Harmonic Gauss Maps and Self-Dual Equations in String Theory

1994/11/06 by R. Parthasarathy, Parthasarathy, R., K. S. Viswanathan +1
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9411043

24 pages

arxiv created 1994/11/06 · arxiv updated 2009/11/30

Abstract

The string world sheet, regarded as Riemann surface, in background R³ and R⁴ is described by the generalised Gauss map. When the Gauss map is harmonic or equivalently for surfaces of constant mean scalar curvature, we obtain an Abelian self-dual system, using SO(3) and SO(4) gauge fields constructed in our earlier studies. This compliments 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. \vspace0.2cm The world sheet in background Rⁿ, n>4 is described by the generalized Gauss map. It is first shown that when the Gauss map is harmonic, the scalar mean curvature is constant. SO(n) gauge fields are constructed from the geometry of the surface and expressed in terms of the Gauss map. It is shown that the harmonic map satisfies a non-Abelian self-dual system of equations for the gauge group SO(2)× SO(n-2).

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