The structure of BPS equations for ambi-polar microstate geometries
Abstract
Ambi-polar metrics, defined so as to allow the signature to change from +4 to -4 across hypersurfaces, are a mainstay in the construction of BPS microstate geometries. This paper elucidates the cohomology of these spaces so as to simplify greatly the construction of infinite families of fluctuating 'harmonic' magnetic fluxes. It is argued that such fluxes should come from scalar, harmonic pre-potentials whose source loci are holomorphic divisors. This insight is obtained by exploring the Kähler structure of ambi-polar Gibbons–Hawking spaces and it is shown that differentiating the pre-potentials with respect to Kähler moduli yields solutions to the BPS equations for the electric potentials sourced by the magnetic fluxes. This suggests that harmonic analysis on ambi-polar spaces has a novel, and an extremely rich structure, that is deeply intertwined with the BPS equations. We illustrate our results using a family of two-centered solutions.
- Authors:
-
[1];
- Univ. of Southern California, Los Angeles, CA (United States). Dept. of Physics and Astronomy
- Univ. of Southern California, Los Angeles, CA (United States). Dept. of Physics and Astronomy. Dept. of Mathematics
- Publication Date:
- Research Org.:
- Univ. of Southern California, Los Angeles, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1611651
- Grant/Contract Number:
- SC0011687
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Classical and Quantum Gravity
- Additional Journal Information:
- Journal Volume: 36; Journal Issue: 1; Journal ID: ISSN 0264-9381
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Tyukov, Alexander, Walker, Robert, and Warner, Nicholas P. The structure of BPS equations for ambi-polar microstate geometries. United States: N. p., 2018.
Web. doi:10.1088/1361-6382/aaf133.
Tyukov, Alexander, Walker, Robert, & Warner, Nicholas P. The structure of BPS equations for ambi-polar microstate geometries. United States. https://doi.org/10.1088/1361-6382/aaf133
Tyukov, Alexander, Walker, Robert, and Warner, Nicholas P. Thu .
"The structure of BPS equations for ambi-polar microstate geometries". United States. https://doi.org/10.1088/1361-6382/aaf133. https://www.osti.gov/servlets/purl/1611651.
@article{osti_1611651,
title = {The structure of BPS equations for ambi-polar microstate geometries},
author = {Tyukov, Alexander and Walker, Robert and Warner, Nicholas P.},
abstractNote = {Ambi-polar metrics, defined so as to allow the signature to change from +4 to -4 across hypersurfaces, are a mainstay in the construction of BPS microstate geometries. This paper elucidates the cohomology of these spaces so as to simplify greatly the construction of infinite families of fluctuating 'harmonic' magnetic fluxes. It is argued that such fluxes should come from scalar, harmonic pre-potentials whose source loci are holomorphic divisors. This insight is obtained by exploring the Kähler structure of ambi-polar Gibbons–Hawking spaces and it is shown that differentiating the pre-potentials with respect to Kähler moduli yields solutions to the BPS equations for the electric potentials sourced by the magnetic fluxes. This suggests that harmonic analysis on ambi-polar spaces has a novel, and an extremely rich structure, that is deeply intertwined with the BPS equations. We illustrate our results using a family of two-centered solutions.},
doi = {10.1088/1361-6382/aaf133},
journal = {Classical and Quantum Gravity},
number = 1,
volume = 36,
place = {United States},
year = {Thu Dec 13 00:00:00 EST 2018},
month = {Thu Dec 13 00:00:00 EST 2018}
}
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