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Superfield theory and supermatrix model
Author(s) -
Park J.H.
Publication year - 2005
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200410220
Subject(s) - supermatrix , star product , superspace , commutative property , formalism (music) , superfield , lagrangian , duality (order theory) , mathematics , limit (mathematics) , noncommutative geometry , pure mathematics , functor , mathematical physics , theoretical physics , physics , algebra over a field , supersymmetry , mathematical analysis , musical , current algebra , visual arts , art , affine lie algebra
We show that any superfield theory can be reformulated as a supermatrix model. The claim is based on a formal argument, turning on a non‐commutativity on the superspace and taking a fine tuned commutative limit. Once the non‐commutativity is introduced on the superspace, superfield theories can be formulated in two equivalent ways, through the star product formalism and in terms of the supermatrices. We elaborate the duality between them by constructing the isomorphism explicitly and relating the super space integral of the star product Lagrangian to the supertrace of the supermatrix model Lagrangian. We show there exists an interesting fine tuned commutative limit where the duality can be still maintained. More detailed analysis can be found in [1].