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Solving a family of -like theories
We deform two-dimensional quantum field theories by antisymmetric
combinations of their conserved currents that generalize Smirnov and
Zamolodchikov's deformation. We obtain that energy levels on a
circle obey a transport equation analogous to the Burgers equation found in the
case. This equation relates charges at any value of the deformation
parameter to charges in the presence of a (generalized) Wilson line. We
determine the initial data and solve the transport equations for antisymmetric
combinations of flavor symmetry currents and the stress tensor starting from
conformal field theories. Among the theories we solve is a conformal field
theory deformed by and simultaneously. We check our
answer against results from AdS/CFT.Comment: 42 page
AGT/Z
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 quotients of the sphere (hemisphere and
projective space) but nevertheless interacting with each other. The
six-dimensional origin is a Z quotient of the setup giving rise to the
usual AGT correspondence. To test the correspondence, we work out the RP
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 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.Comment: 56 pages. v2: Clarify discrete theta angle. v3: Published in JHEP;
extra references. v4: Minor sign fix; extra reference
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