- Open Access
Supersymmetric D-brane probes in 4D attractors
Phys. Rev. D 113, 066012 – Published 20 March, 2026
DOI: https://doi.org/10.1103/gnxr-g3fv
Abstract
We extend the -symmetry analysis of supersymmetric D-brane probes in the attractor geometry, originally performed by Simons, Strominger, Thompson, and Yin to also include stationary—but nonstatic—worldlines carrying angular momentum along the 2-sphere. We demonstrate that certain special trajectories, with fixed radius and orbital velocity, solve the equations of motion and moreover satisfy a supersymmetry preserving condition, thus defining new -BPS configurations. Furthermore, these classical paths are shown to saturate a lower bound for the Hamiltonian generating global time translations, with the corresponding minimal energy depending on a generalized angular momentum vector . The direction of the latter, in turn, determines exactly which supercharges remain unbroken. Our results reveal a richer spectrum of (multiparticle) supersymmetric states in , which can be organized into distinct selection sectors labeled by the conserved charges. This construction has direct applications in black hole microstate counting, the analysis of probe dynamics, and holography.
Physics Subject Headings (PhySH)
Article Text
References (50)
- A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379, 99 (1996).
- J. M. Maldacena, A. Strominger, and E. Witten, Black hole entropy in M theory, J. High Energy Phys. 12 (1997) 002.
- C. Vafa, Black holes and Calabi-Yau threefolds, Adv. Theor. Math. Phys. 2, 207 (1998).
- S. Ferrara, R. Kallosh, and A. Strominger, extremal black holes, Phys. Rev. D 52, R5412 (1995).
- A. Strominger, Macroscopic entropy of extremal black holes, Phys. Lett. B 383, 39 (1996).
- S. Ferrara and R. Kallosh, Supersymmetry and attractors, Phys. Rev. D 54, 1514 (1996).
- S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54, 1525 (1996).
- J. M. Maldacena, J. Michelson, and A. Strominger, Anti–de Sitter fragmentation, J. High Energy Phys. 02 (1999) 011.
- B. Pioline and J. Troost, Schwinger pair production in AdS(2), J. High Energy Phys. 03 (2005) 043.
- A. Castellano, D. Lüst, C. Montella, and M. Zatti, Quantum Calabi-Yau black holes and nonperturbative D0-brane effects, arXiv:2505.15920.
- A. Strominger, AdS(2) quantum gravity and string theory, J. High Energy Phys. 01 (1999) 007.
- D. Gaiotto, A. Strominger, and X. Yin, Superconformal black hole quantum mechanics, J. High Energy Phys. 11 (2005) 017.
- D. Gaiotto, A. Simons, A. Strominger, and X. Yin, D0-branes in black hole attractors, J. High Energy Phys. 03 (2006) 019.
- F. Denef, D. Gaiotto, A. Strominger, D. Van den Bleeken, and X. Yin, Black hole deconstruction, J. High Energy Phys. 03 (2012) 071.
- T. Azeyanagi, T. Nishioka, and T. Takayanagi, Near extremal black hole entropy as entanglement entropy via AdS(2)/CFT(1), Phys. Rev. D 77, 064005 (2008).
- A. Sen, Quantum entropy function from AdS(2)/CFT(1) correspondence, Int. J. Mod. Phys. A 24, 4225 (2009).
- K. Becker, M. Becker, and A. Strominger, Five-branes, membranes and nonperturbative string theory, Nucl. Phys. B456, 130 (1995).
- E. Bergshoeff, R. Kallosh, T. Ortin, and G. Papadopoulos, Kappa symmetry, supersymmetry and intersecting branes, Nucl. Phys. B502, 149 (1997).
- M. Billo, S. Cacciatori, F. Denef, P. Fre, A. Van Proeyen, and D. Zanon, The 0-brane action in a general supergravity background, Classical Quantum Gravity 16, 2335 (1999).
- J. Simon, Brane effective actions, Kappa-symmetry and applications, Living Rev. Relativity 15, 3 (2012).
- A. Simons, A. Strominger, D. M. Thompson, and X. Yin, Supersymmetric branes in , Phys. Rev. D 71, 066008 (2005).
- W. Li and A. Strominger, Supersymmetric probes in a rotating 5D attractor, Phys. Lett. B 659, 407 (2008).
- J. C. Breckenridge, R. C. Myers, A. W. Peet, and C. Vafa, D-branes and spinning black holes, Phys. Lett. B 391, 93 (1997).
- D. Gaiotto, A. Strominger, and X. Yin, From AdS(3)/CFT(2) to black holes/topological strings, J. High Energy Phys. 09 (2007) 050.
- H. Ooguri, A. Strominger, and C. Vafa, Black hole attractors and the topological string, Phys. Rev. D 70, 106007 (2004).
- A. Sen, Black hole entropy function, attractors and precision counting of microstates, Gen. Relativ. Gravit. 40, 2249 (2008).
- A. Dabholkar, J. Gomes, and S. Murthy, Quantum black holes, localization and the topological string, J. High Energy Phys. 06 (2011) 019.
- M. Dedushenko and E. Witten, Some details on the Gopakumar-Vafa and Ooguri-Vafa formulas, Adv. Theor. Math. Phys. 20, 1 (2016).
- L. V. Iliesiu, S. Murthy, and G. J. Turiaci, Black hole microstate counting from the gravitational path integral, J. High Energy Phys. 08 (2025) 152.
- D. Cassani and S. Murthy, Quantum black holes: Supersymmetry and exact results, arXiv:2502.15360.
- N. Alonso-Alberca, E. Lozano-Tellechea, and T. Ortin, Geometric construction of Killing spinors and supersymmetry algebras in homogeneous space-times, Classical Quantum Gravity 19, 6009 (2002).
- G. W. Gibbons and P. K. Townsend, Vacuum interpolation in supergravity via super p-branes, Phys. Rev. Lett. 71, 3754 (1993).
- J. M. Maldacena, The large limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998).
- S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428, 105 (1998).
- E. Witten, Anti–de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998).
- O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Large field theories, string theory and gravity, Phys. Rep. 323, 183 (2000).
- G. W. Gibbons and C. M. Hull, A Bogomolny bound for general relativity and solitons in supergravity, Phys. Lett. 109B, 190 (1982).
- G. W. Gibbons and K.-i. Maeda, Black holes and membranes in higher dimensional theories with dilaton fields, Nucl. Phys. B298, 741 (1988).
- D. Garfinkle, G. T. Horowitz, and A. Strominger, Charged black holes in string theory, Phys. Rev. D 43, 3140 (1991); 45, 3888(E) (1992).
- A. Castellano and M. Zatti, Black hole entropy, quantum corrections and EFT transitions, J. High Energy Phys. 08 (2025) 112.
- P. Claus, M. Derix, R. Kallosh, J. Kumar, P. K. Townsend, and A. Van Proeyen, Black holes and superconformal mechanics, Phys. Rev. Lett. 81, 4553 (1998).
- A. Comtet, On the Landau levels on the hyperbolic plane, Ann. Phys. (N.Y.) 173, 185 (1987).
- G. V. Dunne, Hilbert space for charged particles in perpendicular magnetic fields, Ann. Phys. (N.Y.) 215, 233 (1992).
- G. W. Gibbons, Aspects of supergravity theories, in XV GIFT Seminar on Supersymmetry and Supergravity (World Scientific, Singapore, 1985), p. 6.
- R. Kallosh, Supersymmetric black holes, Phys. Lett. B 282, 80 (1992).
- R. Kallosh and A. W. Peet, Dilaton black holes near the horizon, Phys. Rev. D 46, R5223 (1992).
- S. Ferrara, Bertotti-Robinson geometry and supersymmetry, in 12th Italian Conference on General Relativity and Gravitational Physics (1997), 1, pp. 135–147, 1, arXiv:hep-th/9701163.
- A. Ceresole, R. D’Auria, and S. Ferrara, The symplectic structure of supergravity and its central extension, Nucl. Phys. B, Proc. Suppl. 46, 67 (1996).
- L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara, P. Fre, and T. Magri, supergravity and superYang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map, J. Geom. Phys. 23, 111 (1997).
- T. Ortin, Gravity and Strings, Cambridge Monographs on Mathematical Physics, 2nd ed. (Cambridge University Press, Cambridge, England, 2015).