2024/08/15 by Okazaki, Tadashi, Smith, Douglas J.
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2408.07893
We study the line defect half-indices of 3d 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.