TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.5.128
TI  - Three dimensional topological field theories and Nahm sum formulas
PY  - 2025/11/12
UR  - https://www.scipost.org/SciPostPhys.19.5.128
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 5
SP  - 128
A1  - Gang, Dongmin
AU  - Kim, Heeyeon
AU  - Park, Byoungyoon
AU  - Stubbs, Spencer
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.19.5.128,
	title={{Three dimensional topological field theories and Nahm sum formulas}},
	author={Dongmin Gang and Heeyeon Kim and Byoungyoon Park and Spencer Stubbs},
	journal={SciPost Phys.},
	volume={19},
	pages={128},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.5.128},
	url={https://scipost.org/10.21468/SciPostPhys.19.5.128},
}