Bootstrapping the 3d Ising twist defect

Gaiotto, Davide; Mazáč, Dalimil; Paulos, Miguel F.

doi:10.1007/jhep03(2014)100

Cited by 176 publications

(276 citation statements)

References 50 publications

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“…As a consistency check the generalized free scalar, which is described by the curve ∆ = 2∆ σ is well below our bounds in any d; we have also checked that for d = 2 we reproduce existing results in the literature [11]. Notice however that the bound for d = 1.00001 does not match the result in [23] for d = 1. Indeed for d = 1 there is a generalized free fermion (GFF) solution available which has ∆ ε = 1 + 2∆ σ , shown as a dashed line in our figure.…”

Section: Jhep03(2015)167 2 Reviewsupporting

confidence: 69%

“…Here we are actually quite confident that the feature corresponds to a true non-analyticity in the limit where we include infinite constraints, since we expect the d = 1 bound to precisely saturate the straight line ∆ ε = 1 + 2∆ σ . This corresponds to a generalized free fermion [23], whose four point function is given by 12) where…”

Section: Resultsmentioning

confidence: 99%

“…The seminal work [8] proposed an efficient numerical procedure for extracting information about the space of all conformal field theories, and has been followed by many other works in a variety of contexts [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Similarly, the studies [24][25][26][27] have shown that it is even possible to analytically derive completely generic constraints on the spectrum of CFTs.…”

Section: Introductionmentioning

confidence: 99%

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No unitary bootstrap for the fractal Ising model

Golden

Paulos

2015

J. High Energ. Phys.

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We consider the conformal bootstrap for spacetime dimension 1 < d < 2. We determine bounds on operator dimensions and compare our results with various theoretical and numerical models, in particular with resummed -expansion and Monte Carlo simulations of the Ising model on fractal lattices. The bounds clearly rule out that these models correspond to unitary conformal field theories. We also clarify the d → 1 limit of the conformal bootstrap, showing that bounds can be -and indeed are -discontinuous in this limit. This discontinuity implies that for small = d − 1 the expected critical exponents for the Ising model are disallowed, and in particular those of the d − 1 expansion. Altogether these results strongly suggest that the Ising model universality class cannot be described by a unitary CFT below d = 2. We argue this also from a bootstrap perspective, by showing that the 2 ≤ d < 4 Ising "kink" splits into two features which grow apart below d = 2.

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Section: Jhep03(2015)167 2 Reviewsupporting

confidence: 69%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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No unitary bootstrap for the fractal Ising model

Golden

Paulos

2015

J. High Energ. Phys.

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“…Indeed, this will be the reason that we can make progress in studying the conformal phase of (2, 0) SCFTs despite the absence of a conventional definition. Thus in broad terms this work will mirror many recent bootstrap studies [37][38][39]59,60,. We will not review the basic philosophy in any detail here.…”

Section: The Bootstrap Program For (2 0) Theoriesmentioning

confidence: 93%

The (2, 0) superconformal bootstrap

et al. 2016

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We develop the conformal bootstrap program for six-dimensional conformal field theories with (2, 0) supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on operator product expansion (OPE) coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the light cone expansion of the crossing equation. Our principal result is strong evidence that the A 1 theory realizes the minimal allowed central charge (c ¼ 25) for any interacting (2, 0) theory. This implies that the full stress tensor four-point function of the A 1 theory is the unique unitary solution to the crossing symmetry equation at c ¼ 25. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting (2, 0) theory of central charge c. For large c, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.

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“…Finally, as we will review shortly, an explicit formula likely exists for the optimal 1D bootstrap bound, begging for an analytic explanation. Numerous interesting systems exhibit the global conformal symmetry in one dimension, including conformal boundaries in 2D CFTs, line defects in general CFTs [14,15], and various examples of AdS 2 /CFT 1 holography.…”

Section: The Conformal Bootstrap In One Dimensionmentioning

confidence: 99%

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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Bootstrapping the 3d Ising twist defect

Cited by 176 publications

References 50 publications

No unitary bootstrap for the fractal Ising model

No unitary bootstrap for the fractal Ising model

The (2, 0) superconformal bootstrap

Analytic bounds and emergence of AdS2 physics from the conformal bootstrap

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