Chern-Simons theories with defects, Rogers-Ramanujan type functions and eta-products
Abstract
We study the line defect half-indices of $3 \mathrm{~d} \mathcal{N}=2$ 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 the one-point functions of the fundamental Wilson lines form a basis for the line defect indices in terms of Rogers-Ramanujan type functions which correspond to Rogers-Ramanujan type identities relating infinite series and infinite products. Furthermore, the theories with an adjoint chiral admit expressions as eta-products. In particular, for the $S U(N)_{-2 N}$ CS theory, there is a one-to-one correspondence between the BPS boundary local operators and the $N$-core partitions.
Fields of Study & Subjects
Advanced Mathematical Identities
Analytic Number Theory Research
Mathematical functions and polynomials
Publication details
- Journal / source
- Advances in Theoretical and Mathematical Physics
- Publisher
- International Press of Boston
- Volume
- 30
- Issue
- 4
- Pages
- 1057–1134
- Publication date
- 1 January 2026
- Language
- EN