N=2 gauge theories on the hemisphere $H{S}^4$

Abstract

Using localization techniques, we compute the path integral of $N=2$ SUSY gauge theory coupled to matter on the hemisphere $H{S}^4$, with either Dirichlet or Neumann supersymmetric boundary conditions. The resulting quantities are wave-functions of the theory depending on the boundary data. The one-loop determinant are computed using $SO(4)$ harmonics basis. We solve kernel and co-kernel equations for the relevant differential operators arising from gauge and matter localizing actions. The second method utilizes full $SO(5)$ harmonics to reduce the computation to evaluating $Q_{SUSY}^2$ eigenvalues and its multiplicities. In the Dirichlet case, we show how to glue two wave-functions to get back the partition function of round $S^4$. We will also describe how to obtain the same results using $SO(5)$ harmonics basis.

47 pages, discussion on instanton corrections in section 6 revised, typos corrected, two references added

References in corpus (7)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Supersymmetric Gauge Theories on the Five-Sphere
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• Duality walls and defects in 5d N=1 theories
• Boundary F-maximization
• Factorising the 3D Topologically Twisted Index
• S-duality wall of SQCD from Toda braiding

Cited by in corpus (22)

• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• A slow review of the AGT correspondence
• Holographic and Localization Calculations of Boundary F for $\mathcal{N}=4$ SUSY Yang-Mills Theory
• Free energy and defect $C$-theorem in free scalar theory
• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
• Supersymmetric D3/D5 for massive defects on curved space
• Topological Correlators and Surface Defects from Equivariant Cohomology
• Supersymmetric indices on $I\times T^2$, elliptic genera and dualities with boundaries
• AGT/Z${}_2$
• Duality and Transport for Supersymmetric Graphene from the Hemisphere Partition Function
• Supersymmetric localization of refined chiral multiplets on topologically twisted $H^2\times S^1$
• Trinion Conformal Blocks from Topological strings
• Gluing I: Integrals and Symmetries
• Boundary Weyl anomaly of $\mathcal{N}=(2,2)$ superconformal models
• Supersymmetric Graphene on Squashed Hemisphere
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• From $\mathcal{N}=4$ Super-Yang-Mills on ${\mathbb{RP}}^4$ to bosonic Yang-Mills on ${\mathbb{RP}}^2$
• Solving $\mathcal{N}=4$ SYM BCFT matrix models at large $N$
• One-point functions for doubly-holographic BCFTs and backreacting defects