fermion
• ABJ Wilson loops and Seiberg Duality
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and localization in matrix models
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Conformal bounds in three dimensions from entanglement entropy
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• Aspects of N-partite information in conformal field theories
• Multi-cut Solutions in Chern-Simons Matrix Models
• Free Energy on the Sphere for Non-Abelian Gauge Theories
• Anomalous dimensions of monopole operators in scalar QED${}_3$ with Chern-Simons term
• A note on the integral equation for the Wilson loop in N = 2 D=4 superconformal Yang-Mills theory
• Universal Pieces of Holographic Entanglement Entropy and Holographic Subregion Complexity
• Localization and Non-Renormalization in Chern-Simons Theory
• Phase Space Distribution of Riemann Zeros
• 3d $\mathcal{N}=3$ Generalized Giveon-Kutasov Duality
• Quantum phase transitions with dynamical flavors
• More Large $N$ limits of 3d gauge theories
• Microscopics of de Sitter Entropy from Precision Holography
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• Aspects of Massive Gauge Theories on Three Sphere in Infinite Mass Limit
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
• Flavored ABJM theory on the sphere and holographic F-functions
• Large N instantons from topological strings
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Quantum Holographic Entanglement Entropy to All Orders in $1/N$ Expansion
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• 3d dualities with decoupled sectors and brane transitions
• Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators
• Subleading Corrections in N=3 Gaiotto-Tomasiello Theory
• On a Gravity Dual to Flavored Topological Quantum Mechanics
• Construction of a Massive ABJM Theory Without Higgs Superfields
• Reduced Chern-Simons Quiver Theories and Cohomological 3-Algebra Models
• Is the EMI model a QFT? An inquiry on the space of allowed entropy functions
• Loop equations for generalised eigenvalue models
• Disks globally maximize the entanglement entropy in $2+1$ dimensions
• Particles, Forces and the Early Universe
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview