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Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement

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arxiv 1308.2926 v2 pith:OKDBZJQ5 submitted 2013-08-13 hep-th cond-mat.str-elmath.QA

Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement

Anton Kapustin , Ryan Thorngren This is my paper
classification hep-th cond-mat.str-elmath.QA
keywords theorytheta-anglesgaugediscretefieldgrouplatticequantized
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group (the magnetic gauge group). We show that possible theta-angles in such a theory are quantized and labeled by quadratic functions on the magnetic gauge group. When the theta-angles vanish, the theory is dual to an ordinary topological gauge theory, but in general it is not isomorphic to it. We also explain how to couple a lattice Yang-Mills theory to a TQFT of this kind so that the 't Hooft flux is well-defined, and quantized values of the theta-angles are allowed. The quantized theta-angles include the discrete theta-angles recently identified by Aharony, Seiberg and Tachikawa.

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