Abstract
We study interpolation between two multi-center microstate geometries in 4d/5d that represent Lunin-Mathur geometries with circular profiles. The interpolating solution is a Lunin-Mathur geometry with a helical profile, and is represented by a 2-center solution with a codimension-2 source. The interpolating 2-center solution exhibits interesting features such as some of the charges being delocalized, and some of the charges getting transferred from the codimension-2 center to the other, codimension-3 center as the interpolation proceeds. We also discuss the spectral flow of this entire process and speculate on the relevance of such solutions to understanding general microstates of 3-charge black holes.
Highlights
In this note we will call these solutions “harmonic solutions”, because their construction heavily relies on harmonic functions
We extend the examples of codimension-2 harmonic solutions by studying the Lunin-Mathur geometries [24, 25] in the framework
The geometries are parametrized by profile functions which describe the shape in R4 of the worldvolume of a Kaluza-Klein monopole (KKM) produced by the supertube transition of D1- and D5-branes
Summary
We give a brief review of the harmonic solution, which represents multi-center blackhole/ring solutions in 4d/5d. The codimension-3 sources in the harmonic functions (2.13) represent branes in string/M-theory. In the type IIA picture (2.10), the dictionary between the singularities in the harmonic functions and the D-brane sources is [3]. Lifted to M-theory along the ψ direction, this harmonic solution becomes a 5d black hole made of three stacks of M2-branes, the D6-brane becoming the origin of the R4 This 5d black hole can be dualized (using the duality of appendix A) into the original StromingerVafa black hole [36] in a type IIB frame, where the M2/D2 charges are mapped into D1, D5, and P charges. Harmonic functions can have other kinds of source They can have a singularity along a curve in R3 and have non-trivial monodromy around it. Given codimension-2 brane sources, which harmonic functions to become monodromic is a non-trivial matter that depends on the physical situation in question
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