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

Abstract

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.

Authors:
 [1]; ORCiD logo [2];  [3]
  1. Univ. of Texas, Austin, TX (United States)
  2. Weizmann Inst. of Science, Rehovot (Israel); Stony Brook Univ., NY (United States)
  3. Institute for Advanced Study, Princeton, NJ (United States)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF); Israel Science Foundation; European Research Council (ERC); Simons Foundation
OSTI Identifier:
1537661
Grant/Contract Number:  
SC0009988; DMS-1611957; PHY-1607611; 1937/12; 335182; 488657
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Communications in Mathematical Physics
Additional Journal Information:
Journal Volume: 362; Journal Issue: 1; Journal ID: ISSN 0010-3616
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Freed, Daniel S., Komargodski, Zohar, and Seiberg, Nathan. The Sum Over Topological Sectors and θ in the 2+1-Dimensional $\mathbb{CP}^1σ$-Model. United States: N. p., 2018. Web. doi:10.1007/s00220-018-3093-0.
Freed, Daniel S., Komargodski, Zohar, & Seiberg, Nathan. The Sum Over Topological Sectors and θ in the 2+1-Dimensional $\mathbb{CP}^1σ$-Model. United States. https://doi.org/10.1007/s00220-018-3093-0
Freed, Daniel S., Komargodski, Zohar, and Seiberg, Nathan. 2018. "The Sum Over Topological Sectors and θ in the 2+1-Dimensional $\mathbb{CP}^1σ$-Model". United States. https://doi.org/10.1007/s00220-018-3093-0. https://www.osti.gov/servlets/purl/1537661.
@article{osti_1537661,
title = {The Sum Over Topological Sectors and θ in the 2+1-Dimensional $\mathbb{CP}^1σ$-Model},
author = {Freed, Daniel S. and Komargodski, Zohar and Seiberg, Nathan},
abstractNote = {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.},
doi = {10.1007/s00220-018-3093-0},
url = {https://www.osti.gov/biblio/1537661}, journal = {Communications in Mathematical Physics},
issn = {0010-3616},
number = 1,
volume = 362,
place = {United States},
year = {Tue Jan 30 00:00:00 EST 2018},
month = {Tue Jan 30 00:00:00 EST 2018}
}

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Cited by: 13 works
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Works referencing / citing this record:

Metastable vacua in large-N QCD3
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Charting the phase diagram of QCD3
journal, August 2019


Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
journal, January 2018