Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories
Abstract
For G = G(ℝ), a split, simply connected, semisimple Lie group of rank n and K the maximal compact subgroup of G, we give a method for computing Iwasawa coordinates of K∖G using the Chevalley generators and the Steinberg presentation. When K∖G is a scalar coset for a supergravity theory in dimensions ≥3, we determine the action of the integral form G(ℤ) on K∖G. We give explicit results for the action of the discrete U-duality groups SL{sub 2}(ℤ) and E{sub 7}(ℤ) on the scalar cosets SO(2)∖SL{sub 2}(ℝ) and [SU(8)/( ± Id)]∖E{sub 7(+7)}(ℝ) for type IIB supergravity in ten dimensions and 11-dimensional supergravity reduced to D = 4 dimensions, respectively. For the former, we use this to determine the discrete U-duality transformations on the scalar sector in the Borel gauge and we describe the discrete symmetries of the dyonic charge lattice. We determine the spectrum-generating symmetry group for fundamental BPS solitons of type IIB supergravity in D = 10 dimensions at the classical level and we propose an analog of this symmetry at the quantum level. We indicate how our methods can be used to study the orbits of discrete U-duality groups in general.
- Authors:
-
- Mathematics Rutgers University, Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854 (United States)
- Mathematics & Statistics, University of Canberra, ACT 2601 (Australia)
- Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260 (United States)
- Publication Date:
- OSTI Identifier:
- 22479547
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Mathematical Physics
- Additional Journal Information:
- Journal Volume: 56; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DUALITY; LIE GROUPS; SOLITONS; SPACE; SUPERGRAVITY
Citation Formats
Carbone, Lisa, Murray, Scott H., and Sati, Hisham. Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories. United States: N. p., 2015.
Web. doi:10.1063/1.4929538.
Carbone, Lisa, Murray, Scott H., & Sati, Hisham. Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories. United States. https://doi.org/10.1063/1.4929538
Carbone, Lisa, Murray, Scott H., and Sati, Hisham. 2015.
"Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories". United States. https://doi.org/10.1063/1.4929538.
@article{osti_22479547,
title = {Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories},
author = {Carbone, Lisa and Murray, Scott H. and Sati, Hisham},
abstractNote = {For G = G(ℝ), a split, simply connected, semisimple Lie group of rank n and K the maximal compact subgroup of G, we give a method for computing Iwasawa coordinates of K∖G using the Chevalley generators and the Steinberg presentation. When K∖G is a scalar coset for a supergravity theory in dimensions ≥3, we determine the action of the integral form G(ℤ) on K∖G. We give explicit results for the action of the discrete U-duality groups SL{sub 2}(ℤ) and E{sub 7}(ℤ) on the scalar cosets SO(2)∖SL{sub 2}(ℝ) and [SU(8)/( ± Id)]∖E{sub 7(+7)}(ℝ) for type IIB supergravity in ten dimensions and 11-dimensional supergravity reduced to D = 4 dimensions, respectively. For the former, we use this to determine the discrete U-duality transformations on the scalar sector in the Borel gauge and we describe the discrete symmetries of the dyonic charge lattice. We determine the spectrum-generating symmetry group for fundamental BPS solitons of type IIB supergravity in D = 10 dimensions at the classical level and we propose an analog of this symmetry at the quantum level. We indicate how our methods can be used to study the orbits of discrete U-duality groups in general.},
doi = {10.1063/1.4929538},
url = {https://www.osti.gov/biblio/22479547},
journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 10,
volume = 56,
place = {United States},
year = {Thu Oct 15 00:00:00 EDT 2015},
month = {Thu Oct 15 00:00:00 EDT 2015}
}