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From 3d dualities to 2d free field correlators and back
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We investigate the relation between 3d N=2 theories and 2d free field correlators or Dotsenko-Fateev (DF) integrals for Liouville CFT. We show that the S^2xS^1 partition functions of some known 3d Seiberg-like dualities reduce, in a suitable 2d limit, to known basic duality identities for DF correlators. These identities are applied in a variety of contexts in CFT, as for example in the derivation of the DOZZ 3-point function. Reversing the logic, we can try to guess new 3d IR dualities which reduce to more intricate duality relations for the DF correlators. For example, we show that a recently proposed duality relating the U(N) theory with one flavor and one adjoint to a WZ model can be regarded as the 3d ancestor of the evaluation formula for the DF integral representation of the 3-point correlator. We are also able to interpret the analytic continuation in the number of screening charges, which is performed on the CFT side to reconstruct the DOZZ 3-point function, as the geometric transition relating the 3d U(N) theory to the 5d T_2 theory.
Forward citations
Cited by 5 Pith papers
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Cardy limit of the 3d superconformal index
In the Cardy limit the 3d superconformal index obeys Z ~ beta^{-#} on the first sheet and Z ~ e^{#/beta} on the second, with gauge-enhancing saddles screened for non-chiral theories.
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Rank $Q$ E-string on a torus with flux
A proposed 4d quiver theory E[USp(2Q)] is claimed to encode torus compactifications of rank-Q E-string theory, with emergent USp(2Q)xUSp(2Q)xU(1)^2 symmetry supported by index and anomaly checks.
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Boundary lines and Askey-Wilson type moments
Wilson line defect half-indices for 3d N=2 theories with confining boundaries are exactly Askey-Wilson type moments, obtained via dual vortex defects and effective spin shifts in the index computation.
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Six Easy Pieces: interplays among dualities in 4d, 3d and 2d
Baryon-deformed SU(N) gauge theory with an antisymmetric tensor is shown to flow to a free magnetic phase, and its reductions yield new 3d SU/SO and 2d SU/USp dualities.
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Quantum vortices, M2-branes and black holes
The Cardy-limit index for M2-brane theories gives a large-N free energy scaling as N^(3/2) that, after a Legendre transform, matches the entropy of BPS black holes in AdS4 x S7.
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