Bootstrapping the minimal 3D SCFT

Self Cite

118

We study the spectrum and OPE coefficients of the three-dimensional critical O(2) model, using four-point functions of the leading scalars with charges 0, 1, and 2 (s, ϕ, and t). We obtain numerical predictions for low-twist OPE data in several charge sectors using the extremal functional method. We compare the results to analytical estimates using the Lorentzian inversion formula and a small amount of numerical input. We find agreement between the analytic and numerical predictions. We also give evidence that certain scalar operators lie on double-twist Regge trajectories and obtain estimates for the leading Regge intercepts of the O(2) model.

Section: Analytic Bootstrapmentioning

confidence: 99%

The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT

Liu

Meltzer

Poland

et al. 2020

Self Cite

118

“…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].…”

Section: July 2019mentioning

confidence: 99%

“…The conformal bootstrap [3][4][5] is a non-perturbative method that places rigorous numerical bounds [6] on scaling dimensions and operator product expansion (OPE) coefficients that appear in a given four-point function of a conformal field theory (CFT) (for reviews, see [7][8][9][10][11]). In the best scenario, these bounds form precise islands in the space of a small number of CFT data that contain the values of a single known CFT, as was originally shown for the 3d Ising model [12][13][14] and later generalized to the 3d O(N ) models [14,15] and N = 1 Ising model [16,17]. In these cases, the small allowed islands were found in the space of scaling dimensions of the two lowest-lying scalar operators which, in these theories, are the only relevant operators in their corresponding global symmetry charge sectors.…”

Section: Introductionmentioning

confidence: 97%

The M-theory archipelago

Agmon

Chester

Pufu

2020

105

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.

“…In this work we carry out the large-spin expansions for the leading twist trajectories and their OPE coefficients to subleading order, in the hope that it will provide a valuable cross-check to future derivations of the Lorentzian inversion formalism for 3d fermions and can be eventually applied to interesting 3d CFTs with fermions. This is in part motivated by recent progress in the numerical bootstrap for such theories, including the 3d Gross-Neveu-Yukawa models [35,36] and the minimal 3d N = 1 SCFT [37,38]. 2 We conclude with a discussion of future directions in section 4 and give a brief review of the embedding formalism and other technical formulas in appendices A and B.…”

Section: Introductionmentioning

confidence: 99%

More analytic bootstrap: nonperturbative effects and fermions

Albayrak

Meltzer

Poland

2019

Self Cite

104

We develop the analytic bootstrap in several directions. First, we discuss the appearance of nonperturbative effects in the Lorentzian inversion formula, which are exponentially suppressed at large spin but important at finite spin. We show that these effects are important for precision applications of the analytic bootstrap in the context of the 3d Ising and O(2) models. In the former they allow us to reproduce the spin-2 stress tensor with error at the 10 −5 level while in the latter requiring that we reproduce the stress tensor allows us to predict the coupling to the leading charge-2 operator. We also extend perturbative calculations in the lightcone bootstrap to fermion 4-point functions in 3d, predicting the leading and subleading asymptotic behavior for the double-twist operators built out of two fermions.