Bootstrapping mixed correlators in three-dimensional cubic theories

Kousvos, Stefanos R.; Stergiou, A.

doi:10.21468/scipostphys.6.3.035

Cited by 46 publications

(78 citation statements)

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“…4 and 6 below. At the second kink we find β = 0.394(5) , ν = 0.590 (8) , (1.4) in good agreement with the measurement β = 0.36(2) of [18].…”

Section: Introduction and Discussion Of Resultssupporting

confidence: 86%

“…3 and 5 below. Although this kink is not as sharp as the one described above, a spectrum analysis yields β = 0.355(5) , ν = 0.576 (8) .…”

Section: Introduction and Discussion Of Resultsmentioning

confidence: 69%

“…Its power has already been showcased in the 3D Ising [3] and O(N ) models [4][5][6], and recently it has suggested the existence of a new cubic universality class in 3D, referred to as C 3 or Platonic [7,8]. Now that the method has showed its strength, it is time for it to be applied to the plethora of examples of CFTs in d = 3 suggested by the ε = 4 − d expansion [9][10][11].…”

Section: Introduction and Discussion Of Resultsmentioning

confidence: 99%

“…5.2.2] we have λ here = λ there − m+2 3(mn+2) g there and g here = g there . 8 Although the theory of n decoupled O(m) models in item 3 on the list also has symmetry MNm,n, we will never characterize it that way; we will reserve that characterization for the fully-interacting case in 4.…”

Section: Mn Anisotropymentioning

confidence: 99%

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Bootstrapping MN and tetragonal CFTs in three dimensions

Stergiou

2019

SciPost Phys.

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Conformal field theories (CFTs) with MN and tetragonal global symmetry in d = 2 + 1 dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions in a wide class of materials. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. In the tetragonal case, no new kinks are found. Estimates for critical exponents are provided for a few cases describing phase transitions in various materials. In two particular MN cases, corresponding to theories with global symmetry groups O(2) 2 S 2 and O(2) 3 S 3 , a second kink is found. In the O(2) 2 S 2 case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO 2 and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the O(2) 3 S 3 case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.

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“…4 and 6 below. At the second kink we find β = 0.394(5) , ν = 0.590 (8) , (1.4) in good agreement with the measurement β = 0.36(2) of [18].…”

Section: Introduction and Discussion Of Resultssupporting

confidence: 86%

“…3 and 5 below. Although this kink is not as sharp as the one described above, a spectrum analysis yields β = 0.355(5) , ν = 0.576 (8) .…”

Section: Introduction and Discussion Of Resultsmentioning

confidence: 69%

Section: Introduction and Discussion Of Resultsmentioning

confidence: 99%

Section: Mn Anisotropymentioning

confidence: 99%

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Bootstrapping MN and tetragonal CFTs in three dimensions

Stergiou

2019

SciPost Phys.

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“…Since S 2 and S 3 have fixed scaling dimensions 1 and 3/2, respectively, we cannot find 1 Scaling dimension islands for these and other theories can be found even from single correlators by imposing gaps in multiple operators that appear in the OPE [18], such as spin 1 operators. Islands have also been found for other theories by considering mixed correlators and imposing gaps on both relevant and irrelevant operators [19,20]. However, all these cases involve gaps that, while in many cases plausible, are not rigorously justified.…”

Section: Introductionmentioning

confidence: 91%

The M-theory archipelago

Agmon

Chester

Pufu

2020

J. High Energ. Phys.

105

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We combine supersymmetric localization results and the numerical conformal bootstrap technique to study the 3d maximally supersymmetric (N = 8) CFT on N coincident M2branes (the U (N ) k × U (N ) −k ABJM theory at Chern-Simons level k = 1). In particular, we perform a mixed correlator bootstrap study of the superconformal primaries of the stress tensor multiplet and of the next possible lowest-dimension half-BPS multiplet that is allowed by 3d N = 8 superconformal symmetry. Of all known 3d N = 8 SCFTs, the k = 1 ABJM theory is the only one that contains both types of multiplets in its operator spectrum. By imposing the values of the short OPE coefficients that can be computed exactly using supersymmetric localization, we are able to derive precise islands in the space of semi-short OPE coefficients for an infinite number of such coefficients. We find that these islands decrease in size with increasing N . More generally, we also analyze 3d N = 8 SCFT that contain both aforementioned multiplets in their operator spectra without inputing any additional information that is specific to ABJM theory. For such theories, we compute upper and lower bounds on the semi-short OPE coefficients as well as upper bounds on the scaling dimension of the lowest unprotected scalar operator. These latter bounds are more constraining than the analogous bounds previously derived from a single correlator bootstrap of the stress tensor multiplet. This leads us to conjecture that the U (N ) 2 × U (N + 1) −2 ABJ theory, and not the k = 1 ABJM theory, saturates the single correlator bounds. July 2019correlator system that is the primary focus of this paper has three advantages:1. In principle, the free multiplet S 1 is allowed to appear in the mixed OPE S 2 × S 3 , so 3 Lower bounds can be computed for the OPE coefficients of the operators that have been assumed to be relevant, since there is now a gap between them and the continuum of irrelevant operators. Islands in the space of these OPE coefficients are reported in [14,17].4 Note that for 4d SCFTs with N ≥ 3, all the protected operators that appear in the four-point function of half-BPS operator are already fixed by the 2d chiral algebra [36], so the bootstrap studies [37-39] could not compute any upper bounds on OPE coefficients. 5 Percent error as computed, for instance, in (4.13). 6 Here, Λ is a parameter counting the number of derivatives in the functionals used for numerical bootstrap. See [41] for the precise definition. 9 Our blocks are normalized as G k12,k34 ∆, (r, η) ∼ r ∆ P (η) as r → 0, where P (η) is a Legendre polynomial.

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Analytic and numerical bootstrap for the long-range Ising model

Behan,

Lauria,

Nocchi

et al. 2024

J. High Energ. Phys.

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We combine perturbation theory with analytic and numerical bootstrap techniques to study the critical point of the long-range Ising (LRI) model in two and three dimensions. This model interpolates between short-range Ising (SRI) and mean-field behaviour. We use the Lorentzian inversion formula to compute infinitely many three-loop corrections in the two-dimensional LRI near the mean-field end. We further exploit the exact OPE relations that follow from bulk locality of the LRI to compute infinitely many two-loop corrections near the mean-field end, as well as some one-loop corrections near SRI. By including such exact OPE relations in the crossing equations for LRI we set up a very constrained bootstrap problem, which we solve numerically using SDPB. We find a family of sharp kinks for two- and three-dimensional theories which compare favourably to perturbative predictions, as well as some Monte Carlo simulations for the two-dimensional LRI.

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Bootstrapping mixed correlators in three-dimensional cubic theories

Cited by 46 publications

References 46 publications

Bootstrapping MN and tetragonal CFTs in three dimensions

Bootstrapping MN and tetragonal CFTs in three dimensions

The M-theory archipelago

Analytic and numerical bootstrap for the long-range Ising model

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