Higher derivative corrections, dimensional reduction and Ehlers duality

Michel, Yann; Pioline, Boris

doi:10.1088/1126-6708/2007/09/103

Cited by 9 publications

(11 citation statements)

References 34 publications

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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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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 need for automorphic forms which transform under the maximal compact subgroup K(U 3 ) was also emphasized in [6], based on the observation that the dilaton exponents in compactified higher curvature corrections correspond to weights of the global symmetry group U 3 , implying that these terms transform non-trivially in some representation of K(U 3 ). An explicit realisation of these arguments was found in [9] for the case of compactification on S 1 of the four-dimensional coupled Einstein-Liouville system, supplemented by a four-derivative curvature correction. The resulting effective action was shown to explicitly break the Ehlers SL(2, R)-symmetry; however, an SL(2, Z) global × U (1) localinvariant effective action was obtained by "lifting" the scalar coefficients to automorphic forms transforming with compensating U (1) weights.…”

Section: Non-perturbative Completion and Automorphic Formsmentioning

confidence: 89%

“…Recently, several authors [5,6,7,8,9] have initiated an investigation aimed at answering the question of whether or not the U-duality group U 3 in three dimensions is preserved also if the tree-level Lagrangian is supplemented by higher order curvature corrections. The consensus has been that toroidal compactifications of quadratic and higher order corrections give rise to terms which are not U 3 -invariant.…”

Section: Non-perturbative Completion and Automorphic Formsmentioning

confidence: 99%

U-Duality and the compactified Gauss-Bonnet term

Bao

Bielecki

Cederwall

et al. 2008

J. High Energy Phys.

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We present the complete toroidal compactification of the Gauss-Bonnet Lagrangian from D dimensions to D − n dimensions. Our goal is to investigate the resulting action from the point of view of the "U-duality" symmetry SL(n + 1, R) which is present in the tree-level Lagrangian when D − n = 3. The analysis builds upon and extends the investigation of the paper [arXiv:0706.1183], by computing in detail the full structure of the compactified Gauss-Bonnet term, including the contribution from the dilaton exponents. We analyze these exponents using the representation theory of the Lie algebra sl(n + 1, R) and determine which representation seems to be the relevant one for quadratic curvature corrections. By interpreting the result of the compactification as a leading term in a large volume expansion of an SL(n+1, Z)-invariant action, we conclude that the overall exponential dilaton factor should not be included in the representation structure. As a consequence, all dilaton exponents correspond to weights of sl(n + 1, R), which, nevertheless, remain on the positive side of the root lattice.

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“…where 1 and 0 in η denote the d-dimensional identity and zero matrices, respectively. Hence, equation (24) implies that G is an indefinite orthogonal matrix. From equation (22) and (23), it is clear that both G and H are symmetric.…”

Section: O(d D)/o(d)×o(d) Group Elementmentioning

confidence: 99%

“…A non-exhaustive list of references on duality and higher derivative corrections in the context of string/M-theory includes[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. For work on duality and higher derivative corrections in the context of four-dimensional gravity see[24][25][26].…”

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confidence: 99%

Duality completion of higher derivative corrections

Godazgar

2013

J. High Energ. Phys.

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We present a new method for completing higher derivative corrections for theories that exhibit duality symmetries under reduction. This proposal is based on the observation that duality symmetry in the reduced theory highly constrains the form of the unreduced theory. We apply this idea to closed bosonic string theory and complete the Riemann squared term to simply derive the known full tree-level effective action to order alpha'

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Higher derivative corrections, dimensional reduction and Ehlers duality

Cited by 9 publications

References 34 publications

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

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

U-Duality and the compactified Gauss-Bonnet term

Duality completion of higher derivative corrections

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