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arxiv 1408.0010 v2 pith:AKKJ7NWV submitted 2014-07-31 hep-th math-phmath.GTmath.MP

Towards U(N|M) knot invariant from ABJM theory

classification hep-th math-phmath.GTmath.MP
keywords characterexpectationmodelabjminvariantknottheoryvalue
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study U(N|M) character expectation value with the supermatrix Chern-Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives U(N|M) character expectation values in terms of U(1|1) averages for a particular type of character representations. This means that the U(1|1) character expectation value is a building block for all the U(N|M) averages, and in particular, by an appropriate limit, for the U(N) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern-Simons matrix model. We obtain the Rosso-Jones-type formula and the spectral curve for this case.

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