Localization of gauge theory on a four-sphere and supersymmetric Wilson loops

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DOI10.1007/s00220-012-1485-0zbMath1257.81056arXiv0712.2824OpenAlexW3103109706MaRDI QIDQ443881

Vasily Pestun

Publication date: 13 August 2012

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.2824

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Yang-Mills and other gauge theories in quantum field theory (81T13) Quantum field theory on lattices (81T25)

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in supersymmetric theories with R-symmetry in curved space ⋮ Two-point correlators in non-conformal \( \mathcal{N} =2 \) gauge theories ⋮ Wilson loops in terms of color invariants ⋮ Schur correlation functions on \(S^3 \times S^1\) ⋮ \( \mathcal{N} = 2 \) gauge theories on unoriented/open four-manifolds and their AGT counterparts ⋮ More on Wilson loops for two touching circles ⋮ Properties of the partition function of \( \mathcal{N}=2 \) supersymmetric QCD with massive matter ⋮ Perturbative solutions of \( \mathcal{N}={1}^{\ast} \) holography on \(S^4\) ⋮ Pentagon identities arising in supersymmetric gauge theory computations ⋮ Web construction of ABCDEFG and affine quiver gauge theories ⋮ Supersymmetry anomalies in new minimal supergravity ⋮ An infrared bootstrap of the Schur index with surface defects ⋮ Wilson loops in five-dimensional super-Yang-Mills ⋮ Supersymmetric states in large \(N\) Chern-Simons-matter theories ⋮ Large rank Wilson loops in \(\mathcal{N} = 2\) superconformal QCD at strong coupling ⋮ Towards non-AdS holography in 3-dimensional higher spin gravity ⋮ On the instantons and the hypermultiplet mass of \(\mathcal{N} = {{2}^{\ast}}\) super Yang-Mills on \(S^{4}\) ⋮ Gluing Nekrasov partition functions ⋮ Strong-coupling phases of planar \(\mathcal{N}=2^\ast\) super-Yang-Mills theory ⋮ Non-perturbative defect one-point functions in planar \(\mathcal{N} = 4\) super-Yang-Mills ⋮ Supersymmetric indices on \(I \times T^2\), elliptic genera and dualities with boundaries ⋮ On precision holography for the circular Wilson loop in \(AdS_5 \times S^5\) ⋮ Chern-Simons perturbative series revisited ⋮ Wilson loops in \(\mathcal{N} = 4\) \(\mathrm{SO}(N)\) SYM and D-branes in \( \mathrm{AdS}_5 \times \mathbb{R} \mathbb{P}^5\) ⋮ A CFT distance conjecture ⋮ The topologically twisted index of \(\mathcal{N} = 4\mathrm{SU} (N)\) super-Yang-Mills theory and a black hole Farey tail ⋮ Strong-coupling results for \(\mathcal{N} = 2\) superconformal quivers and holography ⋮ Gluing II: boundary localization and gluing formulas ⋮ Connected correlator of 1/2 BPS Wilson loops in \( \mathcal{N}=4 \) SYM ⋮ Bootstrapping the half-BPS line defect ⋮ Wilson loops in 5d \( \mathcal{N}=1 \) theories and S-duality ⋮ Superconformal index of higher derivative \( \mathcal{N}=1 \) multiplets in four dimensions ⋮ Euclidean supersymmetric solutions with the self-dual Weyl tensor ⋮ Seifert fibering operators in 3d \( \mathcal{N}=2 \) theories ⋮ 7D supersymmetric Yang-Mills on a 3-Sasakian manifold ⋮ 5d partition functions with a twist ⋮ Supersymmetry breaking phase in three dimensional large \(N\) gauge theories ⋮ Topologically twisted indices in five dimensions and holography ⋮ Interface entropy in four dimensions as Calabi's diastasis on the conformal manifold ⋮ Erratum to: Exact correlators on the Wilson loop in \( \mathcal{N} =4\) SYM: localization, defect CFT, and integrability ⋮ BPS Wilson loops in \( \mathcal{N} \geq 2\) superconformal Chern-Simons-matter theories ⋮ Instanton corrections of 1/6 BPS Wilson loops in ABJM theory ⋮ Surface defects and instanton partition functions ⋮ Holography for \(\mathcal N=1^*\) on \(S^4\) ⋮ Exact results for ABJ Wilson loops and open-closed duality ⋮ \(\mathrm{SU}(2|2)\) supersymmetric mechanics ⋮ Symmetries and couplings of non-relativistic electrodynamics ⋮ Notes on planar resolvents of Chern-Simons-matter matrix models ⋮ Integrability of orbifold ABJM theories ⋮ Infrared computations of defect Schur indices ⋮ Spectra of certain holographic ABJM Wilson loops in higher rank representations ⋮ Conformal Janus on Euclidean sphere ⋮ Wilson punctured network defects in 2D \(q\)-deformed Yang-Mills theory ⋮ Operator mixing in large \(N\) superconformal field theories on \(S^{4}\) and correlators with Wilson loops ⋮ Semichiral fields on \(S^2\) and generalized Kähler geometry ⋮ Mordell integrals and giveon-kutasov duality ⋮ Precision calculation of 1/4-BPS Wilson loops in \(\mathrm{AdS}_5\times S^5\) ⋮ Holographic Wilson loops in symmetric representations in \( \mathcal{N} = {2}^{\ast } \) super-Yang-Mills theory ⋮ Orbifolds, defects and sphere partition function ⋮ Bremsstrahlung function, leading Lüscher correction at weak coupling and localization ⋮ Supersymmetric Rényi entropy in two dimensions ⋮ Large \(N\) behavior of mass deformed ABJM theory ⋮ Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions ⋮ On large \(N\) solution of ABJM theory ⋮ On twisted \(N=2\) 5D super Yang-Mills theory ⋮ From weak to strong coupling in ABJM theory ⋮ Quantum 't Hooft loops of SYM \({{\mathcal N}=4}\) as instantons of \(YM_{2}\) in dual groups SU(N) and SU(N)/Z\(_{N}\) ⋮ Torus knot polynomials and Susy Wilson loops ⋮ Wilson loops in \(\mathcal{N} = 2\) super-Yang-Mills from matrix model ⋮ Non-perturbative topological strings and conformal blocks ⋮ 3d and 5d gauge theory partition functions as \(q\)-deformed CFT correlators ⋮ Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories ⋮ Erratum: Wilson loops in \(N=2\) super-Yang-Mills from matrix model ⋮ A search for \(\mathrm{AdS}_{5} {\times} S^{2}\) IIB supergravity solutions dual to \( \mathcal{N} = 2 \) SCFTs ⋮ \(F\)-theorem without supersymmetry ⋮ Z-extremization and F-theorem in Chern-Simons matter theories ⋮ Localization and non-renormalization in Chern-Simons theory ⋮ Deformations of the circular Wilson loop and spectral (in)dependence ⋮ Cardy formula for 4d SUSY theories and localization ⋮ Dual pairs of gauged linear sigma models and derived equivalences of Calabi-Yau threefolds ⋮ Boundary terms and three-point functions: an AdS/CFT puzzle resolved ⋮ Exact deconstruction of the 6D (2,0) theory ⋮ Spectral curves of \(\mathcal{N} = 1\) theories of class \({\mathcal{S}}_k \) ⋮ Quantum hydrodynamics from large-\(n\) supersymmetric gauge theories ⋮ Reflection positive doubles ⋮ Affine \(sl(N)\) conformal blocks from \({\mathcal N} = 2\) \(SU(N)\) gauge theories ⋮ Exact results and holography of Wilson loops in \({\mathcal N} = 2\) superconformal (quiver) gauge theories ⋮ Affine \(SL(2)\) conformal blocks from 4d gauge theories ⋮ (de)tails of Toda CFT ⋮ Localization and holography in \( \mathcal{N}=2 \) gauge theories ⋮ On the integrability of planar \( \mathcal{N}=2 \) superconformal gauge theories ⋮ Twisted \( \mathcal{N} = 4\) super Yang-Mills theory in \(\Omega\)-background ⋮ Exact results in \( \mathcal{N}=2 \) gauge theories ⋮ AGT relation in the light asymptotic limit ⋮ Analytic solution of bremsstrahlung TBA II: turning on the sphere angle ⋮ Extended supersymmetry on curved spaces ⋮ Quantum black hole entropy and the holomorphic prepotential of \( \mathcal{N}=2 \) supergravity ⋮ Localization on three-manifolds ⋮ Supersymmetry on curved spaces and superconformal anomalies ⋮ The 1/2 BPS Wilson loop in ABJ(M) at two loops: the details ⋮ Three dimensional mirror symmetry and partition function on \(S^{3}\) ⋮ Redeeming bad theories ⋮ Massive \( \mathcal{N} = 2\) gauge theories at large \(N\) ⋮ Exact results in supersymmetric field theories on manifolds with boundaries ⋮ Localization on round sphere revisited ⋮ 3d Chern-Simons theory from M5-branes ⋮ Maximal super Yang-Mills theories on curved background with off-shell supercharges ⋮ Multiple membranes in M-theory ⋮ Duality and transport for supersymmetric graphene from the hemisphere partition function ⋮ Central charges of 2d superconformal defects ⋮ The planar limit of \(\mathcal{N} = 2\) superconformal field theories ⋮ Type-B anomaly matching and the 6D (2,0) theory ⋮ Three-dimensional Maxwellian extended Bargmann supergravity ⋮ Absence of \(D^4R^4\) in M-theory from ABJM ⋮ Genus-2 holographic correlator on \(\mathrm{AdS}_5 \times S^5\) from localization ⋮ Five-dimensional cohomological localization and squashed \(q\)-deformations of two-dimensional Yang-Mills theory ⋮ Quiver CFT at strong coupling ⋮ Loop equation and exact soft anomalous dimension in \(\mathcal{N} = 4\) super Yang-Mills ⋮ Effective gravitational couplings of four-dimensional \(\mathcal{N} = 2\) supersymmetric gauge theories ⋮ Gauge theories on ALE space and super Liouville correlation functions ⋮ Gauge theories and Macdonald polynomials ⋮ The gravity dual of supersymmetric gauge theories on a squashed three-sphere ⋮ Localization and large \(N\) reduction on \(S^3\) for the planar and M-theory limit ⋮ Supersymmetric gauge theories on the five-sphere ⋮ Supersymmetric D3/D5 for massive defects on curved space ⋮ 7D supersymmetric Yang-Mills on curved manifolds ⋮ Five-dimensional maximally supersymmetric Yang-Mills in supergravity backgrounds ⋮ Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation ⋮ Spin chain integrability in non-supersymmetric Wilson loops ⋮ Dyson equations for correlators of Wilson loops ⋮ Vortex-strings in \( \mathcal{N}=2\) quiver \({\times}\) U(1) theories ⋮ Supersymmetric Wilson loops in \({\mathcal N}=6\) super-Chern-Simons-matter theory ⋮ \(q\)-Virasoro modular triple ⋮ Coulomb branches of star-shaped quivers ⋮ On the large R-charge \( \mathcal{N} =2\) chiral correlators and the Toda equation ⋮ Universality of Toda equation in \( \mathcal{N}=2 \) superconformal field theories ⋮ Deconstructing defects ⋮ Correlation functions on the half-BPS Wilson loop: perturbation and hexagonalization ⋮ Spectral form factor and semi-circle law in the time direction ⋮ \(T[ \mathrm{SU} (N)\) duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences] ⋮ \(N = 2^{\ast}\) phase transitions and holography ⋮ Localization and duality for ABJM latitude Wilson loops ⋮ The planar limit of \(\mathcal{N} = 2\) chiral correlators ⋮ Tackling the SDC in AdS with CFTs ⋮ Subleading corrections in \(\mathcal{N} = 3\) Gaiotto-Tomasiello theory ⋮ Generalized Giveon-Kutasov duality ⋮ Exact \(1/N\) expansion of Wilson loop correlators in \(\mathcal{N} = 4\) Super-Yang-Mills theory ⋮ Non-perturbative tests of duality cascades in three dimensional supersymmetric gauge theories ⋮ Exact results in a \(\mathcal{N} = 2\) superconformal gauge theory at strong coupling ⋮ Three dimensional mirror symmetry beyond \textit{ADE} quivers and Argyres-Douglas theories ⋮ Complete factorization in minimal \(\mathcal{N}=4 \) Chern-Simons-matter theory ⋮ Comments on higher rank Wilson loops in \(\mathcal{N} = 2^\ast\) ⋮ Antisymmetric Wilson loops in \(\mathcal{N}=4\) SYM beyond the planar limit ⋮ Analyticity of Nekrasov partition functions ⋮ Minimal area surfaces in \(\mathrm{AdS}_{n+1}\) and Wilson loops ⋮ Five-dimensional fermionic Chern-Simons theory ⋮ Negative branes, supergroups and the signature of spacetime ⋮ Analytic continuation of dimensions in supersymmetric localization ⋮ Spherical transverse M5-branes from the plane wave matrix model ⋮ Vortex-strings in \( \mathcal{N}=2 \) SQCD and bulk-string decoupling ⋮ On the higher spin spectrum of Chern-Simons theory coupled to fermions in the large flavour limit ⋮ String corrections to circular Wilson loop and anomalies ⋮ Chiral algebras, localization and surface defects ⋮ Mass deformations of 5d SCFTs via holography ⋮ Elliptic genus derivation of 4d holomorphic blocks ⋮ On exact correlation functions of chiral ring operators in \(2d \;\) \(\mathcal{N}=(2,\;2)\) SCFTs via localization ⋮ Spheres, charges, instantons, and bootstrap: a five-dimensional odyssey ⋮ Non-supersymmetric Wilson loop in \( \mathcal{N}=4 \) SYM and defect 1d CFT ⋮ A one-dimensional theory for Higgs branch operators ⋮ Wilson loops and its correlators with chiral operators in \( \mathcal{N}=2,4\) SCFT at large \(N\) ⋮ Correlators between Wilson loop and chiral operators in \( \mathcal{N}=2 \) conformal gauge theories ⋮ Wilson loop and its correlators in the limit of large coupling constant ⋮ \(\mathcal{N} = 2\) conformal SYM theories at large \(\mathcal{N}\) ⋮ S-duality and supersymmetry on curved manifolds ⋮ Quantum entropy and exact 4D/5D connection ⋮ Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone ⋮ 5d Higgs branch localization, Seiberg-Witten equations and contact geometry ⋮ \( \mathcal{N}=4 \) super-Yang-Mills on conic space as hologram of STU topological black hole ⋮ \(tt^{*}\) equations, localization and exact chiral rings in \(4d \mathcal{N} =2\) SCFTs ⋮ Dilogarithm ladders from Wilson loops ⋮ Nonperturbative black hole entropy and Kloosterman sums ⋮ Ramond-Ramond couplings of D-branes ⋮ A localization computation in confining phase ⋮ On \( \mathcal{N}=1 \) partition functions without R-symmetry ⋮ Gauge theories with 16 supersymmetries on spheres ⋮ Resurgent analysis of localizable observables in supersymmetric gauge theories ⋮ Spherical branes ⋮ Toward precision holography in type IIA with Wilson loops ⋮ Supersymmetric localization in \(\mathrm{AdS}_{5}\) and the protected chiral algebra ⋮ The M-theory S-matrix from ABJM: beyond 11D supergravity ⋮ Antisymmetric Wilson loops in \( \mathcal{N}=4 \) SYM: from exact results to non-planar corrections ⋮ Sum rules for characters from character-preservation property of matrix models ⋮ Toward the construction of the general multi-cut solutions in Chern-Simons matrix models ⋮ Vortex counting from field theory ⋮ A note on perturbation series in supersymmetric gauge theories ⋮ Thermal string probes in AdS and finite temperature Wilson loops ⋮ Impure aspects of supersymmetric Wilson loops ⋮ Comments on knotted 1/2 BPS Wilson loops ⋮ Supersymmetry on curved spaces and holography ⋮ Exploring curved superspace ⋮ The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere ⋮ Seiberg-Witten theories on ellipsoids ⋮ Free energy v.s. Sasaki-Einstein volume for infinite families of M2-brane theories ⋮ The large \(N\) limit of toric Chern-Simons matter theories and their duals ⋮ Rigid supersymmetric backgrounds of minimal off-shell supergravity ⋮ Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories ⋮ Large \(N\) limit of \({\mathcal N}=2\text{SU}(N)\) gauge theories from localization ⋮ 5-dim superconformal index with enhanced \(E_n\) global symmetry ⋮ Superconformal index with duality domain wall ⋮ The gravity duals of \( \mathcal{N}=2 \) superconformal field theories ⋮ Analytic solution of bremsstrahlung TBA ⋮ Torsion and supersymmetry in \(\Omega\)-background ⋮ More on 't Hooft loops in \( \mathcal{N}=4 \) SYM ⋮ Beyond LLM in M-theory ⋮ Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories ⋮ Localization of the four-dimensional \({\mathcal N}=4\) SYM to a two-sphere and 1/8 BPS Wilson loops ⋮ On 't Hooft defects, monopole bubbling and supersymmetric quantum mechanics ⋮ Boundary conditions and localization on AdS. I. ⋮ BRST quantization and equivariant cohomology: localization with asymptotic boundaries ⋮ Sphere Partition Functions and the Kähler Metric on the Conformal Manifold ⋮ Supersymmetric partition functions on Riemann surfaces ⋮ 4-Manifold topology, Donaldson–Witten theory, Floer homology and higher gauge theory methods in the BV-BFV formalism ⋮ On the abundance of supersymmetric strings in AdS₃ × S ³ × S ³ × S ¹ describing BPS line operators ⋮ Index of the transversally elliptic complex in Pestunization ⋮ Newton–Cartan (super)gravity as a non-relativistic limit ⋮ Gauge theories on spheres with 16 supercharges and non-constant couplings ⋮ Phase transitions and Wilson loops in antisymmetric representations in Chern–Simons-matter theory ⋮ Quiver ${\text{W}}_{{\boldsymbol{{\epsilon}}}_{\mathbf{1}},{\boldsymbol{{\epsilon}}}_{\mathbf{2}}}$ algebras of 4D $\boldsymbol{\mathcal{N}}\mathbf{=}\mathbf{2}$ gauge theories ⋮ Wilson loops and integrability ⋮ Instanton counting in class Sk ⋮ Roadmap on Wilson loops in 3d Chern–Simons-matter theories ⋮ On supermatrix models, Poisson geometry, and noncommutative supersymmetric gauge theories ⋮ Partition functions for supersymmetric gauge theories on spheres ⋮ Introduction to localization in quantum field theory ⋮ Review of localization in geometry ⋮ Supersymmetric localization in two dimensions ⋮ Gromov–Witten invariants and localization ⋮ An introduction to supersymmetric field theories in curved space ⋮ Localization on three-dimensional manifolds ⋮ Localization at largeNin Chern–Simons-matter theories ⋮ TheF-theorem andF-maximization ⋮ ${{{\mathcal N}}=2}$ SUSY gauge theories on S⁴ ⋮ Localization and AdS/CFT correspondence ⋮ A brief review of the 2d/4d correspondences ⋮ The supersymmetric index in four dimensions ⋮ Review of localization for 5d supersymmetric gauge theories ⋮ Matrix models for 5d super Yang–Mills ⋮ Holomorphic blocks and the 5d AGT correspondence ⋮ Indices for 6 dimensional superconformal field theories ⋮ More largeNlimits of 3d gauge theories ⋮ Elliptic modular double and 4d partition functions ⋮ LargeNexpansion of Wilson loops in the Gross–Witten–Wadia matrix model ⋮ Integrated correlators in \(\mathcal{N} = 4\) SYM via \(\mathrm{SL}(2, \mathbb{Z})\) spectral theory ⋮ Massive flows in \(\mathrm{AdS}_6/\mathrm{CFT}_5\) ⋮ Wilson Loops in Antisymmetric Representations from Localization in Supersymmetric Gauge Theories ⋮ Supersymmetric field theories and geometric Langlands: The other side of the coin ⋮ Chiral algebra, localization, modularity, surface defects, and all that ⋮ Algebraic structures on the moduli spaces in gauge theories ⋮ Exact Results on $${\mathcal N}=2$$ Supersymmetric Gauge Theories ⋮ A Review on Instanton Counting and W-Algebras ⋮ Supersymmetric Gauge Theories, Quantization of $${\mathcal M}_\mathrm{flat}$$ , and Conformal Field Theory ⋮ N = ( 4 , 4 ) vector multiplets on curved two-manifolds ⋮ Comments on the multi-spin solution to the Yang–Baxter equation and basic hypergeometric sum/integral identity ⋮ An Index Formula for Supersymmetric Quantum Mechanics ⋮ Derived representation schemes and supersymmetric gauge theory ⋮ Charged conformal Killing spinors ⋮ SUPERSYMMETRIC WILSON LOOPS WITH GENERAL CONTOURS IN ABJM THEORY ⋮ Surface operators in the 6d N = (2, 0) theory ⋮ DEFORMED SUPERSYMMETRIC GAUGE THEORIES FROM THE FLUXTRAP BACKGROUND ⋮ A slow review of the AGT correspondence ⋮ A profusion of 1/2 BPS Wilson loops in \( \mathcal{N}=4 \) Chern-Simons-matter theories ⋮ Line operators in theories of class \( \mathcal{S} \), quantized moduli space of flat connections, and Toda field theory ⋮ Ellipsoid partition function from Seiberg-Witten monopoles ⋮ On rigid supersymmetry and notions of holomorphy in five dimensions ⋮ Ladder exponentiation for generic large symmetric representation Wilson loops ⋮ Spectral zeta function and non-perturbative effects in ABJM Fermi-gas ⋮ Supersymmetric D3/D7 for holographic flavors on curved space ⋮ Newton-Cartan supergravity with torsion and Schrödinger supergravity ⋮ Supersymmetric localization for BPS black hole entropy: 1-loop partition function from vector multiplets ⋮ On exact correlation functions in \(\mathrm{SU}(N)\) \(\mathcal{N}=2 \) superconformal QCD ⋮ Supersymmetric Wilson loops in \( \mathcal{N}=4 \) super Chern-Simons-matter theory ⋮ Partition function of \( \mathcal{N}={2}^{\ast } \) SYM on a large four-sphere ⋮ Functional determinants, index theorems, and exact quantum black hole entropy ⋮ New supersymmetric index of heterotic compactifications with torsion ⋮ Euclidean Wilson loops and minimal area surfaces in Lorentzian \(\mathrm{AdS}_{3}\) ⋮ Partially twisted superconformal M5 brane in R-symmetry gauge field backgrounds ⋮ 2d partition function in \(\Omega\)-background and vortex/instanton correspondence ⋮ Smooth Wilson loops in \( \mathcal{N}=4 \) non-chiral superspace ⋮ Exact results and Schur expansions in quiver Chern-Simons-matter theories ⋮ Strong coupling expansion of circular Wilson loops and string theories in \(\mathrm{AdS}_5 \times S^5\) and \(\mathrm{AdS}_4 \times CP^3\) ⋮ \(\mathcal{N} = 2\) dualities and \(Z\)-extremization in three dimensions ⋮ S-duality wall of SQCD from Toda braiding ⋮ Spectral theories and topological strings on del Pezzo geometries ⋮ Three-dimensional Maxwellian extended Newtonian gravity and flat limit ⋮ Modular invariance in superstring theory from \(\mathcal{N} = 4\) super-Yang-Mills ⋮ Giant Wilson loops and \( \mathrm{AdS}_2/ \mathrm{dCFT}_1\) ⋮ Towards the classification of rank-\(r\) \(\mathcal{N} = 2\) SCFTs. I: Twisted partition function and central charge formulae ⋮ Large \(N\) superconformal indices for 3d holographic SCFTs ⋮ Chiral dualities for \(\mathrm{SQCD}_3\) with D-type superpotential ⋮ Constant primary operators and where to find them: the strange case of BPS defects in ABJ(M) theory ⋮ Maximally symmetric nuts in 4d \(\mathcal{N} = 2\) higher derivative supergravity ⋮ Multipoint correlators on the supersymmetric Wilson line defect CFT. II: Unprotected operators ⋮ Erratum to: ``Supersymmetric localization: \(\mathcal{N} = (2, 2)\) theories on \(\mathrm{S}^2\) and \(\mathrm{AdS}_2\) ⋮ Partition functions of non-Lagrangian theories from the holomorphic Anomaly ⋮ Discrete analogue of the Weil-Petersson volume in double scaled SYK ⋮ Exceptionally simple integrated correlators in \(\mathcal{N} = 4\) supersymmetric Yang-Mills theory ⋮ Beyond \(\mathrm{AdS}_2/\mathrm{dCFT}_1\): insertions in two Wilson loops ⋮ Modular anomaly equation for Schur index of \(\mathcal{N} = 4\) super-Yang-Mills ⋮ One-dimensional sectors from the squashed three-sphere ⋮ Multipoint correlators on the supersymmetric Wilson line defect CFT ⋮ BPS coherent states and localization ⋮ Ironing out the crease ⋮ Harnessing S-duality in \(\mathcal{N} = 4\) SYM \& supergravity as \(\mathrm{SL}(2, \mathbb{Z})\)-averaged strings ⋮ Three-point functions in a \(\mathcal{N} = 2\) superconformal gauge theory and their strong-coupling limit ⋮ Wilson loops in large symmetric representations through a double-scaling limit ⋮ Exact large charge in \(\mathcal{N} = 4\) SYM and semiclassical string theory ⋮ Interpolating Wilson loops and enriched RG flows ⋮ Symplectic gauge group on the lens space ⋮ 't Hooft loops and integrability ⋮ Quantized strings and instantons in holography ⋮ Chaos and the reparametrization mode on the \(\mathrm{AdS}_2\) string ⋮ The planar limit of integrated 4-point functions ⋮ Generating functions and large-charge expansion of integrated correlators in \(\mathcal{N} = 4\) supersymmetric Yang-Mills theory ⋮ From 5d flat connections to 4d fluxes (the art of slicing the cone) ⋮ Comments on ABJM free energy on \(S^3\) at large \(N\) and perturbative expansions in M-theory and string theory ⋮ Defect localized entropy: renormalization group and holography ⋮ Free energy on the sphere for non-abelian gauge theories ⋮ Modular-invariant large-\(N\) completion of an integrated correlator in \(\mathcal{N} = 4\) supersymmetric Yang-Mills theory ⋮ 't Hooft expansion of \(\mathrm{SO}(N)\) and \(\mathrm{Sp}(N)\) \(\mathcal{N} = 4\) SYM revisited ⋮ The quantum UV-IR map for line defects in \(\mathfrak{gl}(3)\)-type class \(S\) theories ⋮ Strong coupling expansion in \(\mathcal{N} = 2\) superconformal theories and the Bessel kernel ⋮ Integrability treatment of AdS/CFT orbifolds ⋮ Twisted index on hyperbolic four-manifolds ⋮ 1/2 BPS structure constants and random matrices ⋮ Integrated correlators with a Wilson line in \(\mathcal{N} = 4\) SYM ⋮ Phases of Wilson lines: conformality and screening ⋮ Localization vs holography in \(4d\) \(\mathcal{N} = 2\) quiver theories ⋮ Quantum phases of \(4d\) \(\mathrm{SU}(N)\) \(\mathcal{N} = 4\) SYM ⋮ Worldsheet dual of free \(\mathcal{N} = 2\) quiver gauge theories ⋮ Defect correlators in a \(\mathcal{N} = 2\) SCFT at strong coupling ⋮ 1/3 BPS loops and defect CFTs in ABJM theory ⋮ Wilson loops and defect RG flows in ABJM ⋮ Wilson loop correlators at strong coupling in \(\mathcal{N} = 2\) quiver gauge theories ⋮ The spindle index from localization ⋮ A derivation of the planar limit of \(\mathcal{N} = 2\) chiral correlators ⋮ Non-perturbative defects in tensor models from melonic trees ⋮ Large \(N\) expansion of an integrated correlator in \(\mathcal{N} = 4\) SYM ⋮ A quantum mechanics for magnetic horizons ⋮ Non-planar corrections in orbifold/orientifold \(\mathcal{N} = 2\) superconformal theories from localization ⋮ Orbit averaging coherent states: holographic three-point functions of AdS giant gravitons ⋮ Seiberg-Witten geometry of four-dimensional \(\mathcal{N}=2\) quiver gauge theories ⋮ Laplace-difference equation for integrated correlators of operators with general charges in \(\mathcal{N} = 4\) SYM ⋮ Gravitating anisotropic merons and squashed spheres in the three-dimensional Einstein-Yang-Mills-Chern-Simons theory ⋮ Equivariant localization and holography ⋮ Blowups in BPS/CFT correspondence, and Painlevé VI ⋮ A matrix-model approach to integrated correlators in a \(\mathcal{N} = 2\) SYM theory ⋮ Remarks on BPS Wilson loops in non-conformal \(\mathcal{N} = 2\) gauge theories and localization ⋮ Supersymmetric localization of (higher-spin) JT gravity: a bulk perspective ⋮ Partition functions and fibering operators on the Coulomb branch of 5d SCFTs ⋮ Exact strong coupling results in \(\mathcal{N} = 2\) \(\mathrm{Sp}(2N)\) superconformal gauge theory from localization ⋮ Bootstrapping \(\mathcal{N} = 4\) super-Yang-Mills on the conformal manifold ⋮ Bootstrapping 4d \(\mathcal{N} = 2\) gauge theories: the case of SQCD ⋮ Strong coupling expansions in \(\mathcal{N} = 2\) quiver gauge theories ⋮ Black hole spectra in holography: consequences for equilibration of dual gauge theories ⋮ Partition function of \(N = 2\) gauge theories on a squashed \(S^4\) with \(\mathit{SU}(2) \times U(1)\) isometry ⋮ Wilson loops and chiral correlators on squashed spheres ⋮ Wilson loops and chiral correlators on squashed spheres ⋮ Observations on BPS observables in 6D ⋮ Harmonic forms on asymptotically ADS metrics ⋮ The SAGEX review on scattering amplitudes Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their N=4 supersymmetric Yang–Mills duals

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