Microstate geometries from gauged supergravity in three dimensions
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Springer
Received: June 20, 2020 Accepted: August 25, 2020 Published: October 6, 2020
Daniel R. Mayerson,a Robert A. Walkera,b and Nicholas P. Warnera,b,c a
Universit´e Paris Saclay, CNRS, CEA, Institut de Physique Th´eorique, 91191, Gif sur Yvette, France b Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, U.S.A. c Department of Mathematics, University of Southern California, Los Angeles, CA 90089, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: The most detailed constructions of microstate geometries, and particularly of superstrata, are done using N = (1, 0) supergravity coupled to two anti-self-dual tensor multiplets in six dimensions. We show that an important sub-sector of this theory has a consistent truncation to a particular gauged supergravity in three dimensions. Our consistent truncation is closely related to those recently laid out by Samtleben and Sarıo˘glu [1], which enables us to develop complete uplift formulae from the three-dimensional theory to six dimensions. We also find a new family of multi-mode superstrata, indexed by two arbitrary holomorphic functions of one complex variable, that live within our consistent truncation and use this family to provide extensive tests of our consistent truncation. We discuss some of the future applications of having an intrinsically three-dimensional formulation of a significant class of microstate geometries. Keywords: Black Holes in String Theory, Supergravity Models, Chern-Simons Theories ArXiv ePrint: 2004.13031
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)030
JHEP10(2020)030
Microstate geometries from gauged supergravity in three dimensions
Contents 1 Introduction three-dimensional gauged supergravity Some supergravity background The scalar degrees of freedom The gauge couplings The scalar action The Chern-Simons action Integrating out the Chern-Simons gauge fields The three-dimensional supergravity: summary and comments
4 4 6 7 9 10 10 11
3 From three to six dimensions 3.1 Establishing the consistent truncation 3.2 The six-dimensional theory 3.2.1 The six-dimensional theory for superstrata 3.3 The full six-dimensional uplift 3.3.1 The metric and scalars 3.3.2 The tensor gauge fields 3.3.3 Testing the consistent truncation 3.4 A U(1)2 truncation
12 12 13 13 14 14 15 16 17
4 Superstrata in three dimensions 4.1 The holomorphic functions 4.2 The three-dimensional description of (1, m, n) superstrata 4.3 The solutions in U(1)2 truncations
19 20 20 22
5 Final comments
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A The three-sphere
25
B Six-dimensional and three-dimensional rescalings
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C Matching with the conventions of [1] C.1 Consistency of gauge field actions, Chern-Simons term and conventions C.2 Matching the uplift formulae
26 27 28
D (1, m, n) Superstrata in six dimensions D.1 Six-dimensional BPS equations D.2 The solution D.3 Tuning the asymptotic geometry D.4 Regularity and CTC analysis
30 31 32 34 35
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JHEP10(2020)030
2 The 2.1 2.2 2.3 2
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