相关论文: `Maximal conformality' does not work

For scalar field theory, a new generalization of the Exact RG to curved space is proposed, in which the conformal anomaly is explicitly present. Vacuum terms require regularization beyond that present in the canonical formulation of the…

We prove a fundamental limitation on the efficiency of a wide class of Reinforcement Learning (RL) algorithms. This limitation applies to model-free RL methods as well as a broad range of model-based methods, such as planning with tree…

A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…

Reinforcement learning (RL) experiments have notoriously high variance, and minor details can have disproportionately large effects on measured outcomes. This is problematic for creating reproducible research and also serves as an obstacle…

In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of…

We investigate the consistency of the background-field formalism when applying various regularizations and renormalization schemes. By an example of a two-dimensional $\sigma$ model it is demonstrated that the background-field method gives…

In a low energy effective theory, the fields of heavy particles with mass $m$ and total momentum $p$ depend on both a velocity $v$ and a residual momentum $k$ such that $p =mv +k$. However, there is some arbitrariness in such a description…

The internal model principle is a fundamental result stating a necessary and sufficient condition for a stabilizing controller to be robustly regulating. Its classical formulation is given in terms of coprime factorizations and the largest…

It is shown that for 2D field theories only the first order coefficient of the gravitationally dressed RG $\beta$-function is scheme independent. This is valid even for matter theories with one dimensionless coupling, where the first two…

In this paper, we consider functionals of the form $H_\alpha(u)=F(u)+\alpha G(u)$ with $\alpha\in[0,+\infty)$, where $u$ varies in a set $U\neq\emptyset$ (without further structure). We first revisit a result stating that, excluding at most…

We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result…

The Symmetry Improved Two-Particle-Irreducible (SI2PI) formalism is a powerful tool to calculate the effective potential beyond perturbation theory, whereby infinite sets of selective loop-graph topologies can be resummed in a systematic…

We study time-inconsistent recursive stochastic control problems, i.e., for which the Bellman principle of optimality does not hold. For this class of problems classical optimal controls may fail to exist, or to be relevant in practice, and…

Scheme independence of exact renormalization group equations, including independence of the choice of cutoff function, is shown to follow from general field redefinitions, which remains an inherent redundancy in quantum field theories.…

We study the conformal invariance of non-planar beta-deformed N=4 SYM theory using the coupling constant reduction (CCR) formalism. We show that up to order g^10, differently from the planar case, we can remove the scheme dependence in the…

By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory.…

Let $(M^m,g)$ be an $m$-dimensional closed Riemannian manifold with non-negative sectional curvatures, $m\ge 3$. We define a conformal invariant and prove that, if the conformal invariant is bounded from above by a constant depending only…

Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…

We analyze the prediction error of ridge regression in an asymptotic regime where the sample size and dimension go to infinity at a proportional rate. In particular, we consider the role played by the structure of the true regression…

Structural models with no solution are incoherent, and those with multiple solutions are incomplete. We show that models with occasionally binding constraints are not generically coherent. Coherency requires restrictions on the parameters…