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• W3000553600 abstract "Unlike the mathcal{R}^4 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:msup><mml:mstyle mathvariant=script><mml:mi>ℛ</mml:mi></mml:mstyle><mml:mn>4</mml:mn></mml:msup></mml:math> and nabla^4mathcal{R}^4 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:msup><mml:mi>∇</mml:mi><mml:mn>4</mml:mn></mml:msup><mml:msup><mml:mstyle mathvariant=script><mml:mi>ℛ</mml:mi></mml:mstyle><mml:mn>4</mml:mn></mml:msup></mml:mrow></mml:math> couplings, whose coefficients are Langlands–Eisenstein series of the U-duality group, the coefficient mathcal{E}^{(d)}_{(0,1)} <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:msubsup><mml:mstyle mathvariant=script><mml:mi>ℰ</mml:mi></mml:mstyle><mml:mrow><mml:mo stretchy=false form=prefix>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=false form=postfix>)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=false form=prefix>(</mml:mo><mml:mi>d</mml:mi><mml:mo stretchy=false form=postfix>)</mml:mo></mml:mrow></mml:msubsup></mml:math> of the nabla^6mathcal{R}^4 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:msup><mml:mi>∇</mml:mi><mml:mn>6</mml:mn></mml:msup><mml:msup><mml:mstyle mathvariant=script><mml:mi>ℛ</mml:mi></mml:mstyle><mml:mn>4</mml:mn></mml:msup></mml:mrow></mml:math> interaction in the low-energy effective action of type II strings compactified on a torus T^d <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:msup><mml:mi>T</mml:mi><mml:mi>d</mml:mi></mml:msup></mml:math> belongs to a more general class of automorphic functions, which satisfy Poisson rather than Laplace-type equations. In earlier work [1], 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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>d</mml:mi></mml:math> . 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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math> , the result is shown to coincide with an alternative proposal [2] 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." @default.
• W3000553600 created "2020-01-23" @default.
• W3000553600 creator A5016715903 @default.
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• W3000553600 date "2020-04-08" @default.
• W3000553600 modified "2023-10-14" @default.
• W3000553600 title "$1/8$-BPS couplings and exceptional automorphic functions" @default.
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• W3000553600 doi "https://doi.org/10.21468/scipostphys.8.4.054" @default.
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