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)

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 ${}^L\mathfrak t \subset SO(3)$.