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2016

Twisted compactifications of 3d N = 4 theories and conformal blocks

Gaiotto, Davide

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Three-dimensional N = 4 supersymmetric quantum field theories admit two topological twists, the Rozansky-Witten twist and its mirror.

Either twist can be used to define a supersymmetric compactification on a Riemann surface and a corre- sponding space of supersymmetric ground states.
These spaces of ground states can play an interesting role in the Geometric Langlands program.
We propose a description of these spaces as conformal blocks for certain non-unitary Vertex Operator Algebras and test our conjecture in some important examples.

Twisted compactifications of 3d N = 4 theories and conformal blocks · Around

Built on

S. Cecotti and C. Vafa, Topological antitopological fusion , Nucl. Phys. B367
1991
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F. Lesage, P. Mathieu, J. Rasmussen and H. Saleur, The su (hat)(2)(-1/2) WZW model and the beta gamma system , Nucl. Phys. B647
2002
Earlier work this paper cites.

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Then

D. Gaiotto and E. Witten, S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory , Adv. Theor. Math. Phys. 13
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2009
Later among the works it cites.
S. Cecotti, D. Gaiotto and C. Vafa, t t ∗ tt^{*} geometry in 3 and 4 dimensions , JHEP 05
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2014
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