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Published November 2016 | Submitted + Published
Journal Article Open

A 3d-3d appetizer


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 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_b^3. This enables us to see clearly, at the level of partition function, to what extent Gℂ complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group G.

Additional Information

© 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: June 2, 2016; Revised: October 9, 2016; Accepted: October 26, 2016; Published: November 2, 2016. We are deeply indebted to Sergei Gukov for his valuable suggestions and constant encouragement at various stages of this work, and to Ingmar Saberi for proofreading our manuscript and giving very helpful comments. We also wish to thank Murat Koloğlu, Petr Kravchuk, Pavel Putrov, Kung-Yi Su and Wenbin Yan for stimulating discussions. We are also very grateful for the referee who has offered us many interesting suggestions and insights. This work is funded by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics.

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Published - art_3A10.1007_2FJHEP11_282016_29008.pdf

Submitted - pei.pdf


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