Abstract
In this paper we describe how representation theory of groups can be used to shorten the derivation of two loop partition functions in string theory, giving an intrinsic description of modular forms appearing in the results of D’Hoker and Phong (Nucl Phys B639:129–181, 2002). Our method has the advantage of using only algebraic properties of modular functions and it can be extended to any genus g.
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D’Hoker E. and Phong D.H. (2002). Two-loop superstrings IV: the cosmological constant and modular forms. Nucl. Phys. B639: 129–181
Belavin A.A. and Knizhnik V.G. (1986). Algebraic geometry and the geometry of quantum strings. Phys. Lett. B168: 201–206
Belavin A.A., Knizhnik V., Morozov A. and Perelomov A. (1986). Two and three loop amplitudes in the bosonic string theory. JETP Lett. 43: 411
Moore G.W. (1986). Modular forms and two loop string physics. Phys. Lett. B176: 369
Morozov A. (1987). Explicit formulae for one, two, three and four loop string amplitudes. Phys. Lett. B184: 171
D’Hoker E. and Phong D.H. (2002). Two-loop superstrings I: main formulas. Phys. Lett. B529: 241–255
D’Hoker E. and Phong D.H. (2002). Two-loop superstrings II: the chiral measure on moduli space. Nucl. Phys. B636: 3–60
D’Hoker E. and Phong D.H. (2002). Two-loop superstrings III: Slice independence and absence of ambiguities. Nucl. Phys. B636: 61–79
D’Hoker E. and Phong D.H. (2005). Asyzygies, modular forms and the superstring measure I. Nucl. Phys. B710: 58–82
D’Hoker E. and Phong D.H. (2005). Asyzygies, modular forms and the superstring measure II. Nucl. Phys. B710: 83–116
Fay, J.D.: Theta Functions on Riemann Surfaces. In: Lecture Notes in Mathematics, vol. 352. Springer, Berlin (1973)
Mumford, D.: Tata Lectures on Theta, vol. II. Birkhäuser (1984)
Rauch, H.E., Farkas, H.M.: Theta Functions with Applications to Riemann Surfaces. The Williams & Wilkins Company, (1974)
D’Hoker, E., Phong, D.H.: Lectures on two-loop superstrings (Unpublished, 2002). hep-th/0211111
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This work was partially supported by INFN.
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Cacciatori, S.L., Dalla Piazza, F. Two Loop Superstring Amplitudes and S 6 Representations. Lett Math Phys 83, 127–138 (2008). https://doi.org/10.1007/s11005-007-0213-8
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DOI: https://doi.org/10.1007/s11005-007-0213-8