AGT/Z${}_2$

Abstract

We relate Liouville/Toda CFT correlators on Riemann surfaces with boundaries and cross-cap states to supersymmetric observables in four-dimensional N=2 gauge theories. Our construction naturally involves four-dimensional theories with fields defined on different Z${}_2$ quotients of the sphere (hemisphere and projective space) but nevertheless interacting with each other. The six-dimensional origin is a Z${}_2$ quotient of the setup giving rise to the usual AGT correspondence. To test the correspondence, we work out the RP${}^4$ partition function of four-dimensional N=2 theories by combining a 3d lens space and a 4d hemisphere partition functions. The same technique reproduces known RP${}^2$ partition functions in a form that lets us easily check two-dimensional Seiberg-like dualities on this nonorientable space. As a bonus we work out boundary and cross-cap wavefunctions in Toda CFT.

56 pages. v2: Clarify discrete theta angle. v3: Published in JHEP; extra references. v4: Minor sign fix; extra references

References in corpus (10)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Solving the Schwarzian via the Conformal Bootstrap
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Witten Index and Wall Crossing
• Instanton counting with a surface operator and the chain-saw quiver
• AGT on the S-duality Wall
• A CFT Perspective on Gravitational Dressing and Bulk Locality
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Exact Results in Quiver Quantum Mechanics and BPS Bound State Counting
• Boundary conditions in Toda theories and minimal models

Cited by in corpus (11)

• The Schwarzian Theory - Origins
• A universal Schwarzian sector in two-dimensional conformal field theories
• Shockwave S-matrix from Schwarzian Quantum Mechanics
• Defects in Jackiw-Teitelboim Quantum Gravity
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• A slow review of the AGT correspondence
• Aspects of CFTs on Real Projective Space
• Surface defects, flavored modular differential equations and modularity
• Hartle-Hawking state and its factorization in 3d gravity
• Gauge theories on compact toric manifolds