skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Operator mixing in the ε -expansion: Scheme and evanescent-operator independence

Abstract

We consider theories with fermionic degrees of freedom that have a fixed point of Wilson–Fisher type in noninteger dimension $$d=4{-}2{\epsilon}$$. Due to the presence of evanescent operators, i.e., operators that vanish in integer dimensions, these theories contain families of infinitely many operators that can mix with each other under renormalization. We clarify the dependence of the corresponding anomalous-dimension matrix on the choice of renormalization scheme beyond leading order in $${\epsilon}$$-expansion. In standard choices of scheme, we find that eigenvalues at the fixed point cannot be extracted from a finite-dimensional block. We illustrate in examples a truncation approach to compute the eigenvalues. These are observable scaling dimensions, and, indeed, we find that the dependence on the choice of scheme cancels. As an application, we obtain the IR scaling dimension of four-fermion operators in QED in $$d=4{-}2{\epsilon}$$ at order $$\mathcal{O}({{\epsilon}}^{2})$$.

Authors:
;
Publication Date:
Research Org.:
Univ. of Chicago, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1425520
Alternate Identifier(s):
OSTI ID: 1498881
Grant/Contract Number:  
SC0009924
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 6; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; conformal field theory; critical exponents; lower-dimensional field theories; quantum electrodynamics; quantum spin liquid; renormalization group; strongly correlated systems; Feynman diagrams

Citation Formats

Di Pietro, Lorenzo, and Stamou, Emmanuel. Operator mixing in the ε -expansion: Scheme and evanescent-operator independence. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.97.065007.
Di Pietro, Lorenzo, & Stamou, Emmanuel. Operator mixing in the ε -expansion: Scheme and evanescent-operator independence. United States. doi:10.1103/PhysRevD.97.065007.
Di Pietro, Lorenzo, and Stamou, Emmanuel. Mon . "Operator mixing in the ε -expansion: Scheme and evanescent-operator independence". United States. doi:10.1103/PhysRevD.97.065007.
@article{osti_1425520,
title = {Operator mixing in the ε -expansion: Scheme and evanescent-operator independence},
author = {Di Pietro, Lorenzo and Stamou, Emmanuel},
abstractNote = {We consider theories with fermionic degrees of freedom that have a fixed point of Wilson–Fisher type in noninteger dimension $d=4{-}2{\epsilon}$. Due to the presence of evanescent operators, i.e., operators that vanish in integer dimensions, these theories contain families of infinitely many operators that can mix with each other under renormalization. We clarify the dependence of the corresponding anomalous-dimension matrix on the choice of renormalization scheme beyond leading order in ${\epsilon}$-expansion. In standard choices of scheme, we find that eigenvalues at the fixed point cannot be extracted from a finite-dimensional block. We illustrate in examples a truncation approach to compute the eigenvalues. These are observable scaling dimensions, and, indeed, we find that the dependence on the choice of scheme cancels. As an application, we obtain the IR scaling dimension of four-fermion operators in QED in $d=4{-}2{\epsilon}$ at order $\mathcal{O}({{\epsilon}}^{2})$.},
doi = {10.1103/PhysRevD.97.065007},
journal = {Physical Review D},
number = 6,
volume = 97,
place = {United States},
year = {2018},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.97.065007

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Bootstrapping SCFTs with four supercharges
journal, August 2015

  • Bobev, Nikolay; El-Showk, Sheer; Mazáč, Dalimil
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)142

Anisotropic non-Fermi liquids
journal, November 2016


Accidental symmetries and the conformal bootstrap
journal, January 2016

  • Chester, Shai M.; Giombi, Simone; Iliesiu, Luca V.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)110

Evanescent operators, scheme dependences and double insertions
journal, November 1995


Quantum Electrodynamics in d = 3 from the ε Expansion
journal, April 2016


Ultraviolet properties of the generalized thirring model with U(N) symmetry
journal, January 1989


Bootstrapping O(N ) vector models with four supercharges in 3 ≤ d ≤ 4
journal, May 2016

  • Chester, Shai M.; Iliesiu, Luca V.; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)103

On C J and C T in conformal QED
journal, August 2016

  • Giombi, Simone; Tarnopolsky, Grigory; Klebanov, Igor R.
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)156

On the vanishing of evanescent operators
journal, March 1991


A scaling theory for the long-range to short-range crossover and an infrared duality
journal, August 2017

  • Behan, Connor; Rastelli, Leonardo; Rychkov, Slava
  • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 35
  • DOI: 10.1088/1751-8121/aa8099

Four loop renormalization of the Gross-Neveu model
journal, December 2016


Unitarity violation at the Wilson-Fisher fixed point in 4 ε dimensions
journal, June 2016


Quantum Field - Theory Models in Less Than 4 Dimensions
journal, May 1973


Bootstrapping O ( N ) vector models in 4 < d < 6
journal, April 2015


QCD nonleading corrections to weak decays in dimensional regularization and 't Hooft-Veltman schemes
journal, March 1990


Notes on spinning operators in fermionic CFT
journal, May 2017

  • Giombi, S.; Kirilin, V.; Skvortsov, E.
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)041

Critical behavior of the QED 3 -Gross-Neveu model: Duality and deconfined criticality
journal, November 2017


Callan-Symanzik Equations and ε Expansions
journal, May 1973


Conformal QED d , F -theorem and the ϵ expansion
journal, February 2016

  • Giombi, Simone; Klebanov, Igor R.; Tarnopolsky, Grigory
  • Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 13
  • DOI: 10.1088/1751-8113/49/13/135403

Fermi Surfaces in General Codimension and a New Controlled Nontrivial Fixed Point
journal, January 2009


Scaling dimensions in QED3 from the ϵ-expansion
journal, December 2017

  • Di Pietro, Lorenzo; Stamou, Emmanuel
  • Journal of High Energy Physics, Vol. 2017, Issue 12
  • DOI: 10.1007/JHEP12(2017)054

Wilson's Theory of Critical Phenomena and Callan-Symanzik Equations in 4 ε Dimensions
journal, July 1973

  • Brezin, E.; Le Guillou, J. C.; Zinn-Justin, J.
  • Physical Review D, Vol. 8, Issue 2
  • DOI: 10.1103/PhysRevD.8.434

Critical Exponents in 3.99 Dimensions
journal, January 1972


Metric and central charge in the perturbative approach to two dimensional fermionic models
journal, May 1990


Quasilocal strange metal
journal, March 2015


Conformal Field Theories in Fractional Dimensions
journal, April 2014


Yukawa conformal field theories and emergent supersymmetry
journal, November 2016

  • Fei, Lin; Giombi, Simone; Klebanov, Igor R.
  • Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 12
  • DOI: 10.1093/ptep/ptw120

Clifford algebras in 2ω dimensions
journal, July 1981

  • Kennedy, A. D.
  • Journal of Mathematical Physics, Vol. 22, Issue 7
  • DOI: 10.1063/1.525069

Approach to Scaling in Renormalized Perturbation Theory
journal, October 1973


Truncated conformal space approach in d dimensions: A cheap alternative to lattice field theory?
journal, January 2015


Emergence of a control parameter for the antiferromagnetic quantum critical metal
journal, June 2017


Deep-inelastic scattering beyond the leading order in asymptotically free gauge theories
journal, December 1978


Ultraviolet renormalons in abelian gauge theories
journal, July 1996


On ${C}_{J}$ and ${C}_{T}$ in the Gross–Neveu and O ( N ) models
journal, September 2016


Perturbative non-Fermi liquids from dimensional regularization
journal, December 2013