Intersecting Surface Defects and Two-Dimensional CFT

Abstract

We initiate the study of intersecting surface operators/defects in four-dimensional quantum field theories (QFTs). We characterize these defects by coupled 4d/2d/0d theories constructed by coupling the degrees of freedom localized at a point and on intersecting surfaces in spacetime to each other and to the four-dimensional QFT. We construct supersymmetric intersecting surface defects preserving just two supercharges in N = 2 gauge theories. These defects are amenable to exact analysis by localization of the partition function of the underlying 4d/2d/0d QFT. We identify the 4d/2d/0d QFTs that describe intersecting surface operators in N = 2 gauge theories realized by intersecting M2-branes ending on N M5-branes wrapping a Riemann surface. We conjecture and provide evidence for an explicit equivalence between the squashed four-sphere partition function of these intersecting defects and correlation functions in Liouville/Toda CFT with the insertion of arbitrary degenerate vertex operators, which are labeled by representations of SU(N).

74 pages, one-column version of the version published in 2017

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Cited by in corpus (20)

• Central Charges of 2d Superconformal Defects
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• A slow review of the AGT correspondence
• Surface defects and instanton-vortex interaction
• Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
• Riemann-Hilbert correspondence and blown up surface defects
• Wilson Surface Central Charge from Holographic Entanglement Entropy
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• 3d Mirror Symmetry from S-duality
• Conformal Bootstrap near the edge
• Vertex Algebras at the Corner
• Surface defects, flavored modular differential equations and modularity
• Intersecting Defects and Supergroup Gauge Theory
• Bootstrapping the $S^5$ partition function
• Vortex-Strings in N=2 SQCD and Bulk-String Decoupling
• Seiberg-Witten geometry of four-dimensional N=2 SO-USp quiver gauge theories, I
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Deconstructing Defects
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Intersecting Surface defects and 3d Superconformal indices