Abstract
We consider Schur line defect correlators in four dimensional \( \mathcal{N} \) = 4 U(N) SYM and their giant graviton expansion encoding finite N corrections to the large N limit. We compute in closed form the single giant graviton contribution to correlators with general insertions of \( \frac{1}{2} \)-BPS charged Wilson lines. For the 2-point function with fundamental and anti-fundamental Wilson lines, we match the result from fluctuations of two half-infinite strings ending on the giant graviton, recently proposed in arXiv:2403.11543. In particular, we prove exact factorization of the defect contribution with respect to wrapped D3 brane fluctuations representing the single giant graviton correction to the undecorated Schur index. This follows from a finite-difference representation of the Schur line defect index in terms of the index without defects, and similar factorization holds quite generally for more complicated defect configurations. In particular, the single giant graviton contribution to the 4-point function with two fundamental and two anti-fundamental lines is computed and discussed in this perspective.
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J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An Index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].
C. Romelsberger, Counting Chiral Primaries in \( \mathcal{N} \) = 1, d = 4 Superconformal Field Theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
C. Romelsberger, Calculating the Superconformal Index and Seiberg Duality, arXiv:0707.3702 [INSPIRE].
E. Witten, Constraints on Supersymmetry Breaking, Nucl. Phys. B 202 (1982) 253 [INSPIRE].
P. Agarwal et al., AdS Black Holes and Finite N Indices, Phys. Rev. D 103 (2021) 126006 [arXiv:2005.11240] [INSPIRE].
S. Murthy, The growth of the \( \frac{1}{16} \)-BPS index in 4d \( \mathcal{N} \) = 4 SYM, arXiv:2005.10843 [INSPIRE].
J. McGreevy, L. Susskind and N. Toumbas, Invasion of the Giant Gravitons from Anti-de Sitter Space, JHEP 06 (2000) 008 [hep-th/0003075] [INSPIRE].
C.-M. Chang and Y.-H. Lin, Holographic Covering and the Fortuity of Black Holes, arXiv:2402.10129 [INSPIRE].
E. Deddo, J.T. Liu, L.A. Pando Zayas and R.J. Saskowski, The Giant Graviton Expansion from Bubbling Geometry, arXiv:2402.19452 [INSPIRE].
Y. Imamura, Finite-N Superconformal Index via the AdS/CFT Correspondence, PTEP 2021 (2021) 123B05 [arXiv:2108.12090] [INSPIRE].
D. Gaiotto and J.H. Lee, The Giant Graviton Expansion, arXiv:2109.02545 [INSPIRE].
J.H. Lee, Exact Stringy Microstates from Gauge Theories, JHEP 11 (2022) 137 [arXiv:2204.09286] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The 4D Superconformal Index from Q-Deformed 2D Yang-Mills, Phys. Rev. Lett. 106 (2011) 241602 [arXiv:1104.3850] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, Gauge Theories and Macdonald Polynomials, Commun. Math. Phys. 319 (2013) 147 [arXiv:1110.3740] [INSPIRE].
C. Beem et al., Infinite Chiral Symmetry in Four Dimensions, Commun. Math. Phys. 336 (2015) 1359 [arXiv:1312.5344] [INSPIRE].
D. Gaiotto and T. Okazaki, Dualities of Corner Configurations and Supersymmetric Indices, JHEP 11 (2019) 056 [arXiv:1902.05175] [INSPIRE].
J. Bourdier, N. Drukker and J. Felix, The \( \mathcal{N} \) = 2 Schur index from free fermions, JHEP 01 (2016) 167 [arXiv:1510.07041] [INSPIRE].
J. Bourdier, N. Drukker and J. Felix, The exact Schur index of \( \mathcal{N} \) = 4 SYM, JHEP 11 (2015) 210 [arXiv:1507.08659] [INSPIRE].
Y. Pan and W. Peelaers, Exact Schur Index in Closed Form, Phys. Rev. D 106 (2022) 045017 [arXiv:2112.09705] [INSPIRE].
Y. Hatsuda and T. Okazaki, \( \mathcal{N} \) = 2∗ Schur indices, JHEP 01 (2023) 029 [arXiv:2208.01426] [INSPIRE].
B.-N. Du, M.-X. Huang and X. Wang, Schur indices for \( \mathcal{N} \) = 4 super-Yang-Mills with more general gauge groups, JHEP 03 (2024) 009 [arXiv:2311.08714] [INSPIRE].
R. Arai, S. Fujiwara, Y. Imamura and T. Mori, Schur index of the \( \mathcal{N} \) = 4U(N) supersymmetric Yang-Mills theory via the AdS/CFT correspondence, Phys. Rev. D 101 (2020) 086017 [arXiv:2001.11667] [INSPIRE].
R. Arai and Y. Imamura, Finite N Corrections to the Superconformal Index of S-fold Theories, PTEP 2019 (2019) 083B04 [arXiv:1904.09776] [INSPIRE].
R. Arai, S. Fujiwara, Y. Imamura and T. Mori, Finite N corrections to the superconformal index of orbifold quiver gauge theories, JHEP 10 (2019) 243 [arXiv:1907.05660] [INSPIRE].
R. Arai, S. Fujiwara, Y. Imamura and T. Mori, Finite N corrections to the superconformal index of toric quiver gauge theories, PTEP 2020 (2020) 043B09 [arXiv:1911.10794] [INSPIRE].
R. Arai et al., Finite-N corrections to the M-brane indices, JHEP 11 (2020) 093 [arXiv:2007.05213] [INSPIRE].
S. Fujiwara, Y. Imamura and T. Mori, Flavor symmetries of six-dimensional \( \mathcal{N} \) = (1, 0) theories from AdS/CFT correspondence, JHEP 05 (2021) 221 [arXiv:2103.16094] [INSPIRE].
Y. Imamura and S. Murayama, Holographic index calculation for Argyres-Douglas and Minahan-Nemeschansky theories, PTEP 2022 (2022) 113B01 [arXiv:2110.14897] [INSPIRE].
S. Fujiwara et al., Simple-Sum Giant Graviton Expansions for Orbifolds and Orientifolds, PTEP 2024 (2024) 023B02 [arXiv:2310.03332] [INSPIRE].
Y. Imamura, Analytic Continuation for Giant Gravitons, PTEP 2022 (2022) 103B02 [arXiv:2205.14615] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, (2,0) theory on S5 × S1 and quantum M2 branes, Nucl. Phys. B 998 (2024) 116400 [arXiv:2309.10786] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Large N expansion of superconformal index of k = 1 ABJM theory and semiclassical M5 brane partition function, Nucl. Phys. B 1001 (2024) 116507 [arXiv:2312.01917] [INSPIRE].
M. Beccaria and A. Cabo-Bizet, Large N Schur index of \( \mathcal{N} \) = 4 SYM from semiclassical D3 brane, JHEP 04 (2024) 110 [arXiv:2402.12172] [INSPIRE].
F.F. Gautason and J. van Muiden, One-Loop Quantization of Euclidean D3-Branes in Holographic Backgrounds, arXiv:2402.16779 [INSPIRE].
J.H. Lee, Trace Relations and Open String Vacua, JHEP 02 (2024) 224 [arXiv:2312.00242] [INSPIRE].
G. Eleftheriou, S. Murthy and M. Rosselló, The giant graviton expansion in AdS5 × S5, arXiv:2312.14921 [INSPIRE].
M. Beccaria and A. Cabo-Bizet, Giant Graviton Expansion of Schur Index and Quasimodular Forms, JHEP 05 (2024) 282 [arXiv:2403.06509] [INSPIRE].
T. Dimofte, D. Gaiotto and S. Gukov, 3-Manifolds and 3D Indices, Adv. Theor. Math. Phys. 17 (2013) 975 [arXiv:1112.5179] [INSPIRE].
D. Gang, E. Koh and K. Lee, Line Operator Index on S1 × S3, JHEP 05 (2012) 007 [arXiv:1201.5539] [INSPIRE].
N. Drukker, The \( \mathcal{N} \) = 4 Schur index with Polyakov loops, JHEP 12 (2015) 012 [arXiv:1510.02480] [INSPIRE].
C. Cordova, D. Gaiotto and S.-H. Shao, Infrared Computations of Defect Schur Indices, JHEP 11 (2016) 106 [arXiv:1606.08429] [INSPIRE].
A. Neitzke and F. Yan, Line defect Schur indices, Verlinde algebras and U(1)r fixed points, JHEP 11 (2017) 035 [arXiv:1708.05323] [INSPIRE].
Y. Hatsuda and T. Okazaki, Exact \( \mathcal{N} \) = 2∗ Schur line defect correlators, JHEP 06 (2023) 169 [arXiv:2303.14887] [INSPIRE].
Y. Hatsuda and T. Okazaki, Large N and large representations of Schur line defect correlators, JHEP 01 (2024) 096 [arXiv:2309.11712] [INSPIRE].
Y. Hatsuda and T. Okazaki, Excitations of bubbling geometries for line defects, Phys. Rev. D 109 (2024) 066013 [arXiv:2311.13740] [INSPIRE].
Z. Guo, Y. Li, Y. Pan and Y. Wang, \( \mathcal{N} \) = 2 \( \mathcal{N} \) = 2 Schur Index and Line Operators, Phys. Rev. D 108 (2023) 106002 [arXiv:2307.15650] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
A. Faraggi and L.A. Pando Zayas, The Spectrum of Excitations of Holographic Wilson Loops, JHEP 05 (2011) 018 [arXiv:1101.5145] [INSPIRE].
Y. Imamura, Giant Graviton Expansions for Line Operator Index, arXiv:2403.11543 [INSPIRE].
S. Murthy, Unitary matrix models, free fermions, and the giant graviton expansion, Pure Appl. Math. Quart. 19 (2023) 299 [arXiv:2202.06897] [INSPIRE].
M. Beccaria and A. Cabo-Bizet, On the Brane Expansion of the Schur Index, JHEP 08 (2023) 073 [arXiv:2305.17730] [INSPIRE].
F.F. Gautason, V.G.M. Puletti and J. van Muiden, Quantized strings and instantons in holography, JHEP 08 (2023) 218 [arXiv:2304.12340] [INSPIRE].
F.A. Dolan, Counting BPS Operators in \( \mathcal{N} \) = 4 Sym, Nucl. Phys. B 790 (2008) 432 [arXiv:0704.1038] [INSPIRE].
R. Stanley, Enumerative combinatorics: volume 2, Cambridge University Press (2023).
D.S. Eniceicu, R. Mahajan and C. Murdia, Complex Eigenvalue Instantons and the Fredholm Determinant Expansion in the Gross-Witten-Wadia Model, JHEP 01 (2024) 129 [arXiv:2308.06320] [INSPIRE].
J.T. Liu and N.J. Rajappa, Finite N indices and the giant graviton expansion, JHEP 04 (2023) 078 [arXiv:2212.05408] [INSPIRE].
D.S. Eniceicu, Comments on the Giant-Graviton Expansion of the Superconformal Index, arXiv:2302.04887 [INSPIRE].
N. Drukker, D.J. Gross and A.A. Tseytlin, Green-Schwarz string in AdS5 × S5: Semiclassical partition function, JHEP 04 (2000) 021 [hep-th/0001204] [INSPIRE].
Acknowledgments
We thank Arkady Tseytlin, Ji Hoon Lee, and Alejandro Cabo-Bizet for useful discussions related to various aspects of this work. Financial support from the INFN grant GAST is acknowledged.
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Beccaria, M. Schur line defect correlators and giant graviton expansion. J. High Energ. Phys. 2024, 88 (2024). https://doi.org/10.1007/JHEP06(2024)088
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DOI: https://doi.org/10.1007/JHEP06(2024)088