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The matrix regularization for Riemann surfaces with magnetic fluxes

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arxiv 2002.02993 v3 pith:QXG5P5OF submitted 2020-02-07 hep-th

Hiroyuki Adachi , Goro Ishiki , Takaki Matsumoto , Kaishu Saito This is my paper · ORCID
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keywords matrixregularizationfieldsdiscussmagneticmatricesrectangularriemann
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We consider the matrix regularization of fields on a Riemann surface which couple to gauge fields with a nonvanishing magnetic flux. We show that such fields are described as rectangular matrices in the matrix regularization. We construct the matrix regularization explicitly for the case of the sphere and torus based on the Berezin-Toeplitz quantization, and also discuss a possible generalization to cases with higher genera. We also discuss the matrix version of the Laplacian acting on the rectangular matrices.

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    The quantum fluctuation spectrum of the 1/2-BPS ABJM domain wall is diagonalized and shown to organize into supersymmetric multiplets with conformal dimensions differing by 1/2.

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