Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N=4, d=4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality invariants of the dyonic charges, the symmetry group of the...
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National Academy of Science of Ukraine
2008-10-01
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Online Access: | http://dx.doi.org/10.3842/SIGMA.2008.068 |
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doaj-f2cb03953f10434c90d989e3b3b42c642020-11-25T02:47:33ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592008-10-014068Wall Crossing, Discrete Attractor Flow and Borcherds AlgebraMiranda C.N. ChengErik P. VerlindeThe appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N=4, d=4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality invariants of the dyonic charges, the symmetry group of the root system as the extended S-duality group PGL(2,Z) of the theory, and the walls of Weyl chambers as the walls of marginal stability for the relevant two-centered solutions. This leads to an interpretation for the Weyl group as the group of wall-crossing, or the group of discrete attractor flows. Furthermore we propose an equivalence between a ''second-quantized multiplicity'' of a charge- and moduli-dependent highest weight vector and the dyon degeneracy, and show that the wall-crossing formula following from our proposal agrees with the wall-crossing formula obtained from the supergravity analysis. This can be thought of as providing a microscopic derivation of the wall-crossing formula of this theory.http://dx.doi.org/10.3842/SIGMA.2008.068generalized Kac-Moody algebrablack holedyons |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Miranda C.N. Cheng Erik P. Verlinde |
spellingShingle |
Miranda C.N. Cheng Erik P. Verlinde Wall Crossing, Discrete Attractor Flow and Borcherds Algebra Symmetry, Integrability and Geometry: Methods and Applications generalized Kac-Moody algebra black hole dyons |
author_facet |
Miranda C.N. Cheng Erik P. Verlinde |
author_sort |
Miranda C.N. Cheng |
title |
Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
title_short |
Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
title_full |
Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
title_fullStr |
Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
title_full_unstemmed |
Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
title_sort |
wall crossing, discrete attractor flow and borcherds algebra |
publisher |
National Academy of Science of Ukraine |
series |
Symmetry, Integrability and Geometry: Methods and Applications |
issn |
1815-0659 |
publishDate |
2008-10-01 |
description |
The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N=4, d=4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality invariants of the dyonic charges, the symmetry group of the root system as the extended S-duality group PGL(2,Z) of the theory, and the walls of Weyl chambers as the walls of marginal stability for the relevant two-centered solutions. This leads to an interpretation for the Weyl group as the group of wall-crossing, or the group of discrete attractor flows. Furthermore we propose an equivalence between a ''second-quantized multiplicity'' of a charge- and moduli-dependent highest weight vector and the dyon degeneracy, and show that the wall-crossing formula following from our proposal agrees with the wall-crossing formula obtained from the supergravity analysis. This can be thought of as providing a microscopic derivation of the wall-crossing formula of this theory. |
topic |
generalized Kac-Moody algebra black hole dyons |
url |
http://dx.doi.org/10.3842/SIGMA.2008.068 |
work_keys_str_mv |
AT mirandacncheng wallcrossingdiscreteattractorflowandborcherdsalgebra AT erikpverlinde wallcrossingdiscreteattractorflowandborcherdsalgebra |
_version_ |
1724752866780905472 |