Bootstrapping mixed correlators in three-dimensional cubic theories II

Abstract

Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the \varepsilonε expansion. In an earlier work, we used the nonperturbative numerical conformal bootstrap to provide evidence for the existence of a previously unknown 3D CFT with cubic symmetry, dubbed “Platonic CFT”. In this work, we make further use of the numerical conformal bootstrap to perform a three-dimensional scan in the space of scaling dimensions of three low-lying operators. We find a three-dimensional isolated allowed region in parameter space, which includes both the 3D (decoupled) Ising model and the Platonic CFT. The essential assumptions on the spectrum of operators used to provide the isolated allowed region include the existence of a stress-energy tensor and the irrelevance of certain operators (in the renormalization group sense).

Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D

“…The dependence of bootstrap bounds on assumptions in sectors that contain conserved operators have been studied in other cases in e.g. [59][60][61][62].…”

Dynamic scaling in the quenched disordered classicalN-vector model

“…It would also be interesting to explore how long range quenched disorder may affect the results from this study [3]. It would be interesting to see how nonperturbative RG, applied in the related problem of dilute Ising model [27] and conformal field theory methods [28], apply to the current model. For the N = 3 case, i.e., for the classical Heisenberg model, the conserved dynamics of the spin model includes mode coupling terms [13,16], which affects the dynamic scaling near the critical point, but not the static critical exponents.…”

“…at this stable RG fixed point: Using the fact that μ 1 ≡D/u diverges, i.e.,D u, we getD = 3v at the RG fixed point. Notice that we can arrive at the above condition directly by using either (26) or (28) above and setting u = 0 = D at the RG fixed point. In other words, if u = 0 = D then anyD > 0 and v > 0 satisfyingD = 3v are fixed point values, or equivalently, μ 3 =D/v appears as a fixed ratio in the problem, i.e., the precise bare (unrenormalized) or microscopic values of D and v may affect the large scale scaling behavior.…”

Crossover exponents, fractal dimensions and logarithms in Landau–Potts field theories

“…(2) S 1.64(4) 0.82(2) 0.16 (3) ators V and T of this paper are identified with X and Y of [74,75] (see also [72,73] for the discussion of the underlying irreps). The combined numerical effort gives the scaling dimensions ϕ ≈ 0.520, S ≈ 1.521, X ≈ 1.221, and Y ≈ 1.181.…”