Published March 17, 2017
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Refined large N duality for torus knots
- Creators
- Kameyama, Masaya
- Nawata, Satoshi
Abstract
We formulate large N duality of U(N) refined Chern-Simons theory with a torus knot/link in S^3. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate refined Chern-Simons invariants of a torus knot/link in S^3 to refined BPS invariants in the resolved conifold. Assuming that the extra U(1) global symmetry acts on BPS states trivially, the duality predicts graded dimensions of cohomology groups of moduli spaces of M2-M5 bound states associated to a torus knot/link in the resolved conifold.
Additional Information
The authors are indebted to P. Su lkowski for collaboration at the initial stage of this project. The motivation of this paper originated from the paper [GKS16]. They would like to thank H. Awata, M. Dedushenko, S. Gukov, H. Kanno, A. Klemm, M. Mari˜no, A. Morozov, A. Mironov, P. Putrov, P. Ramadevi, I. Saberi, A. Sleptsov, Zodinmawia for discussion and correspondence. In particular, they are grateful to S. Shakirov for sharing Maple files of refined Chern-Simons invariants obtained in [Sha13]. S.N. would like to thank the American Institute of Mathematics for supporting this research with a SQuaRE grant "New connections between link homologies and physics". The work of S.N. is supported by ERC Starting Grant no. 335739 "Quantum fields and knot homologies", the center of excellence grant "Center for Quantum Geometry of Moduli Space" from the Danish National Research Foundation (DNRF95), and Walter Burke Institute for Theoretical Physics, California Institute of Technology as well as the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632.Attached Files
Submitted - 1703.05408.pdf
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Additional details
- Alternative title
- Refined large N duality for knots
- Eprint ID
- 75193
- Resolver ID
- CaltechAUTHORS:20170316-202039601
- 335739
- European Research Council (ERC)
- DNRF95
- Danish National Research Foundation
- DE-SC0011632
- Department of Energy (DOE)
- Walter Burke Institute for Theoretical Physics, Caltech
- Created
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2017-03-17Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2017-010