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Bootstrapping Mixed Correlators in the 3D Ising Model
Open accessAbstract
We study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a Z2 global symmetry. For the leading Z2-odd operator σ and Z2-even operator ϵ, we obtain numerical constraints on the allowed dimensions (Δ σ , Δ ϵ ) assuming that σ and ϵ are the only relevant scalars in the theory. These constraints yield a small closed region in (Δ σ , Δ ϵ ) space compatible with the known values in the 3D Ising CFT.
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Cites
Critical phenomena and renormalization-group theory
Pelissetto, A., & Vicari, E. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00219-3 · Cited by 1,630
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Critical Phenomena and Renormalization-Group TheoryPreprint
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Scaling, universality, and renormalization: Three pillars of modern critical phenomena
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Bounding scalar operator dimensions in 4 D CFT
Rattazzi, R., Rychkov, V. S., Tonni, E., & Vichi, A. (2008) · Journal of High Energy Physics · doi:10.1088/1126-6708/2008/12/031 · Cited by 913
Solving the 3D Ising model with the conformal bootstrap
El-Showk, S., Paulos, M. F., Poland, D., Rychkov, S., Simmons–Duffin, D., & Vichi, A. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.025022 · Cited by 833
Holography from conformal field theory
Heemskerk, I., Penedones, J., Polchinski, J., & Sully, J. (2009) · Journal of High Energy Physics · doi:10.1088/1126-6708/2009/10/079 · Cited by 787
Conformal four point functions and the operator product expansion
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El-Showk, S., Paulos, M. F., Poland, D., Rychkov, S., Simmons–Duffin, D., & Vichi, A. (2014) · Journal of Statistical Physics · doi:10.1007/s10955-014-1042-7 · Cited by 626
Spinning conformal correlators
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Cited by
The conformal bootstrap: Theory, numerical techniques, and applications
Poland, D., Rychkov, S., & Vichi, A. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015002 · Cited by 760
The nonperturbative functional renormalization group and its applications
Dupuis, N., Canet, L., Eichhorn, A., Metzner, W., Pawlowski, J. M., Tissier, M., & Wschebor, N. (2021) · Physics Reports · doi:10.1016/j.physrep.2021.01.001 · Cited by 660
EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions
Rychkov, S. (2017) · SpringerBriefs in Physics · doi:10.1007/978-3-319-43626-5 · Cited by 305
Metadata
- Authors
- Kosa, F., Pol, D., & Simmons-duffinb, D.
- Venue
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)
- Publisher
- Office of Scientific and Technical Information
- Published
- 2016-08-16
- OpenAlex
- W3099294508
- Cited by
- 317
- References
- 65
- FWCI
- 19.14
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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