On four-derivative terms in IIB Calabi-Yau orientifold reductions

2020

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In this work we analyze F-theory and Type IIB orientifold compactifications to study α-corrections to the four-dimensional, N = 1 effective actions. In particular, we obtain corrections to the Kählermoduli space metric and its complex structure for generic dimension originating from eight-derivative corrections to eleven-dimensional supergravity. We propose a completion of the G 2 R 3 and (∇G) 2 R 2-sector in eleven-dimensions relevant in Calabi-Yau fourfold reductions. We suggest that the three-dimensional, N = 2 Kähler coordinates may be expressed as topological integrals depending on the first, second, and third Chern-forms of the divisors of the internal Calabi-Yau fourfold. The divisor integral Ansatz for the Kähler potential and Kähler coordinates may be lifted to four-dimensional, N = 1 F-theory vacua. We identify a novel correction to the Kähler potential and coordinates at order α 2 , which is leading compared to other known corrections in the literature. At weak string coupling the correction arises from the intersection of D7-branes and O7-planes with base divisors and the volume of self-intersection curves of divisors in the base. In the presence of the conjectured novel α-correction resulting from the divisor interpretation the no-scale structure may be broken. Furthermore, we propose a model independent scenario to achieve non-supersymmetric AdS vacua for Calabi-Yau orientifold backgrounds with negative Euler-characteristic.

Section: Jhep04(2020)032mentioning

confidence: 99%

“…Possible obstructions and subtleties to this step for higher-derivative couplings of non-topological nature were discussed in[31].…”

mentioning

confidence: 99%

F-theory vacua and α′-corrections

2020

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“…In this section we summarize the four-derivative couplings involving Kähler moduli derived in [49] via the same logic as in the previous section but starting from type IIB supergravity in ten dimensions. The intention is to present a complete discussion in this work.…”

Section: Type Iib Supergravity On Calabi-yau Threefolds At Four Derivmentioning

confidence: 99%

Higher derivatives in Type II and M-theory on Calabi-Yau threefolds

Grimm

Mayer

2018

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The four-and five-dimensional effective actions of Calabi-Yau threefold compactifications are derived with a focus on terms involving up to four space-time derivatives. The starting points for these reductions are the ten-and eleven-dimensional supergravity actions supplemented with the known eight-derivative corrections that have been inferred from Type II string amplitudes. The corrected background solutions are determined and the fluctuations of the Kähler structure of the compact space and the form-field background are discussed. It is concluded that the two-derivative effective actions for these fluctuations only takes the expected supergravity form if certain additional ten-and eleven-dimensional higher-derivative terms for the form-fields are included. The main results on the four-derivative terms include a detailed treatment of higher-derivative gravity coupled to Kähler structure deformations. This is supplemented by a derivation of the vector sector in reductions to five dimensions. While the general result is only given as an expansion in the fluctuations, a complete treatment of the one-Kähler modulus case is presented for both Type II theories and M-theory.

“…Throughout this paper, we let higher derivatives act in the internal space, working at two-derivative level in the external directions. Recently, α ′3 external four-derivative couplings between Kähler moduli and gravity were derived in [29] for the same class of type IIB orientifold setups considered in this work, with potential applications to Kähler moduli inflation studies.…”

Section: Introductionmentioning

confidence: 99%

The Euler characteristic correction to the Kähler potential — revisited

Bonetti

2017

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We confirm the leading α ′ 3 correction to the 4d, N = 1 Kähler potential of type IIB orientifold compactifications, proportional to the Euler characteristic of the Calabi-Yau threefold (BBHL correction). We present the explicit solution for the α ′ 3 -modified internal background metric in terms of the non-harmonic part of the third Chern form of the leading order Calabi-Yau manifold. The corrected internal manifold is almost Calabi-Yau and admits an SU(3) structure with non-vanishing torsion. We also find that the full ten-dimensional Einstein frame background metric is multiplied by a non-trivial Weyl factor. Performing a Kaluza-Klein reduction on the modified background we derive the α ′ 3 -corrected kinetic terms for the dilaton and the Kähler deformations of the internal Calabi-Yau threefold for arbitrary h 1,1 . We analyze these kinetic terms in the 4d, N = 2 un-orientifolded theory, confirming the expected correction to the Kähler moduli space prepotential, as well as in the 4d, N = 1 orientifolded theory, thus determining the corrections to the Kähler potential and Kähler coordinates.