The Sum Over Topological Sectors and θ in the 2+1-Dimensional $\mathbb{CP}^1σ$-Model

Freed, Daniel S.; Komargodski, Zohar; Seiberg, Nathan

doi:10.1007/s00220-018-3093-0

Title: The Sum Over Topological Sectors and θ in the 2+1-Dimensional $$\mathbb{CP}^1σ$$-Model

Journal Article · Tue Jan 30 00:00:00 EST 2018 · Communications in Mathematical Physics

DOI:https://doi.org/10.1007/s00220-018-3093-0· OSTI ID:1537661

Freed, Daniel S. ^[1];

^[2]; Seiberg, Nathan ^[3]

Univ. of Texas, Austin, TX (United States)
Weizmann Inst. of Science, Rehovot (Israel); Stony Brook Univ., NY (United States)
Institute for Advanced Study, Princeton, NJ (United States)

Here we discuss the three spacetime dimensional $$\mathbb{CP}^N$$ model and specialize to the $$\mathbb{CP}^1$$ model. Because of the Hopf map $$\pi_3(\mathbb{CP}^1$$) =$$\mathbb{Z}$$ one might try to couple the model to a periodic θ parameter. However, we argue that only the values θ = 0 and θ = π are consistent. For these values the Skyrmions in the model are bosons and fermions respectively, rather than being anyons. We also extend the model by coupling it to a topological quantum field theory, such that the Skyrmions are anyons. We use techniques from geometry and topology to construct the θ = π theory on arbitrary 3-manifolds, and use recent results about invertible field theories to prove that no other values of θ satisfy the necessary locality.

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Research Organization:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF); Israel Science Foundation; European Research Council (ERC); Simons Foundation

Grant/Contract Number:: SC0009988; DMS-1611957; PHY-1607611; 1937/12; 335182; 488657

OSTI ID:: 1537661

Journal Information:: Communications in Mathematical Physics, Vol. 362, Issue 1; ISSN 0010-3616

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 13 works

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Charting the phase diagram of QCD3 Argurio, Riccardo; Bertolini, Matteo; Mignosa, Francesco Journal of High Energy Physics, Vol. 2019, Issue 8 https://doi.org/10.1007/jhep08(2019)153	journal	August 2019
Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups Cordova, Clay; Hsin, Po-Shen; Seiberg, Nathan SciPost Physics, Vol. 4, Issue 4 https://doi.org/10.21468/scipostphys.4.4.021	journal	January 2018
Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups Cordova, Clay; Hsin, Po-Shen; Seiberg, Nathan arXiv https://doi.org/10.48550/arxiv.1711.10008	text	January 2017

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