Dongmin Gang, Heeyeon Kim, Byoungyoon Park, Spencer Stubbs
SciPost Phys. 19, 128 (2025) ·
published 12 November 2025
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It is known that a large class of characters of 2d conformal field theories (CFTs) can be written in the form of a Nahm sum. In [D. Zagier, in Frontiers in number theory, physics, and geometry II, Springer, Berlin (2007)], D. Zagier identified a list of Nahm sum expressions that are modular functions under a congruence subgroup of $SL(2,\mathbb{Z})$, which can be thought of as candidates for characters of rational CFTs. Motivated by the observation that the same formulas appear as the half-indices of certain 3d $\mathcal{N}=2$ supersymmetric gauge theories, we perform a general search over low-rank 3d $\mathcal{N}=2$ Abelian Chern-Simons matter theories which either flow to unitary TFTs or $\mathcal{N}=4$ rank-zero SCFTs in the infrared. These are exceptional classes of 3d theories, which are expected to support rational and $C_2$-cofinite chiral algebras on their boundary. We compare and contrast our results with Zagier's and comment on a possible generalization of Nahm's conjecture.
SciPost Phys. 17, 064 (2024) ·
published 23 August 2024
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We introduce a novel class of two-dimensional non-unitary rational conformal field theories (RCFTs) whose modular data are identical to the generalized Haagerup-Izumi modular data. Via the bulk-boundary correspondence, they are related to the three-dimensional non-unitary Haagerup topological field theories, recently constructed by a topological twisting of three-dimensional $\mathcal{N}=4$ rank-zero superconformal field theories (SCFTs), called S-fold SCFTs. We propose that, up to the overall factors, the half-indices of the rank-zero SCFTs give the explicit Nahm representation of four conformal characters of the RCFTs including the vacuum character. Using the theory of Bantay-Gannon, we can successfully complete them into the full admissible conformal characters of the RCFTs.
