Conformal Field Theories in Fractional Dimensions
Abstract
We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary conformal field theories connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of Φ4 theory in the ϵ expansion.
- Authors:
-
- Alternative Energies and Atomic Energy Commission (CEA), Saclay (France); European Organization for Nuclear Research (CERN), Geneva (Switzerland)
- Brown Univ., Providence, RI (United States)
- Yale Univ., New Haven, CT (United States)
- European Organization for Nuclear Research (CERN), Geneva (Switzerland); Pierre and Marie Curie Univ., Paris (France)
- Inst. for Advanced Study, Princeton, NJ (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Institute for Advanced Study, Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1599108
- Grant/Contract Number:
- SC0009988
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 112; Journal Issue: 14; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
El-Showk, Sheer, Paulos, Miguel, Poland, David, Rychkov, Slava, Simmons-Duffin, David, and Vichi, Alessandro. Conformal Field Theories in Fractional Dimensions. United States: N. p., 2014.
Web. doi:10.1103/PhysRevLett.112.141601.
El-Showk, Sheer, Paulos, Miguel, Poland, David, Rychkov, Slava, Simmons-Duffin, David, & Vichi, Alessandro. Conformal Field Theories in Fractional Dimensions. United States. https://doi.org/10.1103/PhysRevLett.112.141601
El-Showk, Sheer, Paulos, Miguel, Poland, David, Rychkov, Slava, Simmons-Duffin, David, and Vichi, Alessandro. Mon .
"Conformal Field Theories in Fractional Dimensions". United States. https://doi.org/10.1103/PhysRevLett.112.141601. https://www.osti.gov/servlets/purl/1599108.
@article{osti_1599108,
title = {Conformal Field Theories in Fractional Dimensions},
author = {El-Showk, Sheer and Paulos, Miguel and Poland, David and Rychkov, Slava and Simmons-Duffin, David and Vichi, Alessandro},
abstractNote = {We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary conformal field theories connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of Φ4 theory in the ϵ expansion.},
doi = {10.1103/PhysRevLett.112.141601},
journal = {Physical Review Letters},
number = 14,
volume = 112,
place = {United States},
year = {Mon Apr 07 00:00:00 EDT 2014},
month = {Mon Apr 07 00:00:00 EDT 2014}
}
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