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Eisenstein Series in String Theory [PDF]

Classical and Quantum Gravity, 1999
We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only.
Antoniadis I, Bachas C, Berkovits N, Berkovits N, Berkovits N, Boris Pioline, Elitzur S, Giveon A, Green M B, Green M B, Green M B, Gregori A, Harish-Chandra, Harvey J A, Hull C M, Kehagias A, Kiritsis E, Kiritsis E, Kiritsis E, Kiritsis E, Kiritsis E, Niels A Obers, Obers N A, Obers N A, Obers N A, Obers N A, Ooguri H, Paban S, Paban S, Pioline B, Townsend P K, Witten E   +31 more
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Higher d Eisenstein series and a duality-invariant distance measure [PDF]

Journal of High Energy Physics
The Petersson inner product is a natural inner product on the space of modular invariant functions. We derive a formula, written as a convergent sum over elementary functions, for the inner product E s (G, B) of the real analytic Eisenstein series $${E}_{
Nathan Benjamin, A. Liam Fitzpatrick
doaj   +2 more sources

Eisenstein Series and String Thresholds [PDF]

Communications in Mathematical Physics, 1998
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 $Sl(d,Z)$, $
Peixoto, M. M., Rocha, A. C., Sutherland, S., Veerman, J. J. P.   +3 more
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On a formula of spin sums, Eisenstein-Kronecker series in higher genus Riemann surfaces

Nuclear Physics B, 2023
We discuss a decomposition formula of simple products of fermion correlation functions with cyclic constrains and its applications to spin sums of super string amplitudes.Based on some facts which are noted or derived in this paper, we propose a ...
A.G. Tsuchiya
doaj   +2 more sources

The global Gan-Gross-Prasad conjecture for unitary groups. II. From Eisenstein series to Bessel periods

Forum of Mathematics, Pi
We state and prove an extension of the global Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture to the case of some Eisenstein series on unitary groups $U_n\times U_{n+1}$ .
Raphaël Beuzart-Plessis, Pierre-Henri Chaudouard   +1 more
doaj   +2 more sources

Eisenstein series [PDF]

, 2010
Shahidi, Freydoon
openalex   +2 more sources

Poincaré series for modular graph forms at depth two. Part II. Iterated integrals of cusp forms

Journal of High Energy Physics, 2022
We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincaré series in a companion paper. The source term of the Laplace equation is a product of (derivatives of)
Daniele Dorigoni, Axel Kleinschmidt, Oliver Schlotterer   +2 more
doaj   +1 more source

Cusps, Kleinian groups, and Eisenstein series

Forum of Mathematics, Sigma, 2023
We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group $\Gamma
Beibei Liu, Shi Wang
doaj   +1 more source

Poincaré series for modular graph forms at depth two. Part I. Seeds and Laplace systems

Journal of High Energy Physics, 2022
We derive new Poincaré-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus one.
Daniele Dorigoni, Axel Kleinschmidt, Oliver Schlotterer   +2 more
doaj   +1 more source

Elliptic modular graph forms. Part I. Identities and generating series

Journal of High Energy Physics, 2021
Elliptic modular graph functions and forms (eMGFs) are defined for arbitrary graphs as natural generalizations of modular graph functions and forms obtained by including the character of an Abelian group in their Kronecker-Eisenstein series. The simplest
Eric D’Hoker, Axel Kleinschmidt, Oliver Schlotterer   +2 more
doaj   +1 more source