- Letter
- Open Access
Defect two-point functions in 6D (2,0) theories
Phys. Rev. D 109, L061903 – Published 27 March, 2024
DOI: https://doi.org/10.1103/PhysRevD.109.L061903
Abstract
We consider correlation functions in 6D (2,0) theories of two -Bogomol’nyi-Prasad-Sommerfield (BPS) operators inserted away from a -BPS surface defect. In the large central-charge limit the leading connected contribution corresponds to sums of tree-level Witten diagram in in the presence of an defect. We show that these correlators can be uniquely determined by imposing only superconformal symmetry and consistency conditions, eschewing the details of the complicated effective Lagrangian. We explicitly compute all such two-point functions. The result exhibits remarkable hidden simplicity.
Physics Subject Headings (PhySH)
Article Text
References (62)
- K. G. Wilson, Confinement of quarks, Phys. Rev. D 10, 2445 (1974).
- D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, Generalized global symmetries, J. High Energy Phys. 02 (2015) 172.
- P. Liendo, L. Rastelli, and B. C. van Rees, The bootstrap program for boundary , J. High Energy Phys. 07 (2013) 113.
- M. Billò, V. Gonçalves, E. Lauria, and M. Meineri, Defects in conformal field theory, J. High Energy Phys. 04 (2016) 091.
- M. Lemos, P. Liendo, M. Meineri, and S. Sarkar, Universality at large transverse spin in defect CFT, J. High Energy Phys. 09 (2018) 091.
- P. Liendo, Y. Linke, and V. Schomerus, A Lorentzian inversion formula for defect CFT, J. High Energy Phys. 08 (2020) 163.
- A. Bissi, T. Hansen, and A. Söderberg, Analytic bootstrap for boundary CFT, J. High Energy Phys. 01 (2019) 010.
- A. Kaviraj and M. F. Paulos, The functional bootstrap for boundary CFT, J. High Energy Phys. 04 (2020) 135.
- D. Mazac, L. Rastelli, and X. Zhou, An analytic approach to , J. High Energy Phys. 12 (2019) 004.
- J. Barrat, A. Gimenez-Grau, and P. Liendo, A dispersion relation for defect CFT, J. High Energy Phys. 02 (2023) 255.
- L. Bianchi and D. Bonomi, Conformal dispersion relations for defects and boundaries, SciPost Phys. 15, 055 (2023).
- H. W. Diehl, Field-theoretical approach to critical behaviour at surfaces, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, London, 1986), Vol. 10, pp. 75–267.
- J. Cardy, Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes in Physics (Cambridge University Press, Cambridge, England, 1996).
- D. M. McAvity and H. Osborn, Conformal field theories near a boundary in general dimensions, Nucl. Phys. B455, 522 (1995).
- D. Gaiotto, D. Mazac, and M. F. Paulos, Bootstrapping the 3d Ising twist defect, J. High Energy Phys. 03 (2014) 100.
- G. Cuomo, Z. Komargodski, and M. Mezei, Localized magnetic field in the O(N) model, J. High Energy Phys. 02 (2022) 134.
- G. Cuomo, Z. Komargodski, M. Mezei, and A. Raviv-Moshe, Spin impurities, Wilson lines and semiclassics, J. High Energy Phys. 06 (2022) 112.
- S. Giombi, E. Helfenberger, Z. Ji, and H. Khanchandani, Monodromy defects from hyperbolic space, J. High Energy Phys. 02 (2022) 041.
- S. Giombi and H. Khanchandani, CFT in AdS and boundary RG flows, J. High Energy Phys. 11 (2020) 118.
- L. Bianchi, D. Bonomi, and E. de Sabbata, Analytic bootstrap for the localized magnetic field, J. High Energy Phys. 04 (2023) 069.
- A. Gimenez-Grau, Probing magnetic line defects with two-point functions, arXiv:2212.02520.
- A. Raviv-Moshe and S. Zhong, Phases of surface defects in scalar field theories, J. High Energy Phys. 08 (2023) 143.
- M. Trépanier, Surface defects in the O(N) model, J. High Energy Phys. 09 (2023) 074.
- S. Giombi and B. Liu, Notes on a surface defect in the model, J. High Energy Phys. 12 (2023) 004.
- M. Chiodaroli, J. Estes, and Y. Korovin, Holographic two-point functions for Janus interfaces in the CFT, J. High Energy Phys. 04 (2017) 145.
- S. Giombi, R. Roiban, and A. A. Tseytlin, Half-BPS Wilson loop and , Nucl. Phys. B922, 499 (2017).
- N. Drukker, S. Giombi, A. A. Tseytlin, and X. Zhou, Defect CFT in the 6d (2, 0) theory from M2 brane dynamics in , J. High Energy Phys. 07 (2020) 101.
- P. Ferrero and C. Meneghelli, Bootstrapping the half-BPS line defect CFT in supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. D 104, L081703 (2021).
- J. Barrat, A. Gimenez-Grau, and P. Liendo, Bootstrapping holographic defect correlators in super Yang-Mills, J. High Energy Phys. 04 (2022) 093.
- C. Meneghelli and M. Trépanier, Bootstrapping string dynamics in the 6d theories, J. High Energy Phys. 07 (2023) 165.
- A. Gimenez-Grau, The Witten diagram bootstrap for holographic defects, arXiv:2306.11896.
- S. Giombi, S. Komatsu, B. Offertaler, and J. Shan, Boundary reparametrizations and six-point functions on the string, arXiv:2308.10775.
- L. Rastelli and X. Zhou, Mellin amplitudes for , Phys. Rev. Lett. 118, 091602 (2017).
- L. Rastelli and X. Zhou, How to succeed at holographic correlators without really trying, J. High Energy Phys. 04 (2018) 014.
- L. F. Alday, V. Gonçalves, M. Nocchi, and X. Zhou, Six-point AdS gluon amplitudes from flat space and factorization, Phys. Rev. Res. 6, L012041 (2024).
- Z. Huang and E. Y. Yuan, Graviton scattering in at two loops, J. High Energy Phys. 04 (2023) 064.
- Z. Huang, B. Wang, E. Y. Yuan, and X. Zhou, AdS super gluon scattering up to two loops: A position space approach, J. High Energy Phys. 07 (2023) 053.
- A. Bissi, A. Sinha, and X. Zhou, Selected topics in analytic conformal bootstrap: A guided journey, Phys. Rep. 991, 1 (2022).
One can also consider coincident M2-branes but this will only change the results of the paper by an overall factor.
The normalization is in (1).
- C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli, and B. C. van Rees, Infinite chiral symmetry in four dimensions, Commun. Math. Phys. 336, 1359 (2015).
- C. Beem, L. Rastelli, and B. C. van Rees, W symmetry in six dimensions, J. High Energy Phys. 05 (2017) 017.
More precisely, the bulk field transforms in the rank- symmetric traceless representation of the original -symmetry group while the defect field transforms in the rank- representation with respect to the unbroken symmetry.
See, e.g., [34] for details.
The high-energy limit of the Mellin amplitude should be related to the flat-space amplitude similar to [46]. However, this has not been rigorously established in general in the defect case.
- J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, J. High Energy Phys. 03 (2011) 025.
- L. Rastelli and X. Zhou, The Mellin formalism for boundary , J. High Energy Phys. 10 (2017) 146.
- R. Corrado, B. Florea, and R. McNees, Correlation functions of operators and Wilson surfaces in the , (0, 2) theory in the large N limit, Phys. Rev. D 60, 085011 (1999).
- F. Bastianelli and R. Zucchini, Three point functions of chiral primary operators in , and , SCFT at large N, Phys. Lett. B 467, 61 (1999).
Our result for agrees with [48] up to a simple factor. A similar mismatch was also observed in [49] for three-point functions.
- L. Rastelli and X. Zhou, Holographic four-point functions in the (2, 0) theory, J. High Energy Phys. 06 (2018) 087.
- C. Behan, P. Ferrero, and X. Zhou, More on holographic correlators: Twisted and dimensionally reduced structures, J. High Energy Phys. 04 (2021) 008.
- G. Mack, D-independent representation of conformal field theories in D dimensions via transformation to auxiliary dual resonance models. Scalar amplitudes, arXiv:0907.2407.
- V. Goncalves and G. Itsios, A note on defect Mellin amplitudes, J. High Energy Phys. 11 (2023) 001.
- S. Caron-Huot and A.-K. Trinh, All Tree-level correlators in supergravity: Hidden ten-dimensional conformal symmetry, J. High Energy Phys. 01 (2019) 196.
- L. Rastelli, K. Roumpedakis, and X. Zhou, tree-level correlators: Hidden six-dimensional conformal symmetry, J. High Energy Phys. 10 (2019) 140.
- L. F. Alday, C. Behan, P. Ferrero, and X. Zhou, Gluon scattering in AdS from CFT, J. High Energy Phys. 06 (2021) 020.
- T. Abl, P. Heslop, and A. E. Lipstein, Higher-dimensional symmetry of correlators, J. High Energy Phys. 03 (2022) 076.
- L. F. Alday and X. Zhou, All tree-level correlators for M-theory on , Phys. Rev. Lett. 125, 131604 (2020).
- O. Aharony, L. F. Alday, A. Bissi, and E. Perlmutter, Loops in AdS from conformal field theory, J. High Energy Phys. 07 (2017) 036.
- L. F. Alday and X. Zhou, All holographic four-point functions in all maximally supersymmetric CFTs, Phys. Rev. X 11, 011056 (2021).
- J. Chen and X. Zhou, Aspects of higher-point functions in , J. High Energy Phys. 09 (2023) 204.