Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1802.02319

A structural test for the conformal invariance of the critical 3d Ising model

Simao Meneses·Joao Penedones·Slava Rychkov·J. M. Viana Parente Lopes·Pierre Yvernay
View original source ↗Read source document ↗Export metadata ↓

Abstract

How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current -- a non-conserved vector operator of dimension exactly $(d-1)$, whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound $Δ_V>5.0$ on the scaling dimension of the lowest virial current candidate $V$, well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.

Explore related subjects

hep-thcond-mat.stat-mechhep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Simao Meneses, Joao Penedones, Slava Rychkov, J. M. Viana Parente Lopes, Pierre Yvernay. 2021-01-16. A structural test for the conformal invariance of the critical 3d Ising model. https://doi.org/10.1007/jhep04(2019)115

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Six Easy Pieces: interplays among dualities in 4d, 3d and 2d

In this paper we consider 4d $\mathcal{N}=1$ $\mathrm{SU}(N)$ gauge theories with $N+1$ fundamentals, five antifundamentals and a conjugate two index antisymmetric tensor. The model has been shown to be in a mixed phase in the IR, splitting in an interacting non-Abelian Coulomb phase and a free magnetic phase. Through tensor deconfinement, we show that baryonic deformations lead to a non-Abelian free magnetic phase. Along the analysis we obtain a duality with symplectic SQCD that can be further reduced to 3d and 2d. In the 3d case the analysis of the three sphere partition function allows one to obtain dualities between $\mathrm{SU}(N)$ with a two index symmetric tensor and $\mathrm{SO}(N)$ theories. On the other hand, in 2d we recover dualities already known in the literature and propose new ones between special unitary and symplectic gauge theories.

hep-th↗
arXiv2026

Flat holography for spinor fields

We extend the hyperbolic Milne-slicing construction of flat holography in four-dimensional Minkowski spacetime from scalar fields to massless spin-$\frac{1}{2}$ fields. We solve the massive mode equation and restrict the boundary source-response analysis to the massless sector. Decomposition into harmonics on three-dimensional hyperbolic space, labeled by a continuous principal-series parameter, yields a separated-point nonlocal kernel up to the action normalization and local contact terms. The kernel has the universal form required by two-dimensional conformal covariance for spin-$\frac{1}{2}$ principal-series primaries. Then we construct regular source-normalized conformal-primary wavefunctions in planar and global coordinates on the celestial sphere $S^2$. We show that the planar source-response kernel is naturally identified with the spin-$\frac{1}{2}$ shadow transform, while inverse shadowing recovers the angular delta-function structure of the unshadowed basis. We also analyze radial renormalization by analytic continuation from the principal-series problem to a real-mass AdS$_3$ problem.

hep-th↗
arXiv2026

Off-shell recursion for all-loop planar integrands in Yang-Mills theory

In this paper, we develop in detail the off-shell recursion for planar loop integrands in Yang-Mills theory. Starting from the classical equations of motion solved with the perturbiner method, we derive an exact transfer-matrix representation of the pure-gluon sector. We then include the ghost contributions to the loop kernels based on \cite{Tao:2025fch}. Finally, as an example, we work out the two-loop recursion in detail and conclude a general recursion strategy for two-loop planar integrands whose external legs are gluons.

hep-th↗