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Non-Semisimple TQFT's and BPS q-Series

Journal Article · · Symmetry, Integrability and Geometry: Methods and Applications
 [1];  [2];  [3]
  1. Institut de Mathématiques de Toulouse (France); California Institute of Technology
  2. California Institute of Technology (CalTech), Pasadena, CA (United States)
  3. The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
+ Show Author Affiliations
We propose and in some cases prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic q. Both types of invariants are labeled by extra data which plays an important role in the proposed relation. Bridging the two sides - which until recently were developed independently, using very different methods - opens many new avenues. In one direction, it allows to study (and perhaps even to formulate) q-series invariants labeled by spinc structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT's, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory.
Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0011632
OSTI ID:
2223052
Journal Information:
Symmetry, Integrability and Geometry: Methods and Applications, Journal Name: Symmetry, Integrability and Geometry: Methods and Applications Journal Issue: 10 Vol. 19; ISSN 1815-0659
Publisher:
Institute of Mathematics, National Academy of Sciences UkraineCopyright Statement
Country of Publication:
United States
Language:
English

Figures / Tables (5)

Figure 1(p. 4)figure Figure 1
Figure 2(p. 37)figure Figure 2
Figure 3(p. 49)figure Figure 3
Table 1(p. 54)table Table 1
Figure 4(p. 66)figure Figure 4

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Related Subjects

3-manifold invariants
97 MATHEMATICS AND COMPUTING
TQFT
knot invariants