Abstract
The effective action of superstring theory or M-theory is approximated by supergravity in the low energy limit, and quantum corrections to the supergravity are taken into account by including higher derivative terms. In this paper, we consider equations of motion with those higher derivative terms in M-theory and solve them to derive quantum M-wave solution. A quantum black 0-brane solution is also obtained by Kaluza-Klein dimensional reduction of the M-wave solution. The quantum black 0-brane is asymptotically flat and uniquely determined by imposing appropriate conditions. The mass and the R-R charge of the quantum black 0-brane are derived by using the ADM mass and the charge formulae, and we see that only the mass is affected by the quantum correction. Various limits of the quantum black 0-brane are also considered, and especially we show that an internal energy in the near horizon limit is correctly reproduced.
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References
J. Polchinski, Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [INSPIRE].
G.W. Gibbons and K.-I. Maeda, Black holes and membranes in higher dimensional theories with dilaton fields, Nucl. Phys. B 298 (1988) 741 [INSPIRE].
G.T. Horowitz and A. Strominger, Black strings and p-branes, Nucl. Phys. B 360 (1991) 197 [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
A. Dabholkar, Exact counting of black hole microstates, Phys. Rev. Lett. 94 (2005) 241301 [hep-th/0409148] [INSPIRE].
H. Ooguri, A. Strominger and C. Vafa, Black hole attractors and the topological string, Phys. Rev. D 70 (2004) 106007 [hep-th/0405146] [INSPIRE].
D.J. Gross and E. Witten, Superstring modifications of Einstein’s equations, Nucl. Phys. B 277 (1986) 1 [INSPIRE].
D.J. Gross and J.H. Sloan, The quartic effective action for the heterotic string, Nucl. Phys. B 291 (1987) 41 [INSPIRE].
M.T. Grisaru, A.E.M. van de Ven and D. Zanon, Four loop β-function for the N = 1 and N =2 supersymmetric nonlinear σ-model in two-dimensions, Phys. Lett. B 173 (1986) 423 [INSPIRE].
M.T. Grisaru and D. Zanon, σ model superstring corrections to the Einstein-Hilbert action, Phys. Lett. B 177 (1986) 347 [INSPIRE].
A.A. Tseytlin, R 4 terms in 11 dimensions and conformal anomaly of (2, 0) theory, Nucl. Phys. B 584 (2000) 233 [hep-th/0005072] [INSPIRE].
K. Becker and M. Becker, Supersymmetry breaking, M-theory and fluxes, JHEP 07 (2001) 038 [hep-th/0107044] [INSPIRE].
G. Policastro and D. Tsimpis, R 4 , purified, Class. Quant. Grav. 23 (2006) 4753 [hep-th/0603165] [INSPIRE].
M. de Roo, H. Suelmann and A. Wiedemann, Supersymmetric R 4 actions in ten-dimensions, Phys. Lett. B 280 (1992) 39 [INSPIRE].
M. de Roo, H. Suelmann and A. Wiedemann, The supersymmetric effective action of the heterotic string in ten-dimensions, Nucl. Phys. B 405 (1993) 326 [hep-th/9210099] [INSPIRE].
H. Suelmann, String effective actions and supersymmetry, Ph.D. thesis, Groningen University, Groningen The Netherlands (1994) [INSPIRE].
K. Peeters, P. Vanhove and A. Westerberg, Supersymmetric higher derivative actions in ten-dimensions and eleven-dimensions, the associated superalgebras and their formulation in superspace, Class. Quant. Grav. 18 (2001) 843 [hep-th/0010167] [INSPIRE].
Y. Hyakutake and S. Ogushi, Higher derivative corrections to eleven dimensional supergravity via local supersymmetry, JHEP 02 (2006) 068 [hep-th/0601092] [INSPIRE].
Y. Hyakutake, Toward the determination of R 3 F 2 terms in M-theory, Prog. Theor. Phys. 118 (2007) 109 [hep-th/0703154] [INSPIRE].
C.G. Callan Jr., R.C. Myers and M.J. Perry, Black holes in string theory, Nucl. Phys. B 311 (1989) 673 [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 534 (1998) 202 [hep-th/9805156] [INSPIRE].
S. de Haro, A. Sinkovics and K. Skenderis, On α′ corrections to D-brane solutions, Phys. Rev. D 68 (2003) 066001 [hep-th/0302136] [INSPIRE].
A. Sen, Stretching the horizon of a higher dimensional small black hole, JHEP 07 (2005) 073 [hep-th/0505122] [INSPIRE].
A. Buchel, Higher derivative corrections to near-extremal black holes in type IIB supergravity, Nucl. Phys. B 750 (2006) 45 [hep-th/0604167] [INSPIRE].
H. Saida and J. Soda, Statistical entropy of BTZ black hole in higher curvature gravity, Phys. Lett. B 471 (2000) 358 [gr-qc/9909061] [INSPIRE].
Y. Hyakutake, Quantum near-horizon geometry of a black 0-brane, Prog. Theor. Exp. Phys. 2014 (2014) 033B04 [arXiv:1311.7526] [INSPIRE].
D.N. Kabat, G. Lifschytz and D.A. Lowe, Black hole thermodynamics from calculations in strongly coupled gauge theory, Int. J. Mod. Phys. A 16 (2001) 856 [hep-th/0007051] [INSPIRE].
M. Hanada, J. Nishimura and S. Takeuchi, Non-lattice simulation for supersymmetric gauge theories in one dimension, Phys. Rev. Lett. 99 (2007) 161602 [arXiv:0706.1647] [INSPIRE].
S. Catterall and T. Wiseman, Towards lattice simulation of the gauge theory duals to black holes and hot strings, JHEP 12 (2007) 104 [arXiv:0706.3518] [INSPIRE].
M. Hanada, Y. Hyakutake, J. Nishimura and S. Takeuchi, Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics, Phys. Rev. Lett. 102 (2009) 191602 [arXiv:0811.3102] [INSPIRE].
D. Kadoh and S. Kamata, One dimensional supersymmetric Yang-Mills theory with 16 supercharges, PoS(LATTICE 2012)064 [arXiv:1212.4919] [INSPIRE].
J. Nishimura, The origin of space-time as seen from matrix model simulations, Prog. Theor. Exp. Phys. 2012 (2012) 01A101 [arXiv:1205.6870] [INSPIRE].
M. Hanada, Y. Hyakutake, G. Ishiki and J. Nishimura, Holographic description of a quantum black hole on a computer, Science 344 (2014) 882 [INSPIRE].
M. Hanada, Does Yang-Mills theory describe quantum gravity?, arXiv:1407.5322 [INSPIRE].
P.K. Townsend, The eleven-dimensional supermembrane revisited, Phys. Lett. B 350 (1995) 184 [hep-th/9501068] [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
E. Cremmer, B. Julia and J. Scherk, Supergravity theory in eleven-dimensions, Phys. Lett. B 76 (1978) 409 [INSPIRE].
M. Huq and M.A. Namazie, Kaluza-Klein supergravity in ten-dimensions, Class. Quant. Grav. 2 (1985) 293 [Erratum ibid. 2 (1985) 597] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
R. Kallosh and A. Rajaraman, Vacua of M-theory and string theory, Phys. Rev. D 58 (1998) 125003 [hep-th/9805041] [INSPIRE].
M.B. Green, M. Gutperle and P. Vanhove, One loop in eleven-dimensions, Phys. Lett. B 409 (1997) 177 [hep-th/9706175] [INSPIRE].
M.B. Green, H.-H. Kwon and P. Vanhove, Two loops in eleven-dimensions, Phys. Rev. D 61 (2000) 104010 [hep-th/9910055] [INSPIRE].
M.B. Green, J.G. Russo and P. Vanhove, Non-renormalisation conditions in type-II string theory and maximal supergravity, JHEP 02 (2007) 099 [hep-th/0610299] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
Y. Hyakutake, Super Virasoro algebra from supergravity, Phys. Rev. D 87 (2013) 045028 [arXiv:1211.3547] [INSPIRE].
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Hyakutake, Y. Quantum M-wave and black 0-brane. J. High Energ. Phys. 2014, 75 (2014). https://doi.org/10.1007/JHEP09(2014)075
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DOI: https://doi.org/10.1007/JHEP09(2014)075