Abstract
We study correlation functions of two AdS giant gravitons in AdS5 × S5 and a BPS supergravity mode using holography. In the gauge theory these are described by BPS correlators of Schur polynomials of fully-symmetric representations and a single trace operator. We find full agreement between the semiclassical gravity and gauge theory computations at large N, for both diagonal and off-diagonal structure constants. Our analysis in \( \mathcal{N} \) = 4 SYM provides a simpler derivation to the results in the literature, and it can be readily generalized to operators describing bound states of AdS giant gravitons as well as bubbling geometries.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N = 4 SYM theory, Adv. Theor. Math. Phys. 5 (2002) 809 [hep-th/0111222] [INSPIRE].
Y. Jiang, S. Komatsu and E. Vescovi, Structure constants in N = 4 SYM at finite coupling as worldsheet g-function, JHEP 07 (2020) 037 [arXiv:1906.07733] [INSPIRE].
G. Chen, R. de Mello Koch, M. Kim and H.J.R. Van Zyl, Absorption of closed strings by giant gravitons, JHEP 10 (2019) 133 [arXiv:1908.03553] [INSPIRE].
P. Yang, Y. Jiang, S. Komatsu and J.-B. Wu, D-branes and orbit average, SciPost Phys. 12 (2022) 055 [arXiv:2103.16580] [INSPIRE].
A. Bissi, C. Kristjansen, D. Young and K. Zoubos, Holographic three-point functions of giant gravitons, JHEP 06 (2011) 085 [arXiv:1103.4079] [INSPIRE].
D.E. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The operator product expansion for Wilson loops and surfaces in the large N limit, Phys. Rev. D 59 (1999) 105023 [hep-th/9809188] [INSPIRE].
S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large N, Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].
R. Roiban and A.A. Tseytlin, On semiclassical computation of 3-point functions of closed string vertex operators in AdS5 × S5, Phys. Rev. D 82 (2010) 106011 [arXiv:1008.4921] [INSPIRE].
R. Hernandez, Three-point correlation functions from semiclassical circular strings, J. Phys. A 44 (2011) 085403 [arXiv:1011.0408] [INSPIRE].
S. Ryang, Correlators of vertex operators for circular strings with winding numbers in AdS5 × S5, JHEP 01 (2011) 092 [arXiv:1011.3573] [INSPIRE].
G. Georgiou, Two and three-point correlators of operators dual to folded string solutions at strong coupling, JHEP 02 (2011) 046 [arXiv:1011.5181] [INSPIRE].
K. Zarembo, Holographic three-point functions of semiclassical states, JHEP 09 (2010) 030 [arXiv:1008.1059] [INSPIRE].
J.G. Russo and A.A. Tseytlin, Large spin expansion of semiclassical 3-point correlators in AdS5 × S5, JHEP 02 (2011) 029 [arXiv:1012.2760] [INSPIRE].
M.S. Costa, R. Monteiro, J.E. Santos and D. Zoakos, On three-point correlation functions in the gauge/gravity duality, JHEP 11 (2010) 141 [arXiv:1008.1070] [INSPIRE].
D. Bak, B. Chen and J.-B. Wu, Holographic correlation functions for open strings and branes, JHEP 06 (2011) 014 [arXiv:1103.2024] [INSPIRE].
P. Caputa, R. de Mello Koch and K. Zoubos, Extremal versus non-extremal correlators with giant gravitons, JHEP 08 (2012) 143 [arXiv:1204.4172] [INSPIRE].
H. Lin, Giant gravitons and correlators, JHEP 12 (2012) 011 [arXiv:1209.6624] [INSPIRE].
S. Hirano, C. Kristjansen and D. Young, Giant gravitons on AdS4 × CP3 and their holographic three-point functions, JHEP 07 (2012) 006 [arXiv:1205.1959] [INSPIRE].
C. Kristjansen, S. Mori and D. Young, On the regularization of extremal three-point functions involving giant gravitons, Phys. Lett. B 750 (2015) 379 [arXiv:1507.03965] [INSPIRE].
Y. Jiang, S. Komatsu and E. Vescovi, Exact three-point functions of determinant operators in planar N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 123 (2019) 191601 [arXiv:1907.11242] [INSPIRE].
D. Berenstein and S. Wang, BPS coherent states and localization, JHEP 08 (2022) 164 [arXiv:2203.15820] [INSPIRE].
A. Monin, D. Pirtskhalava, R. Rattazzi and F.K. Seibold, Semiclassics, Goldstone bosons and CFT data, JHEP 06 (2017) 011 [arXiv:1611.02912] [INSPIRE].
Z. Bajnok, R.A. Janik and A. Wereszczyński, HHL correlators, orbit averaging and form factors, JHEP 09 (2014) 050 [arXiv:1404.4556] [INSPIRE].
K. Fujii, T. Kashiwa and S. Sakoda, Coherent states over Grassmann manifolds and the WKB exactness in path integral, J. Math. Phys. 37 (1996) 567 [hep-th/9509022] [INSPIRE].
M. Zielenkiewicz, Integration over homogeneous spaces for classical Lie groups using iterated residues at infinity, Open Math. 12 (2014) 574.
H.J. Kim, L.J. Romans and P. van Nieuwenhuizen, The mass spectrum of chiral N = 2 D = 10 supergravity on S5, Phys. Rev. D 32 (1985) 389 [INSPIRE].
D. Berenstein and A. Holguin, Open giant magnons on LLM geometries, JHEP 01 (2021) 080 [arXiv:2010.02236] [INSPIRE].
R. de Mello Koch, J. Smolic and M. Smolic, Giant gravitons — with strings attached (II), JHEP 09 (2007) 049 [hep-th/0701067] [INSPIRE].
A. Holguin and S. Wang, Giant gravitons, Harish-Chandra integrals, and BPS states in symplectic and orthogonal N = 4 SYM, JHEP 10 (2022) 078 [arXiv:2206.00020] [INSPIRE].
H. Lin, Coherent state excitations and string-added coherent states in gauge-gravity correspondence, Nucl. Phys. B 986 (2023) 116066 [arXiv:2206.06524] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].
P. Yang, Y. Jiang, S. Komatsu and J.-B. Wu, Three-point functions in ABJM and Bethe Ansatz, JHEP 01 (2022) 002 [arXiv:2103.15840] [INSPIRE].
Acknowledgments
AH would like to thank David Berenstein for collaboration on related topics. We also thank Shota Komatsu, Charlotte Kristjansen, and particularly Robert de Mello Koch for stimulating discussions, as well as the organizers of the KITP programs Confinement, Flux Tubes, and Large N and Integrability in String, Field, and Condensed Matter Theory. AH and WW were supported in part by funds from the University of California. A.H. was supported in part by the Department of Energy under grant DE-SC0011702. WW was supported in part by the U.S. Department of Energy under Grant No. DE-SC0023275.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2211.03805
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Holguin, A., Weng, W.W. Orbit averaging coherent states: holographic three-point functions of AdS giant gravitons. J. High Energ. Phys. 2023, 167 (2023). https://doi.org/10.1007/JHEP05(2023)167
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2023)167