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Structure constants of heavy operators in ABJM/ABJ Theory

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arxiv 1909.03215 v1 pith:RZTJFDHG submitted 2019-09-07 hep-th

Structure constants of heavy operators in ABJM/ABJ Theory

classification hep-th
keywords operatorstheoryabjmcorrelationeffectivefunctionsintegralrepresentation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Efficient and powerful approaches to the computation of correlation functions involving determinant, sub-determinant and permanent operators, as well as traces, have recently been developed in the setting of ${\cal N}=4$ super Yang-Mills theory. In this article we show that they can be extended to ABJM and ABJ theory. After making use of a novel identity which follows from character orthogonality, an integral representation of certain projection operators used to define Schur polynomials is given. This integral representation provides an effective description of the correlation functions of interest. The resulting effective descriptions have ${1\over N}$ as the loop counting parameter, strongly suggesting their relevance for holography.

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