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首页> 外文期刊>Physical review, D >Supersymmetric electric-magnetic duality in D=3+3 and D=5+5 dimensions as foundation of self-dual supersymmetric Yang-Mills theory
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Supersymmetric electric-magnetic duality in D=3+3 and D=5+5 dimensions as foundation of self-dual supersymmetric Yang-Mills theory

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摘要

We present electric-magnetic (EM)-duality formulations for non-Abelian gauge groups with N = 1 supersymmetry in D = 3 + 3 and 5 + 5 space-time dimensions. We show that these systems generate self-dual N = 1 supersymmetric Yang-Mills (SDSYM) theory in D = 2 + 2. For a N = 2 supersymmetric EM-dual system in D = 3 + 3, we have the Yang-Mills multiplet (A(mu)(I), lambda(I)(A)) and a Hodge-dual multiplet (B-mu upsilon rho(I), chi(I)(A)), with an auxiliary tensors C-mu upsilon rho sigma(I) and K-mu upsilon. Here, I is the adjoint index, while A is for the doublet of Sp(1). The EM-duality conditions are F mu upsilon I = (1/4!)epsilon(rho sigma tau lambda)(mu upsilon)G(rho sigma tau lambda)(I) with its superpartner duality condition lambda(I)(A) = -chi(I)(A). Upon appropriate dimensional reduction, this system generates SDSYM in D = 2 + 2. This system is further generalized to D = 5 + 5 with the EM-duality condition F-mu upsilon(I) = (1/8!)epsilon(rho 1...)(mu upsilon)rho 8G(rho 1...rho 8)(I) with its superpartner condition lambda(I) = -chi(I). Upon appropriate dimensional reduction, this theory also generates SDSYM in D = 2 + 2. As long as we maintain Lorentz covariance, D = 5 + 5 dimensions seems to be the maximal space-time dimensions that generate SDSYM in D = 2 + 2. Namely, EM-dual system in D = 5 + 5 serves as the Master Theory of all supersymmetric integrable models in dimensions 1 <= D <= 3.

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