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Edge modes in Chern-Simons theory on a strip

Erica Bertolini1,*, Michael Doyle2,†, Nicola Maggiore3,4,‡, Conor Murphy2,§, and Carlotta Piras2,∥

  • *Contact author: ebertolini@stp.dias.ie
  • †Contact author: doylem55@tcd.ie
  • ‡Contact author: nicola.maggiore@ge.infn.it
  • §Contact author: murphy33@tcd.ie
  • ∥Contact author: pirasc@tcd.ie
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Phys. Rev. D 113, 085022 – Published 28 April, 2026

DOI: https://doi.org/10.1103/byqq-p2v9

Abstract

We investigate abelian Chern-Simons gauge theory on a strip geometry with two spatial boundaries. In the presence of boundaries, gauge invariance is broken by boundary conditions, leading to physical edge excitations. By deriving the most general local boundary conditions consistent with power counting in the sense of Symanzik, we show that the bulk equations of motion determine the boundary degrees of freedom through a broken gauge Ward identity, yielding boundary Kac-Moody current algebras with opposite central charges on the two edges. The corresponding two-dimensional boundary actions are of Tomonaga-Luttinger type and describe chiral bosons propagating in opposite directions along the two boundaries. A consistency condition, interpreted as a holographic-like bulk-boundary matching, relates the Chern-Simons coupling constant and the boundary parameters to the physical edge velocities. Within this framework, the equality and opposite sign of the two velocities in a symmetric setup follow directly from the boundary structure rather than from model-dependent assumptions about confining potentials, and the velocities are independent of the strip width. Our analysis provides a fully field-theoretic realization of bulk-boundary correspondence in Chern-Simons theory with two boundaries, with direct applications to edge physics in quantum Hall systems and related topological/hydrodynamic settings.

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References (41)

  1. X. G. Wen, Int. J. Mod. Phys. B 06, 1711 (1992).
  2. M. Stone, Ann. Phys. (N.Y.) 207, 38 (1991).
  3. E. Fradkin and A. Lopez, Phys. Rev. B 44, 5246 (1991).
  4. D. Tong, arXiv:1606.06687.
  5. N. Maggiore, Int. J. Mod. Phys. A 33, 1850013 (2018).
  6. S. C. Zhang, Int. J. Mod. Phys. B 06, 25 (1992).
  7. A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, and N. Magnoli, Phys. Rev. D 90, 125006 (2014).
  8. A. Blasi and N. Maggiore, Symmetry 11, 921 (2019).
  9. L. Susskind, arXiv:hep-th/0101029.
  10. X. G. Wen, Quantum Field Theory of Many-Body Systems (Oxford University Press, New York, 2010), 10.1093/acprof:oso/9780199227259.001.0001.
  11. K. Symanzik, Nucl. Phys. B190, 1 (1981).
  12. H. B. G. Casimir, Indagat. Math 10, 261 (1948).
  13. A. Blasi, R. Collina, and J. Sassarini, Int. J. Mod. Phys. A 09, 1677 (1994).
  14. K. A. Milton, The Casimir Effect: Physical Manifestations of Zero-Point Energy (World Scientific, Singapore, 2001), ISBN [Amazon][WorldCat].
  15. N. Maggiore, Eur. Phys. J. Plus 133, 281 (2018).
  16. E. Bertolini and N. Maggiore, Symmetry 12, 1134 (2020).
  17. E. Bertolini, G. Gambuti, and N. Maggiore, Phys. Rev. D 104, 105011 (2021).
  18. N. Maggiore, J. Phys. A 52, 115401 (2019).
  19. D. Tong, SciPost Phys. 14, 102 (2023).
  20. A. Kapustin and N. Saulina, Nucl. Phys. B845, 393 (2011).
  21. J. R. Fliss, X. Wen, O. Parrikar, C. T. Hsieh, B. Han, T. L. Hughes, and R. G. Leigh, J. High Energy Phys. 09 (2017) 056.
  22. J. R. Fliss and R. G. Leigh, J. High Energy Phys. 07 (2020) 009.
  23. M. Gutperle and J. D. Miller, Phys. Rev. D 99, 026014 (2019).
  24. E. Witten, Commun. Math. Phys. 121, 351 (1989).
  25. N. Nakanishi, Prog. Theor. Phys. 35, 1111 (1966).
  26. B. Lautrup, Kong. Dan. Vid. Sel. Mat. Fys. Medd. 35, 11 (1967).
  27. G. Gambuti and N. Maggiore, Phys. Lett. B 807, 135530 (2020).
  28. H. W. Diehl, Int. J. Mod. Phys. B 11, 3503 (1997).
  29. C. de C. Chamon and X.-G. Wen, Phys. Rev. B 49, 8227 (1994).
  30. D. B. Chklovskii, B. I. Shklovskii, and L. I. Glazman, Phys. Rev. B 46, 4026 (1992).
  31. M. Srednicki, Quantum Field Theory (Cambridge University Press, Cambridge, England, 2007), ISBN [Amazon][WorldCat], 10.1017/CBO9780511813917.
  32. V. G. Kac, Funct. Anal. Appl. 1, 328 (1967).
  33. R. V. Moody, Bull. Am. Math. Soc. 73, 217 (1967).
  34. F. D. M. Haldane, J. Phys. C 14, 2585 (1981).
  35. X. G. Wen, Phys. Rev. B 41, 12838 (1990).
  36. B. I. Halperin, Phys. Rev. B 25, 2185 (1982).
  37. M. Büttiker, Phys. Rev. B 38, 9375 (1988).
  38. A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, and N. Magnoli, Adv. High Energy Phys. 2014, 635286 (2014).
  39. E. Bertolini, F. Fecit, and N. Maggiore, Symmetry 14, 675 (2022).
  40. E. Bertolini, N. Maggiore, and G. Palumbo, Phys. Rev. D 108, 025009 (2023).
  41. E. Bertolini and N. Maggiore, Phys. Rev. D 108, 105012 (2023).

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Phys. Rev. D 113, 085022– Published 28 April, 2026
  • Received 24 December 2025
  • Accepted 7 April 2026
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