Index theory and dynamical symmetry enhancement of M-horizons

Gutowski, J.; Papadopoulos, G.

doi:10.1007/JHEP05(2013)088

Index theory and dynamical symmetry enhancement of M-horizons

Mar 4, 2013

22 pages

Published in:

JHEP 05 (2013) 088

e-Print:

1303.0869 [hep-th]

DOI:

10.1007/JHEP05(2013)088

Report number:

DMUS--MP--13-05

View in:

pdf

reference search30 citations

Citations per year

Abstract: (Springer)

We show that near-horizon geometries of 11-dimensional supergravity preserve an even number of supersymmetries. The proof follows from Lichnerowicz type theorems for two horizon Dirac operators, the field equations and Bianchi identities, and the vanishing of the index of a Dirac operator on the 9-dimensional horizon sections. As a consequence of this, we also prove that all M-horizons with non-vanishing fluxes admit a subalgebra of symmetries.

Note:

Minor typos corrected. 22 pages, latex. Repeats equations and descriptions from arXiv:1207.7086

operator: Dirac
symmetry: enhancement
horizon
Bianchi identity
field equations
supersymmetry
supergravity

References(34)

Figures(0)

[1]

Vacuum interpolation in supergravity via super p-branes

G.W. Gibbons
(
- Cambridge U.
)
,
P.K. Townsend
(
- Cambridge U.
)

- Phys.Rev.Lett. 71 (1993) 3754-3757
•
e-Print:
- hep-th/9307049
•
DOI:
- 10.1103/PhysRevLett.71.3754

[2]

Symmetries of cosmological Cauchy horizons

Vincent Moncrief
(
- Yale U.
)
,
James Isenberg
(
- Oregon U., Dept. Math.
)

- Commun.Math.Phys. 89 (1983) 3, 387-413
•
DOI:
- 10.1007/BF01214662

[3]

On the rigidity theorem for space-times with a stationary event horizon or a compact Cauchy horizon

- Commun.Math.Phys. 204 (1999) 691-707
•
e-Print:
- gr-qc/9811021
•
DOI:
- 10.1007/s002200050662

[4]

Static M-horizons

- JHEP 01 (2012) 005
•
e-Print:
- 1106.3085
•
DOI:
- 10.1007/JHEP01(2012)005

[5]

M-Horizons

- JHEP 12 (2012) 100
•
e-Print:
- 1207.7086
•
DOI:
- 10.1007/JHEP12(2012)100

[6]

Large N field theories, string theory and gravity

Ofer Aharony
(
- Rutgers U., Piscataway
)
,
Steven S. Gubser
(
- Harvard U.
)
,
Juan Martin Maldacena
(
- Princeton, Inst. Advanced Study and
- Harvard U.
)
,
Hirosi Ooguri
(
- LBL, Berkeley and
- UC, Berkeley
)
,
Yaron Oz
(
- CERN
)

- Phys.Rept. 323 (2000) 183-386
•
e-Print:
- hep-th/9905111
•
DOI:
- 10.1016/S0370-1573(99)00083-6

[7]

Event horizons in static vacuum space-times

Werner Israel
(
- Alberta U. and
- Dublin Inst.
)

- Phys.Rev. 164 (1967) 1776-1779
•
DOI:
- 10.1103/PhysRev.164.1776

[8]

Axisymmetric Black Hole Has Only Two Degrees of Freedom

B. Carter
(
- Cambridge U., Inst. of Astron.
)

- Phys.Rev.Lett. 26 (1971) 331-333
•
DOI:
- 10.1103/PhysRevLett.26.331

[9]

Black holes in general relativity

S.W. Hawking
(
- Cambridge U.
)

- Commun.Math.Phys. 25 (1972) 152-166
•
DOI:
- 10.1007/BF01877517

[10]

Uniqueness of the Kerr black hole

D.C. Robinson
(
- King's Coll. London
)

- Phys.Rev.Lett. 34 (1975) 905-906
•
DOI:
- 10.1103/PhysRevLett.34.905

[11]

Event horizons in static electrovac space-times

Werner Israel
(
- Dublin Inst.
)

- Commun.Math.Phys. 8 (1968) 245-260
•
DOI:
- 10.1007/BF01645859

[12]

PROOF OF UNIQUENESS OF THE KERR-NEWMAN BLACK HOLE SOLUTION

P.O. Mazur
(
- Jagiellonian U.
)

- J.Phys.A 15 (1982) 3173-3180,
- J. Phys. A15 ( 1982) 3173-3180
•
DOI:
- 10.1088/0305-4470/15/10/021

[13]

Four decades of black hole uniqueness theorems, appeared in The Kerr spacetime: Rotating black holes in General Relativity, D. L. Wiltshire, M. Visser and S. M. Scott (eds.) Cambridge University Press (2009), pp 115-143