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Volume 11, Issue 2, May 2004, Pages 141 - 150
Geometrical Formulation of the Conformal Ward Identity
Authors
Mohamed Kachkachi
Corresponding Author
Mohamed Kachkachi
Received 20 December 2002, Accepted 22 May 2003, Available Online 1 May 2004.
- DOI
- 10.2991/jnmp.2004.11.2.1How to use a DOI?
- Abstract
In this paper we use deep ideas in complex geometry that proved to be very powerful in unveiling the Polyakov measure on the moduli space of Riemann surfaces and lead to obtain the partition function of perturbative string theory for 2, 3, 4 loops. Indeed a geometrical interpretation of the conformal Ward identity in two dimensional confomal field theory is proposed: the conformal anomaly is interpreted as a deformation of the complex structure of the basic Riemann surface. This point of view is in line with the modern trend of geometric quantizations that are based on deformations of classcal structures. Then, we solve the conformal Ward identity by using this geometrical formalism.
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- © 2006, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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Cite this article
TY - JOUR AU - Mohamed Kachkachi PY - 2004 DA - 2004/05/01 TI - Geometrical Formulation of the Conformal Ward Identity JO - Journal of Nonlinear Mathematical Physics SP - 141 EP - 150 VL - 11 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2004.11.2.1 DO - 10.2991/jnmp.2004.11.2.1 ID - Kachkachi2004 ER -