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Peer-reviewedCC BY 4.0Journal of High Energy Physics

3d-3d correspondence for knot complements with finite and large N

  • Hee-Joong Chung1
  1. 1Jeju National University
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Abstract

For G = SU(N) at finite and large N, with a totally symmetric representation, we realize the homological block FK for a knot complement S3\K, given in the form of the inverted Habiro series, as a half-index of a 3d 𝒩 = 2 theory, which is expected to provide a UV description of T[M3]. From the half-index expression, it is also possible to realize the colored HOMFLY-PT polynomial by summing the residues at a certain set of poles. Through the half-index realization, we describe a method for obtaining the G = SU(N) homological block and its a-deformed version for S3\K in the form of the inverted Habiro series from a given Habiro series expression for the colored HOMFLY-PT polynomial. We also discuss some properties of partition functions for arbitrary N.

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Cite

BibTeXRIS
BibTeX
@article{chung20263d3d,
  title = {{3d-3d correspondence for knot complements with finite and large N}},
  author = {Hee-Joong Chung},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = nov,
  doi = {10.1007/jhep11(2026)001},
  url = {https://link.springer.com/article/10.1007/JHEP11(2026)001},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - 3d-3d correspondence for knot complements with finite and large N
AU  - Hee-Joong Chung
PY  - 2026
DA  - 2026/11/02
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep11(2026)001
UR  - https://link.springer.com/article/10.1007/JHEP11(2026)001
AB  - For G = SU(N) at finite and large N, with a totally symmetric representation, we realize the homological block FK for a knot complement S3\K, given in the form of the inverted Habiro series, as a half-index of a 3d 𝒩 = 2 theory, which is expected to provide a UV description of T[M3]. From the half-index expression, it is also possible to realize the colored HOMFLY-PT polynomial by summing the residues at a certain set of poles. Through the half-index realization, we describe a method for obtaining the G = SU(N) homological block and its a-deformed version for S3\K in the form of the inverted Habiro series from a given Habiro series expression for the colored HOMFLY-PT polynomial. We also discuss some properties of partition functions for arbitrary N.
SN  - 1029-8479
ER  -