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Title: O ( N ) model in 4 < d < 6 : Instantons and complex CFTs

Abstract

We revisit the scalar O($$\textit{N}$$) model in the dimension range 4 < $$\mathit{d}$$ < 6 and study the effects caused by its metastability. As shown in previous work, this model formally possesses a fixed point where, perturbatively in the 1/$$\textit{N}$$ expansion, the operator scaling dimensions are real and above the unitarity bound. Here, we further show that these scaling dimensions do acquire small imaginary parts due to the instanton effects. In d dimensions and for large $$\textit{N}$$, we find that they are of order $$e^{₋ Nf(d)}$$, where, remarkably, the function $$\textit{f(d)}$$ equals the sphere free energy of a conformal scalar in $$\mathit{d}$$ ₋ 2 dimensions. The non-perturbatively small imaginary parts also appear in other observables, such as the sphere free energy and two and three-point function coefficients, and we present some of their calculations. Therefore, at sufficiently large $$\textit{N}$$, the O($$\textit{N}$$) models in 4 < $$\mathit{d}$$ < 6 may be thought of as complex CFTs. When $$\textit{N}$$ is large enough for the imaginary parts to be numerically negligible, the five-dimensional O($$\textit{N}$$) models may be studied using the techniques of numerical bootstrap.

Authors:
; ; ORCiD logo; ;
Publication Date:
Research Org.:
Harvard Univ., Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF); Simons Foundation; US Army Research Office (ARO)
OSTI Identifier:
1600078
Alternate Identifier(s):
OSTI ID: 1801777
Grant/Contract Number:  
SC0007870; SC0019030; PHY-1620059; PHY-1620542; PHY-1820651; PHY-1914860; 488653; W911NF-14-1-0003
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 4; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics

Citation Formats

Giombi, Simone, Huang, Richard, Klebanov, Igor R., Pufu, Silviu S., and Tarnopolsky, Grigory. O ( N ) model in 4 < d < 6 : Instantons and complex CFTs. United States: N. p., 2020. Web. doi:10.1103/PhysRevD.101.045013.
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Giombi, Simone, Huang, Richard, Klebanov, Igor R., Pufu, Silviu S., & Tarnopolsky, Grigory. O ( N ) model in 4 < d < 6 : Instantons and complex CFTs. United States. https://doi.org/10.1103/PhysRevD.101.045013
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Giombi, Simone, Huang, Richard, Klebanov, Igor R., Pufu, Silviu S., and Tarnopolsky, Grigory. Tue . "O ( N ) model in 4 < d < 6 : Instantons and complex CFTs". United States. https://doi.org/10.1103/PhysRevD.101.045013.
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@article{osti_1600078,
title = {O ( N ) model in 4 < d < 6 : Instantons and complex CFTs},
author = {Giombi, Simone and Huang, Richard and Klebanov, Igor R. and Pufu, Silviu S. and Tarnopolsky, Grigory},
abstractNote = {We revisit the scalar O($\textit{N}$) model in the dimension range 4 < $\mathit{d}$ < 6 and study the effects caused by its metastability. As shown in previous work, this model formally possesses a fixed point where, perturbatively in the 1/$\textit{N}$ expansion, the operator scaling dimensions are real and above the unitarity bound. Here, we further show that these scaling dimensions do acquire small imaginary parts due to the instanton effects. In d dimensions and for large $\textit{N}$, we find that they are of order $e^{₋ Nf(d)}$, where, remarkably, the function $\textit{f(d)}$ equals the sphere free energy of a conformal scalar in $\mathit{d}$ ₋ 2 dimensions. The non-perturbatively small imaginary parts also appear in other observables, such as the sphere free energy and two and three-point function coefficients, and we present some of their calculations. Therefore, at sufficiently large $\textit{N}$, the O($\textit{N}$) models in 4 < $\mathit{d}$ < 6 may be thought of as complex CFTs. When $\textit{N}$ is large enough for the imaginary parts to be numerically negligible, the five-dimensional O($\textit{N}$) models may be studied using the techniques of numerical bootstrap.},
doi = {10.1103/PhysRevD.101.045013},
journal = {Physical Review D},
number = 4,
volume = 101,
place = {United States},
year = {Tue Feb 18 00:00:00 EST 2020},
month = {Tue Feb 18 00:00:00 EST 2020}
}
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https://doi.org/10.1103/PhysRevD.101.045013
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Works referenced in this record:

1/n Expansion: Calculation of the exponent ? in the order 1/n3 by the Conformal Bootstrap Method
journal, February 1982

  • Vasil'ev, A. N.; Pis'mak, Yu. M.; Khonkonen, Yu. R.
  • Theoretical and Mathematical Physics, Vol. 50, Issue 2
  • DOI: 10.1007/BF01015292

Conformality lost
journal, December 2009

Large N field theory and AdS tachyons
journal, April 2009

Critical O ( N ) models in 6 − ε dimensions
journal, July 2014

More on equations of motion for interacting massless fields of all spins in 3+1 dimensions
journal, July 1992

Bootstrapping the O(N ) vector models
journal, June 2014

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2014, Issue 6
  • DOI: 10.1007/JHEP06(2014)091

The critical O(N) σ-model at dimensions 2 < d < 4: a list of quasi-primary fields
journal, August 1993

Towards a gravity dual of the unitary Fermi gas
journal, May 2012

Gauge theory correlators from non-critical string theory
journal, May 1998

Renormalization of the Nonlinear σ Model in 2 + ε Dimensions—Application to the Heisenberg Ferromagnets
journal, March 1976

Strongly γ -Deformed N = 4 Supersymmetric Yang-Mills Theory as an Integrable Conformal Field Theory
journal, March 2018

Theory of the Condensation Point
journal, April 2000

Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory
journal, August 1998

Yang-Mills instantons in the large-N limit and the AdS/CFT correspondence
journal, December 1998

Quantum field theory in the large N limit: a review
journal, October 2003

The large $N$ limit of superconformal field theories and supergravity
journal, January 1998

Multi-instanton calculus and the AdS/CFT correspondence in superconformal field theory
journal, July 1999

Anti de Sitter space and holography
journal, January 1998

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

Correlation functions in the CFTd/AdSd+1 correspondence
journal, April 1999

Multi-trace deformations in AdS/CFT: exploring the vacuum structure of the deformed CFT
journal, May 2007

Dimensional regularisation and instantons: A scalar field theory model
journal, September 1979

The higher spin/vector model duality
journal, May 2013

Instanton calculations using dimensional regularisation
journal, November 1978

Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973

Field algebra for criticalO(N) vector non-linear ? models at 2
journal, June 1991

  • Lang, K.; R�hl, W.
  • Zeitschrift f�r Physik C Particles and Fields, Vol. 50, Issue 2
  • DOI: 10.1007/BF01474081

F-theorem without supersymmetry
journal, October 2011

  • Klebanov, Igor R.; Pufu, Silviu S.; Safdi, Benjamin R.
  • Journal of High Energy Physics, Vol. 2011, Issue 10
  • DOI: 10.1007/JHEP10(2011)038

The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019

On instanton contributions to anomalous dimensions in supersymmetric Yang–Mills theory
journal, April 2004

AdS dual of the critical O(N) vector model
journal, December 2002

Polylogarithm identities in a conformal field theory in three dimensions
journal, July 1993

Bootstrapping the O(N) archipelago
journal, November 2015

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)106

Non-perturbative renormalisation using dimensional regularisation: applications to the ϵ expansion
journal, June 1984

  • McKane, A. J.; Wallace, D. J.; Bonfim, O. F. de Alcantara
  • Journal of Physics A: Mathematical and General, Vol. 17, Issue 9
  • DOI: 10.1088/0305-4470/17/9/021

Conformally Coupled Scalars, Instantons, and Vacuum Instability in 4D Anti-de Sitter Space
journal, June 2007

  • de Haro, Sebastian; Papadimitriou, Ioannis; Petkou, Anastasios C.
  • Physical Review Letters, Vol. 98, Issue 23
  • DOI: 10.1103/PhysRevLett.98.231601

Walking, weak first-order transitions, and complex CFTs
journal, October 2018

  • Gorbenko, Victor; Rychkov, Slava; Zan, Bernardo
  • Journal of High Energy Physics, Vol. 2018, Issue 10
  • DOI: 10.1007/JHEP10(2018)108

Consistent equations for interacting gauge fields of all spins in 3+1 dimensions
journal, July 1990

Perturbative search for fixed lines in large- N gauge theories
journal, August 2005

CT and CJ up to next-to-leading order in in the conformally invariant O(N) vector model for 2 < d < 4
journal, October 1995

Nonlinear equations for symmetric massless higher spin fields in (A)dSd
journal, August 2003

Comments on higher-spin holography
journal, February 2012

Proof of the Triviality of ϕ d 4 Field Theory and Some Mean-Field Features of Ising Models for d > 4
journal, July 1981

Bounding scalar operator dimensions in 4 D CFT
journal, December 2008

Dynamics of Finite-Temperature Conformal Field Theories from Operator Product Expansion Inversion Formulas
journal, August 2018

Instanton-induced Yang-Mills correlation functions at large N and their AdS 5 × S 5 duals
journal, April 2003

Critical Exponents in 3.99 Dimensions
journal, January 1972

Fate of the false vacuum. II. First quantum corrections
journal, September 1977

Conformality Loss, Walking, and 4D Complex Conformal Field Theories at Weak Coupling
journal, February 2020

Theory of the condensation point
journal, January 1967

The renormalization group and the ε expansion
journal, August 1974

Three loop analysis of the critical O ( N ) models in 6 − ε dimensions
journal, February 2015

Perturbation theory at large order. II. Role of the vacuum instability
journal, March 1977

Vacuum instability in scalar field theories
journal, May 1979

The theory of non-renormalizable interactions
journal, December 1975

Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
journal, January 2018

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