Abstract
Abstract We analyze the BPS solutions of minimal supergravity coupled to an anti-self-dual tensor multiplet in six dimensions and find solutions that fluctuate non-trivially as a function of two variables. We consider families of solutions coming from KKM monopoles fibered over Gibbons-Hawking metrics or, equivalently, non-trivial T 2 fibrations over an $ {{\mathbb{R}}^3} $ base. We find smooth microstate geometries that depend upon many functions of one variable, but each such function depends upon a different direction inside the T 2 so that the complete solution depends non-trivially upon the whole T 2. We comment on the implications of our results for the construction of a general superstratum.
Highlights
We find smooth microstate geometries that depend upon many functions of one variable, but each such function depends upon a different direction inside the T 2 so that the complete solution depends non-trivially upon the whole T 2
It has become evident that while five-dimensional microstate geometries can resolve black-hole singularities and provide rich families of solutions that sample the typical sector of the black-hole conformal field theory, there are not enough such microstate geometries to sample the states of the black hole with sufficient density so as to yield a semi-classical description of the thermodynamics [14,15,16,17]
In our analysis of the BPS equations, we find features that fit very well with the constructive algorithm outlined in [21]: we see that the BPS system can accommodate the tilting and boosting of the parallel D1 and D5 branes, and the addition of momentum and angular momentum densities, in such a manner that one induces d1-d5 dipole densities by reorienting the D1-D5 charge densities and that all of this can be achieved in a way that makes the densities into functions of two variables
Summary
The six-dimensional system we study is N = 1 minimal supergravity coupled to one anti-selfdual tensor multiplet. In the six-dimensional theory, the graviton multiplet contains a self-dual tensor field and so the entire bosonic sector consists of the graviton, the dilaton and an unconstrained 2-form gauge field with a 3-form field strength. Again following [23], we define the Hodge star ∗d to act on a p-form via. The base, B, is required to be “almost hyper-Kahler,” or, more precisely, it is hyper-complex in that there are three anti-self-dual 2-forms:. These forms are required to satisfy the differential identity: dJ (A) = ∂v(β ∧ J (A)) ,. It is convenient to introduce the the anti-self-dual 2-forms, ψ and ψdefined by: ψ
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