Excision of singularities by stringy domain walls

Abstract

We study supersymmetric domain walls on S 1 /Z 2 orbifolds. The supergravity solutions in the bulk are given by the attractor equation associated with Calabi-Yau ͑CY͒ spaces and have a naked space-time singularity at some ͉y s ͉. We are looking for possibilities to cut off this singularity with the second wall by a stringy mechanism. We use the collapse of the CY cycle at ͉y c ͉ which happens before and at a finite distance from the space-time singularity. In our example with three Kähler moduli the second wall is at the end of the moduli space at ͉y c ͉ where also the enhancement of SU͑2͒ gauge symmetry takes place so that ͉y e ͉ϭ͉y c ͉Ͻ͉y s ͉. The physics of the excision of a naked singularity via the enhançon in the context of domain wall has an interpretation on the heterotic side related to R→1/R duality. The supersymmetric domain wall solutions of Dϭ5, Nϭ2, U͑1͒ gauged supergravity 1 with brane sources on S 1 /Z 2 orbifolds have been described recently in Ref.2. It has been observed there that in the context of Calabi-Yau ͑CY͒ compactifications the collapse of CY cycles may put some restrictions on the distance between the walls. 3,4 In this article we will study this type of domain wall both for Dϭ5, Nϭ2, U͑1͒ gauged supergravity 1 ͑GST model͒ and for Calabi-Yau compactifications of 11-D supergravity with fluxes turned on. The latter is the five-dimensional heterotic M-theory 5,6 obtained by a reduction on a CY threefold of Horava-Witten M-theory 7 on S 1 /Z 2 ͑HW model͒. The explicit form of the solution with general dependence on the vector multiplets is obtained for both models by solving the generalized attractor equation. [8][9][10][11] Since the domain wall solutions 2,6 of the two models behave very similarly, we will discuss them in parallel. The purpose of this article is to find a possibility to remove the space-time singularity of the domain wall solution via some particular property of the CY space. Specifically we would like to find a situation when the collapse of the CY cycle at ͉y c ͉ happens closer to the first wall which is at yϭ0 and at a finite distance from the space-time singularity ͉y s ͉, so that ͉y c ͉Ͻ͉y s ͉. ͑1͒In the case of excision of repulson singularities by the enhançon mechanism, 12 the distance between the repulson and enhançon is finite. The hope, therefore, is that also for some domain walls the analogous situation may be possible, particularly if enhancement of gauge symmetry is somehow involved. The finite distance between the naked singularity of the supergravity solution and the position of the collapse of the CY cycle may allow us to use the physics of string theory already at the end of the moduli space which in this case excludes the singularity of the general relativity as unphysical. The generic interest in such a mechanism is supported by some interesting

Time-dependent backgrounds from supergravity with gauged non-compact R -symmetry

“…By using a probe analysis for time independent black holes one can show, that even before one reaches the repulson singularity the tension of the probe brane becomes tensionless and at the enhancement point the supergravity solution cannot be trusted anymore and additional massless degrees of freedom have to be taken into account [27]. An analogous mechanism does also apply for (static) domain walls, where the enhancon locus appears before one reaches the space-time singularity [28] and integrating-in the additional modes, the singularity can be avoided (see [29] and references therein).…”

“…Recall, we use the rescaled section (F I (Y ), Y I ), which ensures that the supergravity solution is invariant under Kähler transformations (by rescaling of the section with the supersymmetry central charge [18]). In this rescaled section we should not set Y 0 = 1 because this would eliminate one harmonic function in (28). Now, if the scalars flow to smaller values and even if one reaches the point where F (z) vanishes, the metric will still be regular as long as c ∼ χ = 0 (see also [19]).…”

Non-extremal and non-BPS extremal five-dimensional black strings from generalized special real geometry

“…Therefore it may happen that, for some choices of integration constants, (H(H i )) 1/3 takes the values zero or infinity at finite ρ > 2c, generically resulting in a naked singularity even if the behaviour at ρ → ∞ and ρ = 2c is regular. This phenomenon was studied for five-dimensional BPS black holes and five-dimensional domain walls in [41] and [38]. It was observed in particular that naked singularities can occur even …”

Gauged supergravity and singular Calabi-Yau manifolds

“…When considering backgrounds where h starts at a positive value and dynamically evolves to zero, one has to study whether and how such solutions can be continued to h < 0. This problem was analyzed for domain walls in the model with X = X 1 in [34]. Since both the metric g xy on the moduli space and the space-time metric describing the domain wall were found to be smooth, it was expected that one could continue the solution using the method introduced in [35].…”