3d TQFTs from Argyres–Douglas theories

Dedushenko, Mykola; Gukov, Sergei; Nakajima, Hiraku; Pei, Du; Ye, Ke

doi:10.1088/1751-8121/abb481

3d TQFTs from Argyres–Douglas theories

Journal Article · Thu Oct 08 00:00:00 EDT 2020 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8121/abb481· OSTI ID:1762776

Dedushenko, Mykola ^[1]; Gukov, Sergei ^[2]; Nakajima, Hiraku ^[3]; ^[4]; Ye, Ke ^[2]

California Institute of Technology (CalTech), Pasadena, CA (United States); Caltech
California Institute of Technology (CalTech), Pasadena, CA (United States)
Univ. of Tokyo, Chiba (Japan)
California Institute of Technology (CalTech), Pasadena, CA (United States); Aarhus Univ. (Denmark); Harvard Univ., Cambridge, MA (United States)

We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres–Douglas theories on S¹ × M³ with a non-trivial holonomy of a discrete global symmetry along the S¹. For the minimal choice of the holonomy, the resulting 3d TQFTs are non-unitary and semisimple, thus distinguishing themselves from theories of Chern–Simons and Rozansky–Witten types respectively. Changing the holonomy performs a Galois transformation on the TQFT, which can sometimes give rise to more familiar unitary theories such as the $${\left({G}_{2}\right)}_{1}$$ and $${\left({F}_{4}\right)}_{1}$$ Chern–Simons theories. Our construction is based on an intriguing relation between topologically twisted partition functions, wild Hitchin characters, and chiral algebras which, when combined together, relate Coulomb branch and Higgs branch data of the same 4d $$\mathcal{N}=2$$ theory. Finally, we test our proposal by applying localization techniques to the conjectural $$\mathcal{N}=1$$ UV Lagrangian descriptions of the (A₁, A₂), (A₁, A₃) and (A₁, D₃) theories.

View Accepted Manuscript (DOE)

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: JSPS; National Science Foundation; USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011632

OSTI ID:: 1762776

Alternate ID(s):: OSTI ID: 23025624

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 43 Vol. 53; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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