U-Duality and the compactified Gauss-Bonnet term

Bao, Ling; Bielecki, Johan; Cederwall, Martin; Nilsson, Bengt E. W.; Persson, Daniel

doi:10.1088/1126-6708/2008/07/048

Cited by 13 publications

(14 citation statements)

References 34 publications

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“…where we use R that is obtained by ( 43)-( 45), and √ −ĝ = e ξD ϕ √ −g = e (4α+β)ψ √ −g for D = 5. We can find exactly the same result by considering the rescaled curvature scalar in Einstein frame, which is once again given by 44,45…”

Section: The Reduced Actions From the Transformed Weyl−yang−kaluza−kl...supporting

confidence: 64%

“…Furthermore, the comparison between the invariants ( 30) and ( 57) causes us to introduce new interaction terms such as ψ 2 R, ψ 2 Dψ, and ψ 4 . Another way of obtaining the reduced Kretschmann scalar (57) is directly using the conformal transformation rule of the squaring curvature R µνλσ R µνλσ , which is expressed as (see, e.g., 44,45 )…”

Section: The Reduced Actions From the Transformed Weyl−yang−kaluza−kl...mentioning

confidence: 99%

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The five dimensional transformed Weyl$-$Yang$-$Kaluza$-$Klein theory of gravity

Kuyrukcu¹

2021

Preprint

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We study that the five dimensional theory is the transformed Weyl−Yang−Kaluza−Klein gravity. The dimensionally reduced equations of motion are derived by considering an alternative form of the master equation of the theory in the coordinate basis. The conformal transformation rules are applied for the invariants. We also discuss the possible specific cases and the new Lorentz force density term, in detail.

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Section: The Reduced Actions From the Transformed Weyl−yang−kaluza−kl...supporting

confidence: 64%

Section: The Reduced Actions From the Transformed Weyl−yang−kaluza−kl...mentioning

confidence: 99%

The five dimensional transformed Weyl$-$Yang$-$Kaluza$-$Klein theory of gravity

Kuyrukcu¹

2021

Preprint

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“…We further assume that a discrete subgroup SL(2, Z) of the four-dimensional Sduality (or, on the type IIB side, Ehlers symmetry), acting in the standard non-linear way on the complex parameter χ + ie −φ on the sliceχ = ψ = 0, is left unbroken by quantum corrections. As in earlier endeavours [48][49][50][51][52], it is difficult to justify this assumption rigorously, but the fact, demonstrated herein, that it leads to physically sensible results can be taken as support for this assumption. 9…”

Section: Rigid Calabi-yau Threefolds and The Picard Modular Groupmentioning

confidence: 71%

Instanton corrections to the universal hypermultiplet and automorphic forms on {$SU(2,1)$}

Nilsson

Bao

Persson

et al. 2010

Communications in Number Theory and Physics

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The hypermultiplet moduli space in Type IIA string theory compactified on a rigid Calabi-Yau threefold X , corresponding to the "universal hypermultiplet", is described at tree-level by the symmetric space SU (2, 1)/(SU (2) × U (1)). To determine the quantum corrections to this metric, we posit that a discrete subgroup of the continuous tree-level isometry group SU (2, 1), namely the Picard modular group SU (2, 1; Z[i]), must remain unbroken in the exact metric -including all perturbative and non-perturbative quantum corrections. This assumption is expected to be valid when X admits complex multiplication by Z[i]. Based on this hypothesis, we construct an SU (2, 1; Z[i])-invariant, non-holomorphic Eisenstein series, and tentatively propose that this Eisenstein series provides the exact contact potential on the twistor space over the universal hypermultiplet moduli space. We analyze its non-Abelian Fourier expansion, and show that the Abelian and non-Abelian Fourier coefficients take the required form for instanton corrections due to Euclidean D2branes wrapping special Lagrangian submanifolds, and to Euclidean NS5-branes wrapping the entire Calabi-Yau threefold, respectively. While this tentative proposal fails to reproduce the correct one-loop correction, the consistency of the Fourier expansion with physics expectations provides strong support for the usefulness of the Picard modular group in constraining the quantum moduli space. E SL(2,Z) 3/2 as a function of the "axio-dilaton" C (0) + ie −φ , valued on the fundamental domain M = SL(2, Z)\SL(2, R)/SO(2) of the Poincaré upper half plane. This proposal reproduced the known tree-level and one-loop corrections [6,7], predicted the absence of higher loop corrections, later verified by an explicit two-loop computation [8], and suggested the exact form of D(-1)-instanton contributions, later corroborated by explicit matrix model computations [9,10]. From the mathematical point of view, perturbative corrections and instanton contributions correspond, respectively, to the constant terms and Fourier coefficients of the automorphic form E SL(2,Z) 3/2 . This work was extended to toroidal compactifications of Mtheory, where the R 4 -type corrections were argued to be given by Eisenstein series of the respective U-duality group [11][12][13], predicting the contributions of Euclidean Dp-brane instantons, and, when n ≥ 6, NS5-branes. Unfortunately, extracting the constant terms and Fourier coefficients of Eisenstein series is not an easy task, and it has been difficult to put the conjecture to the test. Part of our motivation is to develop the understanding of Eisenstein series beyond the relatively well understood case of G(Z) = SL(n, Z). The Hypermultiplet Moduli Space of N = 2 SupergravityCompactifications with fewer unbroken supersymmetries (N ≤ 2 in D = 4) lead to moduli spaces which are generically not symmetric spaces. An interesting example is type IIA string theory compactified on a Calabi-Yau threefold X , leading to N = 2 supergravity in four dimensions coupled to ...

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“…Physical observables, such as scattering amplitudes, must respect the symmetry and are therefore given by functions on G(Z)\G(R)/K(G); to wit, automorphic forms (see [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] for a sample of the vast literature on the subject). Of particular interest for us is the case when X = T d , the d-dimensional torus for d = 0, .…”

Section: Introductionmentioning

confidence: 99%

Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors

Fleig

Kleinschmidt

Persson

2014

Communications in Number Theory and Physics

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Motivated by string theory scattering amplitudes that are invariant under a discrete U-duality, we study Fourier coefficients of Eisenstein series on KacMoody groups. In particular, we analyse the Eisenstein series on E 9 (R), E 10 (R) and E 11 (R) corresponding to certain degenerate principal series at the values s = 3/2 and s = 5/2 that were studied in [1]. We show that these Eisenstein series have very simple Fourier coefficients as expected for their role as supersymmetric contributions to the higher derivative couplings R 4 and ∂ 4 R 4 coming from 1/2-BPS and 1/4-BPS instantons, respectively. This suggests that there exist minimal and next-to-minimal unipotent automorphic representations of the associated Kac-Moody groups to which these special Eisenstein series are attached. We also provide complete explicit expressions for degenerate Whittaker vectors of minimal Eisenstein series on E 6 (R), E 7 (R) and E 8 (R) that have not appeared in the literature before.

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U-Duality and the compactified Gauss-Bonnet term

Cited by 13 publications

References 34 publications

The five dimensional transformed Weyl$-$Yang$-$Kaluza$-$Klein theory of gravity

The five dimensional transformed Weyl$-$Yang$-$Kaluza$-$Klein theory of gravity

Instanton corrections to the universal hypermultiplet and automorphic forms on {$SU(2,1)$}

Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors

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