Smooth non-extremal D1-D5-P solutions as charged gravitational instantons
HJE
Smooth non-extremal D1-D5-P solutions as charged
Bidisha Chakrabarty 0 1 2
Jorge V. Rocha 0 1
Amitabh Virmani 0 1 2
0 Universitat de Barcelona , Mart i Franques 1, E-08028 Barcelona , Spain
1 Sachivalaya Marg , Bhubaneshwar, 751005 India
2 Institute of Physics
We present an alternative and more direct construction of the non-supersymmetric D1-D5-P supergravity solutions found by Jejjala, Madden, Ross and Titchener. We show that these solutions | with all three charges and both rotations turned on | can be viewed as a charged version of the Myers-Perry instanton. We present an inverse scattering construction of the Myers-Perry instanton metric in Euclidean gravity. The angular momentum bounds in this construction turn out to be precisely the ones necessary for the smooth microstate geometries. We add charges on the Myers-Perry instanton using appropriate SO(4; 4) hidden symmetry transformations. The full construction can be viewed as an extension and simpli cation of a previous work by Katsimpouri, Kleinschmidt and Virmani.
Black Holes in String Theory; Black Holes; String Duality
1 Introduction
2 JMaRT as charged Myers-Perry instanton
2.1
2.2
2.3
Myers-Perry instanton Dimensional reduction to 3d and Weyl re ection Charging transformations and 6d elds
3
Conclusions
A Inverse scattering construction of the Myers-Perry instanton
B From 6d to 3d and back
C Construction of the C- eld
D Rod structure of the Cvetic-Youm metric
microstates was the rewriting by Giusto and Mathur [1] of the rst example of a smooth
geometry in the bered form, thus making the connection with the classi cation of
supersymmetric solutions. This exercise led to the realisation that the four-dimensional base
space for such solutions had to be of the so-called \pseudo-hyper-Kahler" form, which
paved the way for generalisations to the multi-center solutions [2, 3].
It is natural to hope that understanding the known non-extremal microstates [4{10]
from various possible perspectives will shed light on how to go about constructing more
general non-extremal microstates. Drawing movitation from properties of the supersymmetric
solutions, one such study was performed in reference [11] for the solutions found by Jejjala,
Madden, Ross, and Titchener (JMaRT) [4]. They found that upon dimensional reduction
from 6d to 5d, the 5d solution features locally non-supersymmetric orbifold singularities.
Upon further reduction to 4d, they found that the two singularities are connected by a
conical singularity. The presence of the conical singularity does not allow for an
unambiguous association of brane charges to the two centers. This led the authors to conclude
that the picture of \half-BPS atoms" making up the multiple centers of supersymmetric
microstates does not extent to the non-supersymmetric ones in any easy way. One must
consider more general kinds of basic building blocks.
{ 1 {
In this paper we add a new dimension to this discussion. We show that the JMaRT
solution can also be thought of as a charged version of Euclidean
ve-dimensional
MyersPerry instanton trivially lifted to six dimensions by the addition of a at timelike direction.
Gravitational instantons in four-dimensions have received much attention under the
Euclidean Gravity paradigm, though their higher-dimensional cousins are not so well explored.
For the cases where these objects have been explored, their classi cation is presented in
terms of turning points of various degenerating Killing vectors [12]; more precisely in terms
of the so-called rod structure [13{15]. Since for the non-supersymmetric microstates only
spacelike Killing vectors degenerate, it is natural to expect that non-supersymmetric
microstates are closely related to gravitational instantons.
For the construction of the multi-center supersymmetric solutions this connection is
the key element [2, 3]. In these constructions the four-dimensional base space is taken
to be multi-center Gibbons-Hawking instanton. For non-extremal microstates such a link
has also been explored, though not yet in a fully systematic way. For example, the rst
generalisation [5] of the JMaRT solution was constructed by adding appropriate charges to
the so-called Kerr-Taub-Bolt instanton. Similar ideas, in di erent guises, were also used in
references [7, 9, 16, 17]. More recently, these and a related circle of ideas have led to the
construction of the rst example of non-extremal multi-bubble microstate geometries [10].
It had been anticipated that the JMaRT solution has a close connection to
gravitational instantons (see e.g. comments in [5, 17]), though it has never been made precise.
A connection was established in reference [18] where it was highlighted that the JMaRT
metric can be related to the Myers-Perry instanton metric via a simple analytic
continuation. In this paper we extend and simplify that construction. There are several di erences:
we consider both angular momentum and all three charges, whereas reference [18] (...truncated)