A 3d-3d appetizer

Abstract

We test the 3d-3d correspondence for theories that are labeled by Lens spaces. We find a full agreement between the index of the 3d \( \mathcal{N}=2 \) “Lens space theory” T [L(p, 1)] and the partition function of complex Chern-Simons theory on L(p, 1). In particular, for p = 1, we show how the familiar S 3 partition function of Chern-Simons theory arises from the index of a free theory. For large p, we find that the index of T[L(p, 1)] becomes a constant independent of p. In addition, we study T[L(p, 1)] on the squashed three-sphere S 3 b . This enables us to see clearly, at the level of partition function, to what extent G complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group G.

A preprint version of the article is available at ArXiv.

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Correspondence to Ke Ye.

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ArXiv ePrint: 1503.04809

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Pei, D., Ye, K. A 3d-3d appetizer. J. High Energ. Phys. 2016, 8 (2016). https://doi.org/10.1007/JHEP11(2016)008

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Keywords

  • Chern-Simons Theories
  • Supersymmetric gauge theory
  • Supersymmetry and Duality
  • Topological Field Theories