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1/8-BPS Couplings and Exceptional Automorphic Functions

Bossard, G., Kleinschmidt, A., & Pioline, B. (2020). 1/8-BPS Couplings and Exceptional Automorphic Functions. SciPost Physics, 8(4): 054. doi:10.21468/SciPostPhys.8.4.054.

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Creators:
Bossard, Guillaume, Author
Kleinschmidt, Axel1, Author
Pioline, Boris, Author
Affiliations:
1Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014

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Free keywords: High Energy Physics - Theory, hep-th
Abstract: Unlike the $\mathcal{R}^4$ and $\nabla^4\mathcal{R}^4$ couplings, whose coefficients are Langlands-Eisenstein series of the U-duality group, the coefficient $\mathcal{E}_{(0,1)}^{(d)}$ of the $\nabla^6\mathcal{R}^4$ interaction in the low-energy effective action of type II strings compactified on a torus $T^d$ belongs to a more general class of automorphic functions, which satisfy Poisson rather than Laplace-type equations. In earlier work, it was proposed that the exact coefficient is given by a two-loop integral in exceptional field theory, with the full spectrum of mutually 1/2-BPS states running in the loops, up to the addition of a particular Langlands-Eisenstein series. Here we compute the weak coupling and large radius expansions of these automorphic functions for any $d$. We find perfect agreement with perturbative string theory up to genus three, along with non-perturbative corrections which have the expected form for 1/8-BPS instantons and bound states of 1/2-BPS instantons and anti-instantons. The additional Langlands-Eisenstein series arises from a subtle cancellation between the two-loop amplitude with 1/4-BPS states running in the loops, and the three-loop amplitude with mutually 1/2-BPS states in the loops. For $d=4$, the result is shown to coincide with an alternative proposal in terms of a covariantised genus-two string amplitude, due to interesting identities between the Kawazumi-Zhang invariant of genus-two curves and its tropical limit, and between double lattice sums for the particle and string multiplets, which may be of independent mathematical interest.

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Dates: 2020-01-152020
Publication Status: Published in print
Pages: 121 pages
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Identifiers: arXiv: 2001.05562
URI: http://arxiv.org/abs/2001.05562
DOI: 10.21468/SciPostPhys.8.4.054
Degree: -

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Title: SciPost Physics
Source Genre: Journal
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Pages: - Volume / Issue: 8 (4) Sequence Number: 054 Start / End Page: - Identifier: -