1993/10/18 by R. Parthasarathy, Parthasarathy, R., K. S. Viswanathan +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9310107
V5A 1S6,26pages, LaTeX, IMSc/93-44 and SFU.HEP.109/1993
arxiv created 1993/10/18 · arxiv updated 2009/11/30
The immersion of the string world sheet, regarded as a Riemann surface, in R3 and R4 is described by the generalized Gauss map. When the Gauss map is harmonic or equivalently for surfaces of constant mean curvature, we obtain Hitchin's self-dual equations, by using SO(3) and SO(4) gauge fields constructed in our earlier studies. This complements our earlier result that h\surd g = 1 surfaces exhibit Virasaro symmetry. The self-dual system so obtained is compared with self-dual Chern-Simons system and a generalized Liouville equation involving extrinsic geometry is obtained. The immersion in Rn, n>4 is described by the generalized Gauss map. It is shown that when the Gauss map is harmonic, the mean curvature of the immersed surface is constant. SO(n) gauge fields are constructed from the geometry of the surface and expressed in terms of the Gauss map. It is found Hitchin's self- duality relations for the gauge group SO(2)× SO(n-2).