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The bosonic string measure at two and three loops and symplectic transformations of the volume form

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Abstract

Symplectic modular invariance of the string integral has been verified at genus 2 and 3 using the period matrix coordinatization of moduli space. A calculation of the transformation of the product of holomorphic coordinates Π i⩽j dτ ij shows that an extra phase arises together with the factor associated with a specific modular weight; the phase is cancelled in the transformation of the entire volume element including the complex conjugate. An argument is given for modular invariance of the reggeon measure at genus 12.

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  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, CB3 9EW, Cambridge, U.K.

    Simon Davis

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  1. Simon Davis
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Davis, S. The bosonic string measure at two and three loops and symplectic transformations of the volume form. Lett Math Phys 34, 407–413 (1995). https://doi.org/10.1007/BF00750072

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