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4d/2d -> 3d/1d: A song of protected operator algebras

Dedushenko, Mykola and Wang, Yifan (2019) 4d/2d -> 3d/1d: A song of protected operator algebras. .

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Superconformal field theories (SCFT) are known to possess solvable yet nontrivial sectors in their full operator algebras. Two prime examples are the chiral algebra sector on a two dimensional plane in four dimensional N=2 SCFTs, and the topological quantum mechanics (TQM) sector on a line in three dimensional N=4 SCFTs. Under Weyl transformation, they respectively map to operator algebras on a great torus in S^1×S^3 and a great circle in S^3, and are naturally related by reduction along the S^1 factor, which amounts to taking the Cardy (high-temperature) limit of the four dimensional theory on S1×S3. We elaborate on this relation by explicit examples that involve both Lagrangian and non-Lagrangian theories in four dimensions, where the chiral algebra sector is generally described by a certain W-algebra, while the three dimensional descendant SCFT always has a (mirror) Lagrangian description. By taking into account a subtle R-symmetry mixing, we provide explicit dictionaries between selected operator product expansion (OPE) data in the four and three dimensional SCFTs, which we verify in the examples using recent localization results in four and three dimensions. Our methods thus provide nontrivial support for various chiral algebra proposals in the literature. Along the way, we also identify three dimensional mirrors for Argyres-Douglas theories of type (A1,D2n+1) reduced on S^1, and find more evidence for earlier proposals in the case of (A_1,A_(2n−2)), which both realize certain superconformal boundary conditions for the four dimensional N=4 super-Yang-Mills. This is a companion paper to arXiv:1911.05741.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Dedushenko, Mykola0000-0002-9273-7602
Wang, Yifan0000-0001-9965-9777
Additional Information:We thank: T. Creutzig, P. Etingof, M. Fluder, N. Nekrasov for discussions. Part of this work was completed when M.D. was a member at (and supported by) the Walter Burke Institute for Theoretical Physics, with the additional support from the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No de-sc0011632, as well as the Sherman Fairchild Foundation. The work of Y.W. is supported in part by the US NSF under Grant No. PHY-1620059 and by the Simons Foundation Grant No. 488653.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Sherman Fairchild FoundationUNSPECIFIED
Simons Foundation488653
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Record Number:CaltechAUTHORS:20200205-145133597
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101147
Deposited By: Joy Painter
Deposited On:06 Feb 2020 15:38
Last Modified:02 Jun 2023 01:02

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