Open Access
VOL. 2005 | 2007 Complex geometry and supergeometry
Eric D'Hoker, D. H. Phong

Editor(s) David Jerison, Barry Mazur, Tomasz Mrowka, Wilfried Schmid, Richard P. Stanley, Shing-Tung Yau

Current Developments in Mathematics, 2007: 1-40 (2007)


Complex geometry and supergeometry are closely entertwined in superstring perturbation theory, since perturbative superstring amplitudes are formulated in terms of supergeometry, and yet should reduce to integrals of holomorphic forms on the moduli space of punctured Riemann surfaces. The presence of supermoduli has been a major obstacle for a long time in carrying out this program. Recently, this obstacle has been overcome at genus 2, which is the first loop order where it appears in all amplitudes. An important ingredient is a better understanding of the relation between geometry and supergeometry, and between holomorphicity and superholomorphicity. This talk provides a survey of these developments and a brief discussion of the directions for further investigation.


Published: 1 January 2007
First available in Project Euclid: 10 October 2008

zbMATH: 1182.81059
MathSciNet: MR2459296

Rights: Copyright © 2007 International Press of Boston

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