Abstract
It has long been conjectured that the large N deconfinement phase transition of \( \mathcal{N} \) = 4 SU(N) super-Yang-Mills corresponds via AdS/CFT to the Hawking-Page transition in which black holes dominate the thermal ensemble, and quantitative evidence of this has come through the recent matching of the superconformal index of \( \frac{1}{16} \)-BPS states to the supersymmetric black hole entropy. We introduce the half-BPS Gukov-Witten surface defect as a probe of the superconformal index, which also serves as an order parameter for the deconfinement transition. This can be studied directly in field theory as a modification of the usual unitary matrix model or in the dual description as a D3-brane probe in the background of a (complex) supersymmetric black hole. Using a saddle point approximation, we determine our defect index in the large N limit as a simple function of the chemical potentials and show independently that it is reproduced by the renormalized action of the brane in the black hole background. Along the way, we also comment on the Cardy limit and the thermodynamics of the D3-brane in the generalized ensemble. The defect index sharply distinguishes between the confining and the deconfining phases of the gauge theory and thus is a supersymmetric non-perturbative order parameter for these large N phase transitions which deserves further investigation. Finally, our work provides an example where the properties of a black hole coupled to an external system can be analyzed precisely.
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Acknowledgments
We would like to thank Ofer Aharony, Francesco Benini, Simone Giombi, Seok Kim, Zohar Komargodski, Shota Komatsu, Henry Lin, Juan Maldacena, Ohad Mamroud, Mark Mezei, Sameer Murthy, Leopoldo Pando Zayas, Sahand Seifnashri, Joaquin Turiaci, and Edward Witten for helpful discussions and comments on the draft. Y.C. is supported by a Procter Fellowship from Princeton University. M.H. is supported by the U.S. Department of Energy Grant DE-SC0009988, the Sivian Fund, and the Institute for Advanced Study. The work of YW was supported in part by NSF grant PHY-2210420 and by the Simons Junior Faculty Fellows program.
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Chen, Y., Heydeman, M., Wang, Y. et al. Probing supersymmetric black holes with surface defects. J. High Energ. Phys. 2023, 136 (2023). https://doi.org/10.1007/JHEP10(2023)136
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DOI: https://doi.org/10.1007/JHEP10(2023)136