Bootstrapping the 3d Ising model at finite temperature

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: Exact Vs Approximate Generating Functionmentioning

confidence: 99%

Section: Additional Applicationsmentioning

confidence: 99%

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

Liu

Meltzer

Poland

et al. 2020

Self Cite

118

“…Because of the presence of multi-twist operators in the other channel, the LIF, naïvely applied, yields only an asymptotic expansion for anomalous dimensions at large spin. To understand finite spin, one can introduce a generating function C(z,h) that is well-defined at finite spin and perform numerical fits to extract anomalous dimensions, as in [27,33,34,99]. Dispersive functionals give an alternative way to control the sum over multi-twists and obtain well-defined results at finite spin.…”

Section: Jhep05(2021)243mentioning

confidence: 99%

Dispersive CFT sum rules

Caron-Huot

Mazáč

Rastelli

et al. 2021

Self Cite

167

We give a unified treatment of dispersive sum rules for four-point correlators in conformal field theory. We call a sum rule “dispersive” if it has double zeros at all double-twist operators above a fixed twist gap. Dispersive sum rules have their conceptual origin in Lorentzian kinematics and absorptive physics (the notion of double discontinuity). They have been discussed using three seemingly different methods: analytic functionals dual to double-twist operators, dispersion relations in position space, and dispersion relations in Mellin space. We show that these three approaches can be mapped into one another and lead to completely equivalent sum rules. A central idea of our discussion is a fully nonperturbative expansion of the correlator as a sum over Polyakov-Regge blocks. Unlike the usual OPE sum, the Polyakov-Regge expansion utilizes the data of two separate channels, while having (term by term) good Regge behavior in the third channel. We construct sum rules which are non-negative above the double-twist gap; they have the physical interpretation of a subtracted version of “superconvergence” sum rules. We expect dispersive sum rules to be a very useful tool to study expansions around mean-field theory, and to constrain the low-energy description of holographic CFTs with a large gap. We give examples of the first kind of applications, notably we exhibit a candidate extremal functional for the spin-two gap problem.

“…It would be nice to use the analytic bootstrap at finite temperature [39][40][41] to compute the values of Υ and H xx and compare them with the predictions given in this work.…”

Section: Conductivity At Finite Temperaturementioning

confidence: 86%

Mixed scalar-current bootstrap in three dimensions

Reehorst

Trevisani

Vichi

2020

We study the mixed system of correlation functions involving a scalar field charged under a global U(1) symmetry and the associated conserved spin-1 current Jμ. Using numerical bootstrap techniques we obtain bounds on new observables not accessible in the usual scalar bootstrap. We then specialize to the O(2) model and extract rigorous bounds on the three-point function coefficient of two currents and the unique relevant scalar singlet, as well as those of two currents and the stress tensor. Using these results, and comparing with a quantum Monte Carlo simulation of the O(2) model conductivity, we give estimates of the thermal one-point function of the relevant singlet and the stress tensor. We also obtain new bounds on operators in various sectors.