Holographic Aspects of Four Dimensional $\mathcal{N}=2$ SCFTs and their Marginal Deformations

Abstract

We study the holographic description of $\mathcal{N}=2$ Super Conformal Field Theories in four dimensions first given by Gaiotto and Maldacena. We present new expressions that holographically calculate characteristic numbers of the CFT and associated Hanany-Witten set-ups, or more dynamical observables, like the central charge. A number of examples of varying complexity are studied and some proofs for these new expressions are presented. We repeat this treatment for the case of the marginally deformed Gaiotto-Maldacena theories, presenting an infinite family of new solutions and compute some of its observables. These new backgrounds rely on the solution of a Laplace equation and a boundary condition, encoding the kinematics of the original conformal field theory.

arXiv comment32 pages plus many appendixes and various figures

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• Electrostatic Description of Five-dimensional SCFTs
• Integrable Fishnet from $\gamma$-Deformed $\mathcal{N}=2$ Quivers
• A slow review of the AGT correspondence
• ${\text{AdS}}_2\times {\text{S}}^2\times {\text{CY}}_2$ solutions in Type IIB with 8 supersymmetries
• Wilson loops in 5d long quiver gauge theories
• Holographic duals of M5-branes on an irregularly punctured sphere
• Electrostatic description of 3d $\mathcal{N}=4$ linear quivers
• Holographic description of SCFT${}_5$ compactifications
• AdS${}_6$/CFT${}_5$ with O7-planes
• Consistent truncations of supergravity and $\frac{1}{2}$-BPS RG flows in $4d$ SCFTs
• Spin 2 operators in holographic 4d $\mathcal{N}=2$ SCFTs
• New AdS${}_2$ backgrounds and $\mathcal{N}=4$ Conformal Quantum Mechanics
• Spin 2 fluctuations in 1/4 BPS AdS${}_3$/CFT${}_2$
• Non-integrability in AdS${}_3$ vacua
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• Holography for 2d $\mathcal{N}=(0,4)$ quantum field theory
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Spin-2 excitations in Gaiotto-Maldacena solutions
• Wilson loops for 5d and 3d conformal linear quivers
• Linear Quivers at Large-$N$
• Integrability and non-integrability for marginal deformations of 4d $\mathcal{N}=2$ SCFTs
• Fragmentation and defragmentation of strings in type IIA and their holographic duals
• Universal Pieces of Holographic Entanglement Entropy and Holographic Subregion Complexity
• Spin $2$ spectrum for marginal deformations of 4d $\mathcal{N}=2$ SCFTs
• Spin-$2$ operators in AdS${}_2$/CFT${}_1$
• Complexity and Operator Growth in Holographic 6d SCFTs
• The conformal brane-scan: an update
• Integrability and non-integrability for holographic dual of Matrix model and non-Abelian T-dual of AdS${}_5\times$S${}^5$
• Field theory aspects of $\eta$-deformed superstring background
• Infinite Linear Quivers and Continuous Rank Functions
• On the planar limit of 3d $T_{\rho }^{\sigma }[SU(N)]$
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• Marginally deformed AdS${}_5$/CFT${}_4$ Backgrounds in Type IIB
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• Nonrelativistic strings and the limits of $\mathcal{N}=2$ dualities