Bootstrapping the O(N) archipelago

Kos, Filip; Poland, David; Simmons-Duffin, David; Vichi, Alessandro

doi:10.1007/jhep11(2015)106

Cited by 218 publications

(404 citation statements)

References 72 publications

(116 reference statements)

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“…We consider a primary operator φ in the fundamental representation and denote the lowest-dimensional scalar singlet operator in the φ × φ OPE by S. It was found in refs. [14,16] that these CFTs have kinks in the bound on ∆ S as a function of ∆ φ similar to that found for the Ising model. Moreover, the kinks coincide, for all values of n that have been studied, with the values of ∆ φ and ∆ S associated with the 3D O(n) models.…”

Section: D Ising and O(n) Modelssupporting

confidence: 73%

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The effective bootstrap

Echeverri

Harling

Serone

2016

J. High Energ. Phys.

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Abstract:We study the numerical bounds obtained using a conformal-bootstrap method -advocated in ref.[1] but never implemented so far -where different points in the plane of conformal cross ratios z andz are sampled. In contrast to the most used method based on derivatives evaluated at the symmetric point z =z = 1/2, we can consistently "integrate out" higher-dimensional operators and get a reduced simpler, and faster to solve, set of bootstrap equations. We test this "effective" bootstrap by studying the 3D Ising and O(n) vector models and bounds on generic 4D CFTs, for which extensive results are already available in the literature. We also determine the scaling dimensions of certain scalar operators in the O(n) vector models, with n = 2, 3, 4, which have not yet been computed using bootstrap techniques.

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Section: D Ising and O(n) Modelssupporting

confidence: 73%

“…[23] and [24]. 16 16 More precisely, ∆ S has been determined also by other means, such as fixed-dimension expansion and Monte Carlo simulations. On the other hand, since ∆ T has been determined only using the -expansion, we have decided to omit the other results for ∆ S .…”

Section: A Closer Look At the Spectrum Of 3d O(n) Modelsmentioning

confidence: 99%

The effective bootstrap

Echeverri

Harling

Serone

2016

J. High Energ. Phys.

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“…Crossing symmetry of mixed correlators dramatically improves the bootstrap bounds [11,24]. Similar improvements are observed to occur in 1D [25].…”

Section: Future Directionssupporting

confidence: 62%

Analytic bounds and emergence of AdS2 physics from the conformal bootstrap

Mazáč

2017

J. High Energ. Phys.

104

167

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We study analytically the constraints of the conformal bootstrap on the lowlying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals acting on the conformal bootstrap equation. In 1D, we use the new basis to construct extremal functionals leading to the optimal upper bound on the gap above identity in the OPE of two identical primary operators of integer or half-integer scaling dimension. We also prove an upper bound on the twist gap in 2D theories with global conformal symmetry. When the external scaling dimensions are large, our functionals provide a direct point of contact between crossing in a 1D CFT and scattering of massive particles in large AdS 2 . In particular, CFT crossing can be shown to imply that appropriate OPE coefficients exhibit an exponential suppression characteristic of massive bound states, and that the 2D flat-space S-matrix should be analytic away from the real axis.

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“…In this paper, we derive universal necessary conditions for such emergent symmetry enhancement from discrete symmetry to continuous symmetry under the renormalization group (RG) flow by using the recently developed technique of numerical conformal bootstrap program in three-dimensions [3][4][5][6][7][8][9][10][11]. We will show that the conformal symmetry imposes a strong constraint on when the emergent symmetry enhancement can or cannot occur.…”

Section: Introductionmentioning

confidence: 99%

Necessary Condition for Emergent Symmetry from the Conformal Bootstrap

Nakayama

Ohtsuki

2016

Phys. Rev. Lett.

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We use the conformal bootstrap program to derive necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g. Zn) to continuous symmetry (e.g. U (1)) under the renormalization group flow. In three dimensions, in order for Z2 symmetry to be enhanced to U (1) symmetry, the conformal bootstrap program predicts that the scaling dimension of the order parameter field at the infrared conformal fixed point must satisfy ∆1 > 1.08. We also obtain the similar conditions for Z3 symmetry with ∆1 > 0.580 and Z4 symmetry with ∆1 > 0.504 from the simultaneous conformal bootstrap analysis of multiple four-point functions. Our necessary conditions impose severe constraints on many controversial physics such as the chiral phase transition in QCD, the deconfinement criticality in Néel-VBS transitions and anisotropic deformations in critical O(n) models. In some cases, we find that the conformal bootstrap program dashes hopes of emergent symmetry enhancement proposed in the literature.

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Bootstrapping the O(N) archipelago

Cited by 218 publications

References 72 publications

The effective bootstrap

The effective bootstrap

Analytic bounds and emergence of AdS2 physics from the conformal bootstrap

Necessary Condition for Emergent Symmetry from the Conformal Bootstrap

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