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Line defect half-indices of SU(N) Chern-Simons theories

Okazaki, Tadashi; Smith, Douglas J.

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Tadashi Okazaki


We study the Wilson line defect half-indices of 3d N = 2 supersymmetric SU(N) Chern-Simons theories of level k ≤ – N with Neumann boundary conditions for the gauge fields, together with 2d Fermi multiplets and fundamental 3d chiral multiplets to cancel the gauge anomaly. We derive some exact results and also make some conjectures based on expansions of the q-series. We find several interesting connections with special functions known in the literature, including Rogers-Ramanujan functions for which we conjecture integral representations, and the appearance of Appell-Lerch sums for certain Wilson line half-index grand canonical ensembles which reveal an unexpected appearance of mock modular functions. We also find intriguing q-difference equations relating half-indices to Wilson line half-indices. Some of these results also have a description in terms of a dual theory with Dirichlet boundary conditions for the vector multiplet in the dual theory.


Okazaki, T., & Smith, D. J. (2024). Line defect half-indices of SU(N) Chern-Simons theories. Journal of High Energy Physics, 2024, Article 6.

Journal Article Type Article
Acceptance Date May 9, 2024
Online Publication Date Jun 4, 2024
Publication Date Jun 4, 2024
Deposit Date Jun 11, 2024
Publicly Available Date Jun 11, 2024
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2024
Article Number 6
Keywords Duality in Gauge Field Theories, ’t Hooft and Polyakov loops, Supersymmetric Gauge Theory, Wilson, Chern-Simons Theories
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