The chiral superstring Siegel form in degree two is a lift

Cris Poor; David S. Yuen

doi:10.4134/JKMS.2012.49.2.293

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2012; 49(2): 293-314

Printed March 1, 2012

https://doi.org/10.4134/JKMS.2012.49.2.293

The chiral superstring Siegel form in degree two is a lift

Cris Poor and David S. Yuen

Fordham University, Lake Forest College

Abstract

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Abstract

We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index $t/2$ over the theta group $\Gamma_1(1,2)$ to Siegel modular cusp forms over certain subgroups $\Gamma^{\rm para}(t;1,2)$ of paramodular groups. The theta group lift given here is a modification of the Gritsenko lift.

Keywords: Siegel modular form, Jacobi form, chiral superstring measure

MSC numbers: Primary 11F46, 11F50; Secondary 81T30