Charged solutions in 5D Chern-Simons supergravity

Máximo Bañados

doi:10.1103/PhysRevD.65.044014

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Charged solutions in 5D Chern-Simons supergravity

Máximo Bañados^*

Departamento de Física, P. Universidad Católica de Chile, Casilla 306, Santiago 22, Chile

^*mbanados@fis.puc.cl

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Phys. Rev. D 65, 044014 – Published 22 January, 2002

DOI: https://doi.org/10.1103/PhysRevD.65.044014

Abstract

A family of solutions with mass and electric charge of five-dimensional Chern-Simons supergravity is displayed. The action contains an extra term that changes the value of the cosmological constant, as considered by Horava. It is shown that the solutions approach asymptotically the Reissner-Nordström spacetime. The role of the torsion tensor in providing charged solutions is stressed.

References (30)

A. Achúcarro and P. K. Townsend, Phys. Lett. B 180, 89 (1986).
E. Witten, Nucl. Phys. B311, 4 (1988).
J. D. Brown and M. Henneaux, Commun. Math. Phys. 104, 207 (1986).
O. Coussaert, M. Henneaux, and P. van Driel, Class. Quantum Grav. 12, 2961 (1995).
M. Bañados, Phys. Rev. D 52, 5816 (1995).
S. Carlip, Phys. Rev. D 51, 632 (1995); ibid.55, 878 (1997).
M. Bañados, T. Brotz, and M. Ortiz, Nucl. Phys. B545, 3470 (1999).
S. Fernando and F. Mansouri, Phys. Lett. B 505, 206 (2001).
A. H. Chamseddine, Nucl. Phys. B346, 213 (1990).
R. Troncoso and J. Zanelli, Phys. Rev. D 58, 101703 (1998); hep-th/9902003.
M. Bañados, R. Troncoso, and J. Zanelli, Phys. Rev. D 54, 2605 (1996).
V. P. Nair and J. Schiff, Phys. Lett. B 246, 423 (1990); Nucl. Phys. B371, 329 (1992).
M. Bañados, L. J. Garay, and M. Henneaux, Phys. Rev. D 53, R593 (1996); Nucl. Phys. B476, 611 (1996).
A. Losev, G. Moore, N. Nekrasov, and S. Shatashvili, Nucl. Phys. B (Proc. Suppl.) 46, 130 (1996); Nucl. Phys. B484, 196 (1997).
J. Gegenberg and G. Kunstatter, Phys. Lett. B 478, 327 (2000).
M. Bañados, hep-th/0107214.
P. Horava, Phys. Rev. D 59, 046004 (1999).
E. Cremmer, B. Julia, and J. Scherk, Phys. Lett. 76B, 409 (1978).
W. Nahm, Nucl. Phys. B135, 149 (1978).
M. Bañados, C. Teitelboim, and J. Zanelli, Phys. Rev. D 49, 975 (1994).
L. Castellani, R. D’ Auria, and P. Fre, Supergravity and Superstrings: A Geometric Perspective. Vol. 2: Supergravity (World Scientific, Singapore, 1991), pp. 607–1371.
M. Bañados, Nucl. Phys. B (Proc. Suppl.) 88, 17 (2000).
D. G. Boulware and S. Deser, Phys. Rev. Lett. 55, 2656 (1985).
J. T. Wheeler, Nucl. Phys. B268, 737 (1986); ibid.B273, 732 (1986).
M. Bañados, C. Teitelboim, and J. Zanelli, Phys. Rev. Lett. 69, 1849 (1992); M. Bañados, M. Henneaux, C. Teitelboim, and J. Zanelli, Phys. Rev. D 48, 1506 (1993).
M. Bañados, Phys. Lett. B 501, 150 (2001).
Charge was introduced in [20] by adding to the action the term $\sqrt{- g} F^{μ ν} F_{μ ν},$ thus breaking the Chern-Simons structure.
See [23] for a description of this mechanism within the group manifold approach to supergravity, and [24] for a generalization.
These are actually a contribution to this equation from $R^{ab} R_{ab}$ as well. On the AdS background $R^{ab} = - Λ_{τ} e^{a} \land e^{b} + D κ^{ab}$ . Using Eq. (26) we find that $κ_{ab} e^{a} e^{b} =^{*} F$ and then $R^{ab} \land R_{ab} = Λ d^{*} F$ .
If $1 - τ < 0$ there are two zeros and the solution is de Sitter type.

[c1] A. Achúcarro and P. K. Townsend, Phys. Lett. B 180, 89 (1986).

[c2] E. Witten, Nucl. Phys. B311, 4 (1988).

[c3] J. D. Brown and M. Henneaux, Commun. Math. Phys. 104, 207 (1986).

[c4] O. Coussaert, M. Henneaux, and P. van Driel, Class. Quantum Grav. 12, 2961 (1995).

[c5] M. Bañados, Phys. Rev. D 52, 5816 (1995).

[c6] S. Carlip, Phys. Rev. D 51, 632 (1995); ibid.55, 878 (1997).

[c7] M. Bañados, T. Brotz, and M. Ortiz, Nucl. Phys. B545, 3470 (1999).

[c8] S. Fernando and F. Mansouri, Phys. Lett. B 505, 206 (2001).

[c9] A. H. Chamseddine, Nucl. Phys. B346, 213 (1990).

[c10] R. Troncoso and J. Zanelli, Phys. Rev. D 58, 101703 (1998); hep-th/9902003.

[c11] M. Bañados, R. Troncoso, and J. Zanelli, Phys. Rev. D 54, 2605 (1996).

[c12] V. P. Nair and J. Schiff, Phys. Lett. B 246, 423 (1990); Nucl. Phys. B371, 329 (1992).

[c13] M. Bañados, L. J. Garay, and M. Henneaux, Phys. Rev. D 53, R593 (1996); Nucl. Phys. B476, 611 (1996).

[c14] A. Losev, G. Moore, N. Nekrasov, and S. Shatashvili, Nucl. Phys. B (Proc. Suppl.) 46, 130 (1996); Nucl. Phys. B484, 196 (1997).

[c15] J. Gegenberg and G. Kunstatter, Phys. Lett. B 478, 327 (2000).

[c16] M. Bañados, hep-th/0107214.

[c17] P. Horava, Phys. Rev. D 59, 046004 (1999).

[c18] E. Cremmer, B. Julia, and J. Scherk, Phys. Lett. 76B, 409 (1978).

[c19] W. Nahm, Nucl. Phys. B135, 149 (1978).

[c20] M. Bañados, C. Teitelboim, and J. Zanelli, Phys. Rev. D 49, 975 (1994).

[c21] L. Castellani, R. D’ Auria, and P. Fre, Supergravity and Superstrings: A Geometric Perspective. Vol. 2: Supergravity (World Scientific, Singapore, 1991), pp. 607–1371.

[c22] M. Bañados, Nucl. Phys. B (Proc. Suppl.) 88, 17 (2000).

[c23] D. G. Boulware and S. Deser, Phys. Rev. Lett. 55, 2656 (1985).

[c24] J. T. Wheeler, Nucl. Phys. B268, 737 (1986); ibid.B273, 732 (1986).

[c25] M. Bañados, C. Teitelboim, and J. Zanelli, Phys. Rev. Lett. 69, 1849 (1992); M. Bañados, M. Henneaux, C. Teitelboim, and J. Zanelli, Phys. Rev. D 48, 1506 (1993).

[c26] M. Bañados, Phys. Lett. B 501, 150 (2001).

[c27] Charge was introduced in [20] by adding to the action the term $\sqrt{- g} F^{μ ν} F_{μ ν},$ thus breaking the Chern-Simons structure.

[c28] See [23] for a description of this mechanism within the group manifold approach to supergravity, and [24] for a generalization.

[c29] These are actually a contribution to this equation from $R^{ab} R_{ab}$ as well. On the AdS background $R^{ab} = - Λ_{τ} e^{a} \land e^{b} + D κ^{ab}$ . Using Eq. (26) we find that $κ_{ab} e^{a} e^{b} =^{*} F$ and then $R^{ab} \land R_{ab} = Λ d^{*} F$ .

[c30] If $1 - τ < 0$ there are two zeros and the solution is de Sitter type.

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Charged solutions in 5D Chern-Simons supergravity

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