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Title: A 3d-3d appetizer

Here, 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 G C complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group G.
Authors:
 [1] ;  [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Grant/Contract Number:
SC0011632
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chern-Simons theories; supersymmetric gauge theory; supersymmetry and duality; topological field theories
OSTI Identifier:
1360110