Interpolating between multi-center microstate geometries

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.

Shockwaves in black hole microstate geometries

“…We observed that the CFT states described by our solutions contain examples of states that interpolate between certain types of different three-charge microstates that have recently attracted attention, expanding upon the classes of states discussed in [82,83].…”

“…Second, our bulk solutions do not differentiate between the polarizations of the long strands, so the same bulk solutions describe interpolations between different pairs of fractionally spectral flowed states. In this sense our bulk description is more coarse-grained than that of [83]. Nevertheless, we have found the bulk description of interesting examples of states of the general form (4.41), allowing us to describe a partial interpolation between strands that have different amounts of spectral flow.…”

“…We now observe that the class of CFT states that we have studied, given in Eq. (4.32), contains some simple examples of states that have attracted recent interest as families that interpolate between different microstate geometries [82,83]. Those works studied sub-families of states of the general form…”

“…In [82] the sub-family k = k 1 = 1, ν = 0, ν 1 > 0 was studied (spectral flowed further to the NS-NS sector). In [83] a general discussion was given, as well as an explicit analysis of the sub-family in which ν 1 = ν − 1 k 1 . It was found that the bulk description of these states involves codimension-2 sources corresponding to an extra KKM dipole charge in the D1-D5 frame.…”

“…In the analysis of [83], emphasis was placed on the ability to interpolate from states involving strands of all one type to states involving strands of all the other type. On this point, let us note that there are two limitations to our construction: first, we cannot interpolate all the way to having only long strands, as this would invalidate the shockwave approximation we have made; the approximation relies on both long and short strands contributing an order-one fraction of the overall strand budget.…”