3,820 research outputs found

    A Conformal Field Theory of Extrinsic Geometry of 2-d Surfaces

    Get PDF
    In the description of the extrinsic geometry of the string world sheet regarded as a conformal immersion of a 2-d surface in R3R^3, it was previously shown that, restricting to surfaces with h√g = 1h\surd{g}\ =\ 1, where hh is the mean scalar curvature and gg is the determinant of the induced metric on the surface, leads to Virasaro symmetry. An explicit form of the effective action on such surfaces is constructed in this article which is the extrinsic curvature analog of the WZNW action. This action turns out to be the gauge invariant combination of the actions encountered in 2-d intrinsic gravity theory in light-cone gauge and the geometric action appearing in the quantization of the Virasaro group. This action, besides exhibiting Virasaro symmetry in zz-sector, has SL(2,C)SL(2,C) conserved currents in the zˉ\bar{z}-sector. This allows us to quantize this theory in the zˉ\bar{z}-sector along the lines of the WZNW model. The quantum theory on h√g = 1h\surd{g}\ =\ 1 surfaces in R3 R^3 is shown to be in the same universality class as the intrinsic 2-d gravity theory.Comment: 30 page
    • …
    corecore