Critical O(N) model to order $\epsilon^4$ from analytic bootstrap - INSPIRE

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Critical O(N) model to order $\epsilon^4$ from analytic bootstrap

Jan 10, 2018

22 pages

Published in:

J.Phys.A 52 (2019) 2, 025401

Published: Dec 10, 2018

e-Print:

1801.03512 [hep-th]

DOI:

10.1088/1751-8121/aaf1e2

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Abstract: (IOP)

We compute, using the method of large spin perturbation theory, the anomalous dimensions and OPE coefficients of all leading twist operators in the critical model, to fourth order in the -expansion. This is done fully within a bootstrap framework, and generalizes a recent result for the CFT-data of the Wilson–Fisher model. The anomalous dimensions we obtain for the singlet operators agree with the literature values, obtained by diagrammatic techniques, while the anomalous dimensions for operators in other representations, as well as all OPE coefficients, are new. From the results for the OPE coefficients, we derive the corrections to the central charges and , which are found to be compatible with the known large expansions. Predictions for the central charge in the strongly coupled 3d model, including the 3d Ising model, are made for various values of , which compare favourably with numerical results and previous predictions.

Note:

18+5 pages, 1 figure, Mathematica file included. v2: revised and extended version

model: O(N)
operator: twist
operator product expansion
anomalous dimension
perturbation theory
central charge
bootstrap
singlet
spin

References(40)

Figures(1)

[1]

Bounding scalar operator dimensions in 4D CFT

Riccardo Rattazzi
(
- ITPP, Lausanne
)
,
Vyacheslav S. Rychkov
(
- INFN, Pisa and
- Pisa, Scuola Normale Superiore
)
,
Erik Tonni
(
- INFN, Pisa and
- Pisa U.
)
,
Alessandro Vichi
(
- ITPP, Lausanne
)

- JHEP 12 (2008) 031
•
e-Print:
- 0807.0004
•
DOI:
- 10.1088/1126-6708/2008/12/031

[2]

Comments on operators with large spin

- JHEP 11 (2007) 019
•
e-Print:
- 0708.0672
•
DOI:
- 10.1088/1126-6708/2007/11/019

[3]

The Analytic Bootstrap and AdS Superhorizon Locality

A.Liam Fitzpatrick
(
- Stanford U., ITP
)
,
Jared Kaplan
(
- Johns Hopkins U. and
- Stanford U., ITP
)
,
David Poland
(
- Yale U.
)
,
David Simmons-Duffin
(
- Princeton, Inst. Advanced Study
)

- JHEP 12 (2013) 004
•
e-Print:
- 1212.3616
•
DOI:
- 10.1007/JHEP12(2013)004

[4]

Convexity and Liberation at Large Spin

- JHEP 11 (2013) 140
•
e-Print:
- 1212.4103
•
DOI:
- 10.1007/JHEP11(2013)140

[5]

and &Lstrok

Alday L.
,
Bissi

[5]

Large spin systematics in CFT

- JHEP 11 (2015) 101
•
e-Print:
- 1502.07707
•
DOI:
- 10.1007/JHEP11(2015)101

[6]

Large Spin Perturbation Theory for Conformal Field Theories

Luis F. Alday
(
- Oxford U., Inst. Math.
)

- Phys.Rev.Lett. 119 (2017) 11, 111601
•
e-Print:
- 1611.01500
•
DOI:
- 10.1103/PhysRevLett.119.111601

[7]

Analyticity in Spin in Conformal Theories

Simon Caron-Huot
(
- McGill U.
)

- JHEP 09 (2017) 078
•
e-Print:
- 1703.00278
•
DOI:
- 10.1007/JHEP09(2017)078

[8]

Gravitational S-matrix from CFT dispersion relations

Luis F. Alday
(
- Oxford U., Inst. Math.
)
,
Simon Caron-Huot
(
- McGill U.
)

- JHEP 12 (2018) 017
•
e-Print:
- 1711.02031
•
DOI:
- 10.1007/JHEP12(2018)017

[9]

A spacetime derivation of the Lorentzian OPE inversion formula

- JHEP 07 (2018) 085
•
e-Print:
- 1711.03816
•
DOI:
- 10.1007/JHEP07(2018)085

[10]

Solving CFTs with Weakly Broken Higher Spin Symmetry

Luis F. Alday
(
- Oxford U., Inst. Math.
)

- JHEP 10 (2017) 161
•
e-Print:
- 1612.00696
•
DOI:
- 10.1007/JHEP10(2017)161

[11]

Loop Corrections to Supergravity on $AdS_5 \times S^5$

- Phys.Rev.Lett. 119 (2017) 17, 171601
•
e-Print:
- 1706.02388
•
DOI:
- 10.1103/PhysRevLett.119.171601

[12]

Simplifying large spin bootstrap in Mellin space

- JHEP 01 (2018) 152
•
e-Print:
- 1709.06110
•
DOI:
- 10.1007/JHEP01(2018)152

[13]

and &Lstrok

Henriksson

[13]

Perturbative Four-Point Functions from the Analytic Conformal Bootstrap

- JHEP 02 (2018) 123
•
e-Print:
- 1710.06242
•
DOI:
- 10.1007/JHEP02(2018)123

[14]

The Analytic Bootstrap in Fermionic CFTs

Mark van Loon
(
- Oxford U., Inst. Math.
)

- JHEP 01 (2018) 104
•
e-Print:
- 1711.02099
•
DOI:
- 10.1007/JHEP01(2018)104

[15]

Taming the $\epsilon$ -expansion with large spin perturbation theory

- JHEP 07 (2018) 131
•
e-Print:
- 1712.02314
•
DOI:
- 10.1007/JHEP07(2018)131

[16]

Critical phenomena and renormalization group theory

Andrea Pelissetto
(
- INFN, Rome and
- Rome U.
)
,
Ettore Vicari
(
- INFN, Pisa and
- Pisa U.
)

- Phys.Rept. 368 (2002) 549-727
•
e-Print:
- cond-mat/0012164
•
DOI:
- 10.1016/S0370-1573(02)00219-3

[17]

Four loop anomalous dimensions of gradient operators in phi**4 theory

- Eur.Phys.J.C 2 (1998) 569-579
•
e-Print:
- hep-ph/9705268
•
DOI:
- 10.1007/s100520050162

[18]

Higher spin currents in the critical $O(N$ ) vector model at $1/N^{2}$

A.N. Manashov
(
- Hamburg U. and
- Munich U., ASC
)
,
E.D. Skvortsov
(
- Lebedev Inst. and
- Munich U., ASC
)
,
M. Strohmaier
(
- Regensburg U.
)

- JHEP 08 (2017) 106
•
e-Print:
- 1706.09256
•
DOI:
- 10.1007/JHEP08(2017)106

[19]

Critical O(N) vector nonlinear sigma models: A Resume of their field structure

Klaus Lang
(
- Kaiserslautern U.
)
,
Werner Rühl
(
- Kaiserslautern U.
)

- Adv.Appl.Clifford Algebras 4 (1994) S1, 203-216
•
e-Print:
- hep-th/9311046

[20]

C(T) and C(J) up to next-to-leading order in 1/N in the conformally invariant 0(N) vector model for 2 < d < 4

Anastasios C. Petkou
(
- Thessaloniki U.
)

- Phys.Lett.B 359 (1995) 101-107
•
e-Print:
- hep-th/9506116
•
DOI:
- 10.1016/0370-2693(95)00936-F

[21]

The Simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion

Sergey E. Derkachov
(
- Nordita
)
,
A.N. Manashov
(
- St. Petersburg State U.
)

- Nucl.Phys.B 522 (1998) 301-320
•
e-Print:
- hep-th/9710015
•
DOI:
- 10.1016/S0550-3213(98)00103-5

[22]

J. Phys. A: Math. Theor. 49 405402

Diab
,
Fei
,
Giombi
,
Klebanov I.
,
Tarnopolsky

•
DOI:
- 10.1088/1751-8121/49/40/405402

[23]

The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points

Ferdinando Gliozzi
(
- Turin U. and
- INFN, Turin
)
,
Andrea L. Guerrieri
(
- Chulalongkorn U. and
- INFN, Rome2
)
,
Anastasios C. Petkou
(
- Aristotle U., Thessaloniki
)
,
Congkao Wen
(
- Caltech and
- UCLA
)

- JHEP 04 (2017) 056
•
e-Print:
- 1702.03938
•
DOI:
- 10.1007/JHEP04(2017)056

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