Exact ∇4ℛ4 couplings and helicity supertraces

Bossard, Guillaume; Pioline, Boris

doi:10.1007/jhep01(2017)050

Cited by 14 publications

(43 citation statements)

References 57 publications

(209 reference statements)

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“…The γ a matrices are integral valued in the canonical null basis associated to the even self-dual lattice II d,d with the normalisation {γ a , γ b } = η ab . As in [1,50], we shall split the theta series θ E d+1 Λ d+1 into contributions where the components (q i , χ i , N i ) along the graded decomposition (3.8) are gradually populated, such that the constraints can be solved explicitly. We shall refer to the gradually populated subsets of charges that arise in this way as 'layers'.…”

Section: Weak Coupling Limit Of the Particle Multiplet Lattice Summentioning

confidence: 99%

$1/8$-BPS couplings and exceptional automorphic functions

2020

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Unlike the R 4 and ∇ 4 R 4 couplings, whose coefficients are Langlands-Eisenstein series of the U-duality group, the coefficient E (d) (0,1) of the ∇ 6 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 [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. 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 [2] in terms of a covariantised genus-two string amplitude, due to interesting identities between the Kawazumi-Zhang invariant of genustwo 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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Section: Weak Coupling Limit Of the Particle Multiplet Lattice Summentioning

confidence: 99%

$1/8$-BPS couplings and exceptional automorphic functions

2020

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“…This partial resolution may be seen as an analogue of the resolution of the conifold singularity on the vector multiplet branch in type II strings compactified on a CY threefold times a circle, or equivalently on the hypermultiplet branch in the mirror description [32]. Singularities associated to generic vectors Q ∈ Λ r− 4,8 are not visible at any order in perturbation theory, and are associated to 'exotic' particles in D = 3 becoming massless [33,34].…”

Section: )mentioning

confidence: 99%

“…To study the behavior of (4.1) in the limit R 1, 8 it is useful to perform a Poisson resummation on m. For a lattice partition function Γ Λ p, q with no insertion, as in the scalar integral (4.1b), this gives…”

Section: O(p Q) → O(p − 1 Q − 1) For Even Self-dual Latticesmentioning

confidence: 99%

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Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

2017

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Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative scalar couplings of the form F (Φ) (∇Φ) 4 in a class of string vacua known as CHL Z N heterotic orbifolds with N prime, generalizing our previous work which dealt with the case of heterotic string on T 6 . We derive the Ward identities that F (Φ) must satisfy, and check that our formula obeys them. We analyze the weak coupling expansion of F (Φ), and show that it reproduces the correct treelevel and one-loop contributions, plus an infinite series of non-perturbative contributions. Similarly, the large radius expansion reproduces the exact F 4 coupling in four dimensions, including both supersymmetric invariants, plus infinite series of instanton corrections from half-BPS dyons winding around the large circle, and from Taub-NUT instantons. The summation measure for dyonic instantons agrees with the helicity supertrace for half-BPS dyons in 4 dimensions in all charge sectors. In the process we clarify several subtleties about CHL models in D = 4 and D = 3, in particular we obtain the exact helicity supertraces for 1/2-BPS dyonic states in all duality orbits.

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“…The Fourier coefficients of such automorphic forms therefore have a direct physical interpretation: the constant terms encode perturbative quantum corrections, while the non-constant terms correspond to non-perturbative, instanton, effects [FK12,FKP14,BV14,BV15a,BV15b,BCHP17b,BP17,BCHP17a]. For a recent book on automorphic representations and the connection with string theory, see [FGKP18].…”

Section: Thenmentioning

confidence: 99%

Fourier coefficients attached to small automorphic representations of SLn(A)

Ahlén

Gustafsson

Kleinschmidt

et al. 2018

Journal of Number Theory

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Abstract. We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of SLn(A) are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro-Shalika formula. In addition, we derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have potential applications for scattering amplitudes in string theory.

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Exact ∇4ℛ4 couplings and helicity supertraces

Cited by 14 publications

References 57 publications

$1/8$-BPS couplings and exceptional automorphic functions

$1/8$-BPS couplings and exceptional automorphic functions

Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

Fourier coefficients attached to small automorphic representations of SLn(A)

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