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Cancellation of divergences up to three loops in exceptional field theory

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Guillaume Bossard, Axel Kleinschmidt

High Energy Physics - Theory · Submitted 7 Dec 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim These sums can be rewritten as Eisenstein series that solve the homogeneous differential equations that supersymmetry implies for the $\nabla^6 R^4$ coupling.

how it is stated · asserted 0.98 read the record →

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arXiv ID1712.02793 (version 1)
Pith IDJPXQSNQV, Pith's permanent record of this paper and its review
CitationAxel Kleinschmidt, Guillaume Bossard. "Cancellation of divergences up to three loops in exceptional field theory." arXiv:1712.02793 (2017). https://pith.science/paper/JPXQSNQV
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,301 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We consider the tetrahedral three-loop diagram in $E_d$ exceptional field theory evaluated as a scalar diagram for four external gravitons. At lowest order in momenta, this diagram contributes to the $\nabla^6 R^4$ term in the low-energy effective action for M-theory. We evaluate explicitly the sums over the discrete exceptional field theory loop momenta that become sums over 1/2-BPS states in the compact exceptional space. These sums can be rewritten as Eisenstein series that solve the homogeneous differential equations that supersymmetry implies for the $\nabla^6 R^4$ coupling. We also show how our results, even though sums over 1/2-BPS states, are consistent with expected 1/4-BPS contributions to the couplings.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider the tetrahedral three-loop diagram in $E_d$ exceptional field theory evaluated as a scalar diagram for four external gravitons. contribution 0.88 0.81 0.05 asserted 0.92
s1 At lowest order in momenta, this diagram contributes to the $\nabla^6 R^4$ term in the low-energy effective action for M-theory. background 0.67 0.24 0.10 asserted 0.99
s2 We evaluate explicitly the sums over the discrete exceptional field theory loop momenta that become sums over 1/2-BPS states in the compact exceptional space. method 0.70 0.94 0.08 asserted 1.00
s3 These sums can be rewritten as Eisenstein series that solve the homogeneous differential equations that supersymmetry implies for the $\nabla^6 R^4$ coupling. result 0.77 0.87 0.39 asserted 0.98
s4 We also show how our results, even though sums over 1/2-BPS states, are consistent with expected 1/4-BPS contributions to the couplings. interpretation 0.54 0.89 0.15 asserted 0.61

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider the tetrahedral three-loop diagram in $E_d$ exceptional field theory evaluated as a scalar diagram for four external gravitons. At lowest order in momenta, this diagram contributes to the $\nabla^6 R^4$ term in the low-energy effective action for M-theory. We evaluate explicitly the sums over the discrete exceptional field theory loop momenta that become sums over 1/2-BPS states in the compact exceptional space. These sums can be rewritten as Eisenstein series that solve the homogeneous differential equations that supersymmetry implies for the $\nabla^6 R^4$ coupling. We also show how our results, even though sums over 1/2-BPS states, are consistent with expected 1/4-BPS contributions to the couplings.

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References
How the literature uses it

12 arXiv papers cite this in 29 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 21 sentences without a confident label

Uses its method or tool 1 paper
  • Implementing an infrared cut-off $μ$ as in [ref] , one obtains [The term $16 π^-ϵ Γ(ϵ) L^2ϵ$ has not been derived but must be there for cancelling the first order pole.] ℐ_2,ϵ + π/3 π^-ϵ Γ(ϵ) μ^-2ϵ ^2_00, ϵ + π^2/3 ( π^-2ϵ Γ(ϵ)^2 + 16 π^-ϵ Γ(ϵ) + 𝒪(ϵ^0) ) μ^-4ϵ ϵ→0∼ 4 π^2/27 log(g_8)^2 + 2π/9 log(g_8) ( 2ζ(2)/g_8^2 + 4 ζ(4) ( E_ Λ_1^0.7$SL(2)$(U)+E_ Λ_1^0.7$SL(2)$(T) ) + π/3 )+ … + 4π^2/3 log( 2πμ)^2 - 2π/3 log(2πμ) ( 2ζ(2)/g_8^2 + 4 ζ(4) ( E_ Λ_1^0.7$SL(2)$(U)+E_ Λ_1^0.7$SL(2)$(T) ) + 4π/3 log(g_8) + π/3 )

    1/8-BPS Couplings and Exceptional Automorphic Functions · Divergences and threshold terms in the weak-coupling limit · 0.86

Cites it as support 1 paper
  • Recent computations suggest that this is indeed the case [ref] .

    Accelerating Solitons · Introduction and Motivation · 0.98

Cites it as background 3 papers

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