Related papers: `Maximal conformality' does not work
It is shown that the gauge invariance and gauge dependence properties of effective action for Yang-Mills theories should be considered as two independent issues in the background field formalism. Application of this formalism to formulate…
The Multiscale Law of Requisite Variety is a scientific law relating, at each scale, the variation in an environment to the variation in internal state that is necessary for effective response by a system. While this law has been used to…
We show that the Invariant Risk Minimization (IRM) formulation of Arjovsky et al. (2019) can fail to capture "natural" invariances, at least when used in its practical "linear" form, and even on very simple problems which directly follow…
The majority of renormalizable field theories possessing the scale invariance at the classical level exhibits the trace anomaly once quantum corrections are taken into account. This leads to the breaking of scale and conformal invariance.…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
The reparametrization transformation between ultrametrically organised states of replicated disordered systems is explicitly defined. The invariance of the longitudinal free energy under this transformation, i.e. reparametrization…
The standard demand for the quantum partition function to be invariant under the renormalization group transformation results in a general class of exact renormalization group equations, different in the form of the kernel. Physical…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
Different phenomenological RG transformations based on scaling relations for the derivatives of the inverse correlation length and singular part of the free-energy density are considered. These transformations are tested on the 2D square…
Rotational invariance of physical laws is a generally accepted principle. We show that it leads to an additional external constraint on local realistic models of physical phenomena involving measurements of multiparticle spin 1/2…
We show that the failure of the real-space RG method in the 1D tight-binding model is not intrinsic to the method as considered so far but depends on the choice of boundary conditions. For fixed BC's the failure does happen. For free BC's…
Maximum Variance Unfolding is one of the main methods for (nonlinear) dimensionality reduction. We study its large sample limit, providing specific rates of convergence under standard assumptions. We find that it is consistent when the…
I argue that the consistency of any resummation method can be established if the method follows a power counting derived from a hierarchy of scales. I.e., whether it encodes a top-down effective field theory. This resolves much confusion…
If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We…
The search of controlled approximations to study strongly coupled systems remains a very general open problem. Wilson's renormalization group has shown to be an ideal framework to implement approximations going beyond perturbation theory.…
An important unanswered question in quantum field theory is to understand precisely under which conditions scale invariance implies invariance under the full conformal group. While the general answer in two dimensions has been known for…
We clarify the notion of Wilsonian renormalization group (RG) invariance in supersymmetric gauge theories, which states that the low-energy physics can be kept fixed when one changes the ultraviolet cutoff, provided appropriate changes are…
A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
The claim that the Principle of Minimal Sensitivity is "disfavored" because it does not satisfy certain "self-consistency requirements" is meaningless, and shows a basic misunderstanding of the renormalization-scheme-dependence problem.