Eisenstein Series in String Theory
نویسندگان
چکیده
We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. The Eisenstein series are constructed using G(Z)-invariant mass formulae and are manifestly invariant modular functions on the symmetric space K\G(R) of noncompact type, with K the maximal compact subgroup of G(R). In particular, we show how Eisenstein series of the T-duality group SO(d, d, Z) can be used to represent oneand g-loop amplitudes in compactified string theory. We also obtain their non-perturbative extensions in terms of the Eisenstein series of the U-duality group Ed+1(d+1)(Z). PACS numbers: 11.25.-w;11.30.-j;2.20.Rt;2.30.Px ? Talk presented by N.O. at Strings ’99, Potsdam, Germany (July 19-24, 1999). Work supported in part by TMR networks ERBFMRXCT96-0045 and ERBFMRXCT96-0090. ∗ On leave of absence from LPTHE, Université Pierre et Marie Curie, PARIS VI and Université Denis Diderot, PARIS VII, Bôıte 126, Tour 16, 1er étage, 4 place Jussieu, F-75252 Paris CEDEX 05, FRANCE Eisenstein Series in String Theory 2
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متن کاملar X iv : h ep - t h / 99 03 11 3 v 3 1 0 D ec 1 99 9 NORDITA - 1999 / 18 HE NBI - HE -
We investigate the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. G(Z) may stand for any of the mapping class, T-duality and U-duality groups Sl(d, Z), SO(d, d, Z) or E d+1(d+1) (Z) respectively. Using G(Z)-invariant mass formulae, we construct invariant modular functions on the symmetric space K\G(...
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