07-151 D. N. Diep, D. V. Duc, H.V. Tan, N. A. Viet
Convolution-Wedge Product of Fields in Anti-Symmetric Metric Regime Is Defined Through Electric-Magnetic Duality and Mirror Symmetry (23K, LaTeX 2e) Jun 24, 07
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Abstract. In this paper we use the pair of electric-magnetic (or GNO, or Langlands) duality groups \$G=Sp(1)\$ and \${}^LG=SO(3)\$ and the T-transformation in mirror symmetry (or the S-duality, or the Fourier-Mukai transformation) to define the wedge product of fields: first by using gauge transformation, we reduce the fields with values in \$Lie G=Sp(1)\$ to the fields with values in the Lie algebra of the maximal torus \$\mathfrak t \subset Lie G=Sp(1)\$. Next we use the Fourier-Mukai transformation of fields to have the images as fields with values in the Lie algebra of the Langlands dual torus \${}^L\mathfrak t\$ in \$Lie {}^LG= SO(3)\$. The desired wedge product of two fields is defined as the pre-image of the ordinary wedge product of images with values in \${}^L\mathfrak t \subset SO(3)\$.

Files: 07-151.src( 07-151.keywords , wedgeprod2.tex )