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Framed defects in ABJ and ABJM theories

Marco S. Bianchi1,*, Luigi Castiglioni2,†, Silvia Penati2,‡, Marcia Tenser3,§, and Diego Trancanelli4,∥

  • *Contact author: marco.bianchi@uss.cl
  • †Contact author: l.castiglioni8@campus.unimib.it
  • ‡Contact author: silvia.penati@mib.infn.it
  • §Contact author: marciatenser@gmail.com
  • ∥Contact author: diego.trancanelli@unimore.it
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Phys. Rev. D 113, 026027 – Published 29 January, 2026

DOI: https://doi.org/10.1103/kfvl-4mgs

Abstract

We investigate the role of framing in a family of 1/24 Bogomol’nyi–Prasad–Sommerfield (BPS) Wilson loops in Aharony-Bergman-Jafferis-(Maldacena) theory, which define flows between 1/6 BPS and the 1/2 BPS superconformal fixed points. We analyze in perturbation theory how framing affects both the expectation values of these operators and the correlation functions of local insertions on the defect, as well as its interplay with renormalization group flow and the g-theorem. We obtain a nontrivial identity between the one-point function of the defect stress tensor and a Q-exact correlator, which establishes a direct link between scale, superconformal invariance, cohomological equivalence and framing. This analysis confirms that framing one preserves supersymmetry and cohomological equivalence of operators at the quantum level, establishing a precise match with localization predictions. Finally, we propose a holographic interpretation of framing at strong coupling, identifying it with a coupling to the background B-field in the dual string theory.

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References (56)

  1. N. Drukker et al., Roadmap on Wilson loops in 3d Chern-Simons-matter theories, J. Phys. A 53, 173001 (2020).
  2. L. Castiglioni, S. Penati, M. Tenser, and D. Trancanelli, Interpolating Wilson loops and enriched RG flows, J. High Energy Phys. 08 (2023) 106.
  3. E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121, 351 (1989).
  4. M. S. Bianchi, L. Griguolo, M. Leoni, A. Mauri, S. Penati, and D. Seminara, Framing and localization in Chern-Simons theories with matter, J. High Energy Phys. 06 (2016) 133.
  5. A. Kapustin, B. Willett, and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, J. High Energy Phys. 03 (2010) 089.
  6. L. Griguolo, G. Martelloni, M. Poggi, and D. Seminara, Perturbative evaluation of circular 1/2 BPS Wilson loops in N=6 Super Chern-Simons theories, J. High Energy Phys. 09 (2013) 157.
  7. M. Marino and P. Putrov, Exact results in ABJM theory from topological strings, J. High Energy Phys. 06 (2010) 011.
  8. N. Drukker, M. Marino, and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys. 306, 511 (2011).
  9. M. S. Bianchi, L. Castiglioni, S. Penati, M. Tenser, and D. Trancanelli, Framing fermionic Wilson loops in ABJ(M), J. High Energy Phys. 12 (2024) 053.
  10. G. Cuomo, Z. Komargodski, and A. Raviv-Moshe, Renormalization group flows on line defects, Phys. Rev. Lett. 128, 021603 (2022).
  11. N. Drukker, Z. Kong, M. Probst, M. Tenser, and D. Trancanelli, Classifying BPS bosonic Wilson loops in 3d N=4 Chern-Simons-matter theories, J. High Energy Phys. 11 (2022) 163.
  12. N. Drukker and D. Trancanelli, A supermatrix model for N=6 super Chern-Simons-matter theory, J. High Energy Phys. 02 (2010) 058.
  13. M. Cooke, N. Drukker, and D. Trancanelli, A profusion of 1/2 BPS Wilson loops in N=4 Chern-Simons-matter theories, J. High Energy Phys. 10 (2015) 140.
  14. H. Ouyang, J.-B. Wu, and J. Zhang, Supersymmetric Wilson loops in N=4 super Chern-Simons-matter theory, J. High Energy Phys. 11 (2015) 213.
  15. H. Ouyang, J.-B. Wu, and J. Zhang, Novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter theories, Phys. Lett. B 753, 215 (2016).
  16. H. Ouyang, J.-B. Wu, and J. Zhang, Construction and classification of novel BPS Wilson loops in quiver Chern-Simons-matter theories, Nucl. Phys. B910, 496 (2016).
  17. A. Mauri, S. Penati, and J. Zhang, New BPS Wilson loops in N=4 circular quiver Chern-Simons-matter theories, J. High Energy Phys. 11 (2017) 174.
  18. A. Mauri, H. Ouyang, S. Penati, J.-B. Wu, and J. Zhang, BPS Wilson loops in N≥2 superconformal Chern-Simons-matter theories, J. High Energy Phys. 11 (2018) 145.
  19. N. Drukker, BPS Wilson loops and quiver varieties, J. Phys. A 53, 385402 (2020).
  20. N. Drukker, M. Tenser, and D. Trancanelli, Notes on hyperloops in N=4 Chern-Simons-matter theories, J. High Energy Phys. 07 (2021) 159.
  21. N. Drukker, Z. Kong, M. Probst, M. Tenser, and D. Trancanelli, Conformal and nonconformal hyperloop deformations of the 1/2 BPS circle, J. High Energy Phys. 08 (2022) 165.
  22. N. Drukker, J. Plefka, and D. Young, Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals, J. High Energy Phys. 11 (2008) 019.
  23. L. Castiglioni, S. Penati, M. Tenser, and D. Trancanelli, Wilson loops and defect RG flows in ABJM, J. High Energy Phys. 06 (2023) 157.
  24. L. Castiglioni, S. Penati, M. Tenser, and D. Trancanelli, Interpolating bremsstrahlung function in ABJM model, Phys. Rev. D 109, 126010 (2024).
  25. L. Castiglioni, S. Penati, M. Tenser, and D. Trancanelli, Conformal defects and RG flows in ABJM, Proc. Sci., CORFU2024 (2025) 345 [arXiv:2502.15877].
  26. E. Guadagnini, M. Martellini, and M. Mintchev, Wilson lines in Chern-Simons theory and link invariants, Nucl. Phys. B330, 575 (1990).
  27. M. Alvarez and J. M. F. Labastida, Analysis of observables in Chern-Simons perturbation theory, Nucl. Phys. B395, 198 (1993).
  28. G. Calugareanu, L’intégrale de gauss et l’analyse des nœuds tridimensionnels, Rev. Math. Pures Appl 4, 5 (1959).
  29. B. Gabai, A. Sever, and D.-l. Zhong, Line operators in Chern-Simons–matter theories and bosonization in three dimensions, Phys. Rev. Lett. 129, 121604 (2022).
  30. B. Gabai, A. Sever, and D.-l. Zhong, Line operators in Chern-Simons-matter theories and bosonization in three dimensions II: Perturbative analysis and all-loop resummation, J. High Energy Phys. 04 (2023) 070.
  31. M. S. Bianchi, A note on multiply wound BPS Wilson loops in ABJM, J. High Energy Phys. 09 (2016) 047.
  32. M. S. Bianchi, L. Griguolo, A. Mauri, S. Penati, and D. Seminara, A matrix model for the latitude Wilson loop in ABJM theory, J. High Energy Phys. 08 (2018) 060.
  33. M. S. Bianchi, G. Giribet, M. Leoni, and S. Penati, 1/2 BPS Wilson loop in N=6 superconformal Chern-Simons theory at two loops, Phys. Rev. D 88, 026009 (2013).
  34. M. S. Bianchi, G. Giribet, M. Leoni, and S. Penati, The 1/2 BPS Wilson loop in ABJ(M) at two loops: The details, J. High Energy Phys. 10 (2013) 085.
  35. H. Dorn, Renormalization of path ordered phase factors and related hadron operators in gauge field theories, Fortschr. Phys. 34, 11 (1986).
  36. N. S. Craigie and H. Dorn, On the renormalization and short distance properties of hadronic operators in QCD, Nucl. Phys. B185, 204 (1981).
  37. D. H. Correa, M. G. Ferro, and V. I. Giraldo-Rivera, Mixed boundary conditions in AdS2/CFT1 from the coupling with a Kalb-Ramond field, J. High Energy Phys. 02 (2024) 141.
  38. C. Closset, T. T. Dumitrescu, G. Festuccia, Z. Komargodski, and N. Seiberg, Contact terms, unitarity, and F-maximization in three-dimensional superconformal theories, J. High Energy Phys. 10 (2012) 053.
  39. C. Closset, T. T. Dumitrescu, G. Festuccia, Z. Komargodski, and N. Seiberg, Comments on Chern-Simons contact terms in three dimensions, J. High Energy Phys. 09 (2012) 091.
  40. N. Gorini, L. Griguolo, L. Guerrini, S. Penati, D. Seminara, and P. Soresina, Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory, J. High Energy Phys. 02 (2023) 013.
  41. T. Shachar, R. Sinha, and M. Smolkin, RG flows on two-dimensional spherical defects, SciPost Phys. 15, 240 (2023).
  42. M. S. Bianchi, L. Griguolo, M. Leoni, S. Penati, and D. Seminara, BPS Wilson loops and Bremsstrahlung function in ABJ(M): A two loop analysis, J. High Energy Phys. 06 (2014) 123.
  43. D. M. McAvity and H. Osborn, Energy momentum tensor in conformal field theories near a boundary, Nucl. Phys. B406, 655 (1993).
  44. M. Billò, V. Gonçalves, E. Lauria, and M. Meineri, Defects in conformal field theory, J. High Energy Phys. 04 (2016) 091.
  45. B. Chen and J.-B. Wu, Supersymmetric Wilson loops in N=6 super Chern-Simons-matter theory, Nucl. Phys. B825, 38 (2010).
  46. S.-J. Rey, T. Suyama, and S. Yamaguchi, Wilson loops in superconformal Chern-Simons theory and fundamental strings in anti-de Sitter supergravity dual, J. High Energy Phys. 03 (2009) 127.
  47. D. Berenstein and D. Trancanelli, Three-dimensional N=6 SCFT’s and their membrane dynamics, Phys. Rev. D 78, 106009 (2008).
  48. O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, J. High Energy Phys. 10 (2008) 091.
  49. O. Bergman and S. Hirano, Anomalous radius shift in AdS(4)/CFT(3), J. High Energy Phys. 07 (2009) 016.
  50. O. Aharony, O. Bergman, and D. L. Jafferis, Fractional M2-branes, J. High Energy Phys. 11 (2008) 043.
  51. O. Aharony, A. Hashimoto, S. Hirano, and P. Ouyang, D-brane charges in gravitational duals of 2+1 dimensional gauge theories and duality cascades, J. High Energy Phys. 01 (2010) 072.
  52. V. Cardinali, L. Griguolo, G. Martelloni, and D. Seminara, New supersymmetric Wilson loops in ABJ(M) theories, Phys. Lett. B 718, 615 (2012).
  53. L. Griguolo, L. Guerrini, and I. Yaakov, Localization and duality for ABJM latitude Wilson loops, J. High Energy Phys. 08 (2021) 001.
  54. D. H. Correa, J. Aguilera-Damia, and G. A. Silva, Strings in AdS4×CP3 Wilson loops in N=6 super Chern-Simons-matter and bremsstrahlung functions, J. High Energy Phys. 06 (2014) 139.
  55. D. H. Correa, V. I. Giraldo-Rivera, and G. A. Silva, Supersymmetric mixed boundary conditions in AdS2 and DCFT1 marginal deformations, J. High Energy Phys. 03 (2020) 010.
  56. A. F. C. Garay, D. H. Correa, A. Faraggi, and G. A. Silva, Interpolating boundary conditions on AdS2, J. High Energy Phys. 02 (2023) 146.

Outline

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Phys. Rev. D 113, 026027– Published 29 January, 2026
  • Received 8 October 2025
  • Accepted 14 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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