Slava Rychkov
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View article: Conformal bootstrap: From Polyakov to our times
Conformal bootstrap: From Polyakov to our times Open
We trace the history of conformal bootstrap from its early days to our times — a great example of unity of physics. We start by describing little-known details about the origins of conformal field theory in the study of strong interactions…
View article: Exact diagonalization, matrix product states and conformal perturbation theory study of a 3D Ising fuzzy sphere model
Exact diagonalization, matrix product states and conformal perturbation theory study of a 3D Ising fuzzy sphere model Open
Numerical studies of phase transitions in statistical and quantum lattice models provide crucial insights into the corresponding Conformal Field Theories (CFTs). In higher dimensions, comparing finite-volume numerical results to infinite-v…
View article: Non-trivial Fixed Point of a $$\psi ^4_d$$ Fermionic Theory, II: Anomalous Exponent and Scaling Operators
Non-trivial Fixed Point of a $$\psi ^4_d$$ Fermionic Theory, II: Anomalous Exponent and Scaling Operators Open
We consider the Renormalization Group (RG) fixed-point theory associated with a fermionic $$\psi ^4_d$$ model in $$d=1,2,3$$ with fractional kinetic term, whose scaling dimension is fixed so that the quartic interaction is we…
View article: Disturbing News About the <i>d</i> = 2 + <i>ϵ</i> Expansion
Disturbing News About the <i>d</i> = 2 + <i>ϵ</i> Expansion Open
The $O(N)$ nonlinear sigma model (NLSM) in $d=2+\epsilon$ has long been conjectured to describe the same conformal field theory (CFT) as the Wilson–Fisher (WF) $O(N)$ fixed point obtained from the $\lambda (\phi ^2)^2$ model in $d=4-\epsil…
View article: Comment on "Redundancy Channels in the Conformal Bootstrap" by S. R. Kousvos and A. Stergiou
Comment on "Redundancy Channels in the Conformal Bootstrap" by S. R. Kousvos and A. Stergiou Open
Recent work by Kousvos and Stergiou criticises our work with Zhong Ming Tan [arXiv:1505.00963]. The issue is CFT scaling dimension computations in perturbative Renormalization Group. We identified operators whose correlation functions diff…
View article: Rotations, Negative Eigenvalues, and Newton Method in Tensor Network Renormalization Group
Rotations, Negative Eigenvalues, and Newton Method in Tensor Network Renormalization Group Open
In the tensor network approach to statistical physics, properties of the critical point of a 2D lattice model are encoded by a four-legged tensor which is a fixed point of a renormalization group (RG) map. The traditional way to find the f…
View article: Tensor Renormalization Group Meets Computer Assistance
Tensor Renormalization Group Meets Computer Assistance Open
Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here we introduce a new renormalization map - the 2x1 map - which…
View article: Transfer Matrix and Lattice Dilatation Operator for High-Quality Fixed Points in Tensor Network Renormalization Group
Transfer Matrix and Lattice Dilatation Operator for High-Quality Fixed Points in Tensor Network Renormalization Group Open
Tensor network renormalization group maps study critical points of 2d lattice models like the Ising model by finding the fixed point of the RG map. In a prior work arXiv:2408.10312 we showed that by adding a rotation to the RG map, the New…
View article: Rotations, Negative Eigenvalues, and Newton Method in Tensor Network Renormalization Group
Rotations, Negative Eigenvalues, and Newton Method in Tensor Network Renormalization Group Open
In the tensor network approach to statistical physics, properties of the critical point of a 2D lattice model are encoded by a four-legged tensor which is a fixed point of an RG map. The traditional way to find the fixed point tensor consi…
View article: Bootstrapping frustrated magnets: the fate of the chiral ${\rm O}(N)\times {\rm O}(2)$ universality class
Bootstrapping frustrated magnets: the fate of the chiral ${\rm O}(N)\times {\rm O}(2)$ universality class Open
We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from pert…
View article: Classifying irreducible fixed points of five scalar fields in perturbation theory
Classifying irreducible fixed points of five scalar fields in perturbation theory Open
Classifying perturbative fixed points near upper critical dimensions plays an important role in understanding the space of conformal field theories and critical phases of matter. In this work, we consider perturbative fixed points of N=5 s…
View article: Report on 2306.09419v2
Report on 2306.09419v2 Open
Classifying perturbative fixed points near upper critical dimensions plays an important role in understanding the space of conformal field theories and critical phases of matter.In this work, we consider perturbative fixed points of N = 5 …
View article: Report on 2306.09419v2
Report on 2306.09419v2 Open
Classifying perturbative fixed points near upper critical dimensions plays an important role in understanding the space of conformal field theories and critical phases of matter.In this work, we consider perturbative fixed points of N = 5 …
View article: 3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory
3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory Open
We consider the transverse field Ising model in (2+1)D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a mea…
View article: New Developments in the Numerical Conformal Bootstrap
New Developments in the Numerical Conformal Bootstrap Open
The numerical conformal bootstrap has become in the last 15 years an indispensable tool for studying strongly coupled CFTs in various dimensions. Here we review the main developments in the field in the last 5 years, since the appearance o…
View article: Report on 2307.02540v2
Report on 2307.02540v2 Open
We consider the transverse field Ising model in (2 + 1)D, putting 12 spins at the vertices of the regular icosahedron.The model is tiny by the exact diagonalization standards, and breaks rotation invariance.Yet we show that it allows a mea…
View article: Report on 2307.02540v2
Report on 2307.02540v2 Open
We consider the transverse field Ising model in (2 + 1)D, putting 12 spins at the vertices of the regular icosahedron.The model is tiny by the exact diagonalization standards, and breaks rotation invariance.Yet we show that it allows a mea…
View article: Report on 2306.09419v2
Report on 2306.09419v2 Open
Classifying perturbative fixed points near upper critical dimensions plays an important role in understanding the space of conformal field theories and critical phases of matter.In this work, we consider perturbative fixed points of N = 5 …
View article: Scale without Conformal Invariance in Dipolar Ferromagnets
Scale without Conformal Invariance in Dipolar Ferromagnets Open
We revisit critical phenomena in isotropic ferromagnets with strong dipolar interactions. The corresponding RG fixed point - dipolar fixed point - was first studied in 1973 by Aharony and Fisher. It is distinct from the Heisenberg fixed po…
View article: Distributions in CFT. Part I. Cross-ratio space
Distributions in CFT. Part I. Cross-ratio space Open
We show that the four-point functions in conformal field theory are defined as distributions on the boundary of the region of convergence of the conformal block expansion. The conformal block expansion converges in the sense of distributio…
View article: Four Lectures on the Random Field Ising Model, Parisi-Sourlas Supersymmetry, and Dimensional Reduction
Four Lectures on the Random Field Ising Model, Parisi-Sourlas Supersymmetry, and Dimensional Reduction Open
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any $…
View article: Distributions in CFT. Part II. Minkowski space
Distributions in CFT. Part II. Minkowski space Open
CFTs in Euclidean signature satisfy well-accepted rules, such as the convergent Euclidean OPE. It is nowadays common to assume that CFT correlators exist and have various properties also in Lorentzian signature. Some of these properties ma…
View article: Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap
Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap Open
We prove that in any unitary CFT, a twist gap in the spectrum of operator product expansion (OPE) of identical scalar primary operators (i.e. $ϕ\times ϕ$) implies the existence of a family of primary operators $\mathcal{O}_{τ, \ell}$ with …
View article: Parisi-Sourlas Supersymmetry in Random Field Models
Parisi-Sourlas Supersymmetry in Random Field Models Open
By the Parisi-Sourlas conjecture, the critical point of a theory with random field (RF) disorder is described by a supersymmeric (SUSY) conformal field theory (CFT), related to a d-2 dimensional CFT without SUSY. Numerical studies indicate…
View article: Parisi-Sourlas Supersymmetry in Random Field Models
Parisi-Sourlas Supersymmetry in Random Field Models Open
By the Parisi-Sourlas conjecture, the critical point of a theory with random field (RF) disorder is described by a supersymmeric (SUSY) conformal field theory (CFT), related to a $d-2$ dimensional CFT without SUSY. Numerical studies indica…
View article: The fate of Parisi-Sourlas supersymmetry in Random Field models
The fate of Parisi-Sourlas supersymmetry in Random Field models Open
By the Parisi-Sourlas conjecture, the critical point of a theory with random field (RF) disorder is described by a supersymmeric (SUSY) conformal field theory (CFT), related to a $d-2$ dimensional CFT without SUSY. Numerical studies indica…