Supersymmetric electric-magnetic duality in D=3+3 and D=5+5 dimensions as foundation of self-dual supersymmetric Yang-Mills theory

Hitoshi Nishino and Subhash Rajpoot
Phys. Rev. D 93, 105041 – Published 25 May 2016

Abstract

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 (AμI,λAI) and a Hodge-dual multiplet (BμνρI,χAI), with an auxiliary tensors CμνρσI and Kμν. Here, I is the adjoint index, while A is for the doublet of Sp(1). The EM-duality conditions are FμνI=(1/4!)εμνρστλGρστλI with its superpartner duality condition λAI=χAI. 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 FμνI=(1/8!)εμνρ1ρ8Gρ1ρ8I with its superpartner condition λI=χI. 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 1D3.

  • Received 16 November 2015

DOI:https://doi.org/10.1103/PhysRevD.93.105041

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Hitoshi Nishino* and Subhash Rajpoot

  • Department of Physics & Astronomy, California State University, 1250 Bellflower Boulevard, Long Beach, California 90840, USA

  • *h.nishino@csulb.edu
  • subhash.rajpoot@csulb.edu

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Vol. 93, Iss. 10 — 15 May 2016

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