Abstract
We study to what extent, and in what form, the notion of gauge-string duality may persist at finite N. It is shown, in the half-BPS sector, that the states of D3 giant graviton branes in AdS5 × S5 are holographically dual to certain auxiliary ghosts that compensate for finite N trace relations in U(N) \( \mathcal{N} \) = 4 super Yang-Mills. The complex formed from spaces of states of bulk D3 giants is observed to furnish a BRST-like resolution of the half-BPS Hilbert space of U(N) \( \mathcal{N} \) = 4 SYM at finite N. We argue that the identification between the states of certain bulk D-branes and the auxiliary ghosts in the boundary holds rather generally at vanishing ’t Hooft coupling λ = 0. We propose that a complex, which furnishes a BRST-like resolution of the finite N Hilbert space of a boundary U(N) gauge theory at λ = 0, should be identified as the space of states of the dual string theory in the α′ → ∞ limit. The Lefschetz trace formula provides the holographic map in this regime, where bulk observables are computed by taking the alternating sum of the expectation values in an ensemble of states built on each open string vacuum. The giant graviton expansion is recovered and generalized in a limit of the resolution.
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Acknowledgments
I thank D. Belayneh, M. R. Gaberdiel, D. Gaiotto, M. Heydeman, L. V. Iliesiu, S. Komatsu, W. Li, E. J. Martinec, H. Murali, S. S. Pufu, S. Raghavendran, P. Vieira, and E. Witten for helpful discussions. I am especially grateful to D. Gaiotto for many valuable suggestions and careful reading of the draft. I thank the organizers of the Precision Holography workshop at CERN and the organizers of the QFT & Strings seminar at ETH Zürich for the opportunity to present early versions of this work. I am thankful for the hospitality of Institut für Theoretische Physik at ETH Zürich, where parts of this work was done.
I am supported by the Perimeter Institute for Theoretical Physics and in part by the NSERC Discovery Grant program and the Simons Collaboration on Confinement and QCD Strings. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
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Lee, J.H. Trace relations and open string vacua. J. High Energ. Phys. 2024, 224 (2024). https://doi.org/10.1007/JHEP02(2024)224
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DOI: https://doi.org/10.1007/JHEP02(2024)224