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arXiv · 2408.07893

Chern-Simons theories with defects, Rogers-Ramanujan type functions and eta-products

Tadashi Okazaki·Douglas J. Smith
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Abstract

We study the line defect half-indices of 3d $\mathcal{N}=2$ supersymmetric Chern-Simons (CS) theories with (special)unitary, symplectic, orthogonal and exceptional gauge groups. We find that they have several beautiful infinite product $q$-series expressions in terms of Ramanujan's general theta function. For the theories with fundamental chiral multiplets, the pairs of the Neumann half-indices and one-point functions of the fundamental Wilson lines form a basis for the line defect indices in terms of the Rogers-Ramanujan type functions. Furthermore, the theories with an adjoint chiral admit the expressions as the eta-products. In particular, for the $SU(N)_{-2N}$ CS theory, there is a one-to-one correspondence between the BPS boundary local operators and the $N$-core partitions.

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Tadashi Okazaki, Douglas J. Smith. 2024-08-15. Chern-Simons theories with defects, Rogers-Ramanujan type functions and eta-products. https://doi.org/10.4310/atmp.260604112942

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