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On classification ofN=2 supersymmetric theories

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Abstract

We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetricN=2 conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A-D-E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.

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Authors and Affiliations

  1. International School for Advanced Studies, SISSA-ISAS, Trieste, Italy

    Sergio Cecotti

  2. I.N.F.N., sez. di Trieste, Trieste, Italy

    Sergio Cecotti

  3. Lyman Laboratory of Physics, Harvard University, 02138, Cambridge, MA, USA

    Cumrun Vafa

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  1. Sergio Cecotti
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  2. Cumrun Vafa
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Communicated by S.-T. Yau

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Cecotti, S., Vafa, C. On classification ofN=2 supersymmetric theories. Commun.Math. Phys. 158, 569–644 (1993). https://doi.org/10.1007/BF02096804

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