R4 couplings in M- and type II theories on Calabi-Yau spaces

Abstract

We discuss several implications of R 4 couplings in M theory when compactified on Calabi-Yau (CY) manifolds. In particular, these couplings can be predicted by supersymmetry from the mixed gauge-gravitational Chern-Simons couplings in five dimensions and are related to the one-loop holomorphic anomaly in four-dimensional N = 2 theories. We find a new contribution to the Einstein term in five dimensions proportional to the Euler number of the internal CY threefold, which corresponds to a one-loop correction of the hypermultiplet geometry. This correction is reproduced by a direct computation in type II string theories. Finally, we discuss a universal non-perturbative correction to the type IIB hyper-metric.

Enhanced supersymmetry from vanishing Euler number

“…Invoking the Calabi-Yau constraints (4.6), this yields 17) JHEP04 (2013)058 which combines nicely with the transformation (5.2) of J to…”

Supergravity instantons for hypermultiplets

“…In the case of non vanishing fivebrane charge the action has a form reminiscent of a non threshold bound state. The investigations reported here were limited to supergravity: both the inclusion of higher derivative corrections like R 4 [44] terms in the dimensional reduction of eleven dimensional supergravity along the lines of [45][1] would be very interesting.…”

“…The supersymmetry transformations for the fermionic hyperino and gravitino fields can be derived by dimensional reduction of the eleven dimensional supersymmetry transformation rules (2). Some details of this can be found in appendix B.…”

“…Even for these solutions the bulk part of the action of the instanton will vanish and the instanton action will be given by the boundary term (45). Using the ansatz for the volume scalar (43) gives…”

R2corrections for 5D black holes and rings

“…The Einstein-frame low energy effective action for the compactification of M-theory on a Calabi-Yau threefold CY 3 down to five dimensions contains the terms [13] …”