Extrinsic geometry of strings and W-gravities

Sotkov, G. M.; Stanishkov, M.; Zhu, Chenchen

doi:10.1016/0550-3213(91)90148-q

Cited by 31 publications

(14 citation statements)

References 13 publications

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“…Further argument with currents and a gauge fixing leaves T zz unfixed and the condition h √ g = 1 (or any constant) then singles out a certain class of surfaces (cf. also [46,47] where light cone gauge is used). In the conformal gauge √ g = exp(ξ) where ξ is the Liouville mode.…”

Section: Conformal Immersionsmentioning

confidence: 99%

Generalized Weierstrass-Enneper Inducing, Conformal Immersions, and Gravity

Carroll

Konopelchenko

1996

Int. J. Mod. Phys. A

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Basic quantities related to 2D gravity. such as Polyakov extrinsic action, Nambu-Goto action, geometrical action and the Euler characteristic, are studied using generalized Weierstrass-Enneper (GWE) inducing of surfaces in R3. Connection of the GWE inducing with conformal immersion is made and various aspects of the theory are shown to be invariant under the modified Veselov-Novikov hierarchy of flows. The geometry of [Formula: see text] surfaces (h ~ mean curvature) is shown to be connected with the dynamics of infinite- and finite-dimensional integrable systems. Connections with Liouville-Beltrami gravity are indicated.

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Section: Conformal Immersionsmentioning

confidence: 99%

Generalized Weierstrass-Enneper Inducing, Conformal Immersions, and Gravity

Carroll

Konopelchenko

1996

Int. J. Mod. Phys. A

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“…A simple way to see why one has doubling of the Virasaro algebra in R 4 is to observe that G 2,4 ≃ CP 1 ⊗ CP 1 , while G 2,3 ≃ CP 1 . For surfaces immersed in R n (n > 4) not much is known although it is expected that one would find W-gravities in certain type of surfaces [6].…”

Section: Introductionmentioning

confidence: 99%

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

Viswanathan¹,

Parthasarathy²

1997

Zeitschrift Für Naturforschung A

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In the description of the extrinsic geometry of the string world sheet regarded as a conformal immersion of a 2-d surface in R 3 , it was previously shown that, restricting to surfaces with h √ g = 1, where h is the mean scalar curvature and g 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 z-sector, has SL(2, C) conserved currents in thē z-sector. This allows us to quantize this theory in thez-sector along the lines of the WZNW model. The quantum theory on h √ g = 1 surfaces in R 3 is shown to be in the same universality class as the intrinsic 2-d gravity theory.3

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“…One can find an appropriate``gauge transformation'' that maps the DS gauge in a gauge where all W s are primary fields (see [25,Sect. 4] for the A 3 -case).…”

Section: N+1 -Algebrasmentioning

confidence: 99%