Abstract
It was shown in arXiv:1410.7168 that compactifying D = 6, mathcal{N}=left(1,0right) ungauged supergravity coupled to a single tensor multiplet on S3 one gets a particular D = 3, mathcal{N}=4 gauged supergravity which is a consistent reduction. We construct two supersymmetric black string solutions in this 3-dimensional model with one and two active scalars respectively. Uplifting the first, one gets a dyonic string solution in D = 6 that has been known for a long time. Whereas, uplifting the second solution, one finds a very interesting configuration where magnetic strings are located uniformly on a circle in a plane within the 4-dimensional flat transverse space and electric strings are distributed homogeneously inside this circle. Both solutions have AdS3 × S3 limits.
Highlights
Are crucial in studying the AdS3/CFT2 correspondence in detail [13,14,15,16,17,18]
Nihat Sadik Deger,a Nicolo Petria and Dieter Van den Bleekenb,c aDepartment of Mathematics, Bogazici University, 34342, Bebek, Istanbul, Turkey bDepartment of Physics, Bogazici University, 34342, Bebek, Istanbul, Turkey cInstitute for Theoretical Physics, KU Leuven, 3001 Leuven, Belgium E-mail: sadik.deger@boun.edu.tr, nicolo.petri@boun.edu.tr, dieter.van@boun.edu.tr. It was shown in arXiv:1410.7168 that compactifying D = 6, N = (1, 0) ungauged supergravity coupled to a single tensor multiplet on S3 one gets a particular D = 3, N = 4 gauged supergravity which is a consistent reduction
The 6d model (1.1) admits a 1/4 supersymmetric dyonic string solution that carries electric and magnetic charges [19, 20] which corresponds to the D1-D5 intersection in type IIB theory and upon dimensional reduction on a circle leads to a black hole in D = 5
Summary
It is clear that the above BPS equations (3.7) simplify drastically if the two scalars are equal, so we consider this case first. By taking the scalar ξ as the radial coordinate, the equation for U in (3.7) is solved as e2U = e−2ξ 2g0 − k0 eξ ,. Where an integration constant is chosen as zero without loss of generality. In the limit ξ → log (2g0/k0), the scalar curvature of (3.11) takes the negative constant value −24g04/k02, while for ξ → −∞ the scalar curvature vanishes. It is easy to see that our domain wall solution interpolates between AdS3 and a cone over R1,1. We have checked that this solution satisfies the field equations of (2.1) too
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