Abstract
We review and extend results on higher-curvature corrections to different configurations describing a superposition of heterotic strings, KK monopoles, solitonic 5-branes and momentum waves. Depending on which sources are present, the low-energy fields describe a black hole, a soliton or a naked singularity. We show that this property is unaltered when perturbative higher-curvature corrections are included, provided the sources are fixed. On the other hand, this character may be changed by appropriate introduction (or removal) of sources regardless of the presence of curvature corrections, which constitutes a non-perturbative modification of the departing system. The general system of multicenter KK monopoles and their 5-brane charge induced by higher-curvature corrections is discussed in some detail, with special attention paid to the possibility of merging monopoles. Our results are particularly relevant for small black holes (Dabholkar-Harvey states, DH), which remain singular after quadratic curvature corrections are taken into account. When there are four non-compact dimensions, we notice the existence of a black hole with regular horizon whose entropy coincides with that of the DH states, but the charges and supersymmetry preserved by both configurations are different. A similar construction with five non-compact dimensions is possible, in this case with the same charges as DH, although it fails to reproduce the DH entropy and supersymmetry. No such configuration exists if d > 5, which we interpret as reflecting the necessity of having a 5-brane wrapping the compact space.
Highlights
Many supergravity theories are known to describe certain low energy limits of string theory
We review and extend results on higher-curvature corrections to different configurations describing a superposition of heterotic strings, KK monopoles, solitonic 5-branes and momentum waves
Our results are relevant for small black holes (Dabholkar-Harvey states, Dabholkar and Harvey (DH)), which remain singular after quadratic curvature corrections are taken into account
Summary
Many supergravity theories are known to describe certain low energy limits of string theory. The system describes a modification of the one studied by Dabholkar and Harvey [25] obtained adding non-perturbative sources, just like Strominger and Vafa did in [19] Since it reproduced the entropy of the DH states but did not match other properties, the solution was called a “fake” small black hole in [50]. The perturbative corrections to the small black ring system have been computed in [55], showing that the field configuration remains singular after their inclusion Motivated by these results, we perform here a more exhaustive study of a large family of supersymmetric solutions of the heterotic theory, which includes singular and regular horizon black holes, as well as other related configurations that serve to gain a broader perspective on the matter. We will not restrain ourselves to spacetimes with four noncompact dimensions, but will study the problem for 4 ≤ d ≤ 9 (DH states describe strings wrapping one compact direction)
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