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.

We study the central charges and levels of a two-dimensional N = (0, 4) superconformal field theory describing four-dimensional BPS black holes in F-theory. These arise from D3-branes wrapping a curve in the base of an elliptically fibered Calabi-Yau threefold times a circle, and probe a transverse Taub-NUT space. The near horizon geometry of these D3-branes is AdS 3 × S 3 /Z m , where m is the NUT charge. Starting from a sixdimensional supergravity effective action we compute three-dimensional Chern-Simons terms to deduce the central charges and levels. We find that it is crucial to integrate out an infinite tower of massive Kaluza-Klein states on S 3 /Z m to match the expected microscopic results. The induced corrections turn out to contribute at leading order to the central charges and levels, which in turn determine the black hole entropy.

In this note we consider M-theory compactified on a warped Calabi-Yau fourfold including the eight-derivative terms in the eleven-dimensional action known in the literature. We dimensionally reduce this theory on geometries with one Kähler modulus and determine the resulting three-dimensional Kähler potential and complex coordinate. The logarithmic form of the corrections suggests that they might admit a physical interpretation in terms of one-loop corrections to the effective action. Including only the known terms the no-scale condition in three dimensions is broken, but we discuss caveats to this conclusion. In particular, we consider additional new eight-derivative terms in eleven dimensions and show that they are strongly constrained by compatibility with the Calabi-Yau threefold reduction. We examine their impact on the Calabi-Yau fourfold reduction and the restoration of the no-scale property.

We study the central charges and levels of 2d N = (0, 4) superconformal field theories that are dual to four-and five-dimensional BPS black holes in compactifications of type IIB string theory on a K3 surface. They arise from wrapping a D3-brane on a curve C inside K3 and have transverse space either an ALE or ALF space. These D3-branes have an AdS 3 × S 3 /Γ near horizon geometry where Γ is a discrete subgroup of SU(2). We compute the central charges and levels of the 2d SCFTs both in the microscopic picture and from six-dimensional N = (2, 0) supergravity. These quantities determine the black hole entropy via Cardy's formula. We find agreement between the microscopic and macroscopic computations. The contributions from one-loop quantum corrections to the macroscopic result are crucial for this matching. c.a.couzens@uu.nl h.hetlam@uu.nl k.mayer@uu.nl s.j.g.vandoren@uu.nl IntroductionThe microscopic counting of the Bekenstein-Hawking entropy of BPS black holes in string theory has had a long and rich history since its inception in [1]. The authors of [1] considered five-dimensional non-spinning black holes arising from the compactification of type II string theory on K3×S 1 , matching the entropy of the macroscopic configuration with the microscopic one. This was later extended to five-dimensional non-spinning black holes in M-theory on a Calabi-Yau threefold [2] and four-dimensional black holes in Mtheory on the product of a Calabi-Yau threefold with a circle by MSW [3]. More recently black holes in F-theory [4] have been given further consideration in [5][6][7] for example.In this paper we are interested in compactifications of type IIB string theory on K3 and the black strings emerging in this theory. The goal is to match macroscopic data with a complimentary microscopic description. The literature on the topic is vast, in particular for black holes arising from the D1-D5-(p) system [1,8]. We shall instead concern ourselves with black strings arising from wrapping D3-branes on a curve inside K3, which, in comparison to the D1-D5-(p) system, has been far less studied. Explicitly we shall consider D3-branes in an asymptotic geometry R × S 1 × M × K3 where the D3branes are wrapped on S 1 × C with C a curve in K3 and probe the transverse space M. The equations of motion and supersymmetry preservation imply that the four-manifold M is a Ricci-flat hyper-Kähler manifold which we take to be non-compact. We consider two families of such manifolds M = M Γ : asymptotically locally Euclidean (ALE) and asymptotically locally flat (ALF) spaces, both of which may be defined by a choice of discrete subgroup Γ ⊂ SU(2) as we review in section 2. Different choices of Γ lead to black strings with different charges, some of which have not been considered before in the literature. In particular, black strings arising from D3-branes probing M Γ corresponding to the D-and E-series within the ADE-classification of discrete subgroups of SU(2) have not been studied previously. Microscopically the strings are dual to (0,4) superconforma...

We study the macroscopics of 2d $$ \mathcal{N} $$ N = (0, 4) SCFTs arising from F-theory constructions. The class of 2d SCFTs we consider live on black strings which are obtained by wrapping D3-branes on a curve in the base of a possibly singular elliptically fibered Calabi-Yau threefold. In addition, we allow the D3-branes to probe ALE or ALF spaces transversely. We compute anomaly coefficients of these SCFTs by determining Chern- Simons terms in the 3d action resulting from the reduction of 6d $$ \mathcal{N} $$ N = (1, 0) supergravity on the compact space surrounding the black string. Essential contributions to these coefficients are from one-loop induced Chern-Simons terms arising from integrating out massive Kaluza-Klein modes.