1,136 research outputs found
Revisiting the dilatation operator of the Wilson-Fisher fixed point
We revisit the order dilatation operator of the Wilson-Fisher
fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results
in conformal field theory. Our approach is algebraic and based only on symmetry
principles. The starting point of our analysis is that the first correction to
the dilatation operator is a conformal invariant, which implies that its form
is fixed up to an infinite set of coefficients associated with the scaling
dimensions of higher-spin currents. These coefficients can be fixed using
well-known perturbative results, however, they were recently re-obtained using
CFT arguments without relying on perturbation theory. Our analysis then implies
that all order- scaling dimensions of the Wilson-Fisher fixed
point can be fixed by symmetry.Comment: 23 pages, v2: typos corrected, references adde
Waiting Time Distribution for the Emergence of Superpatterns
Consider a sequence X_1, X_2,... of i.i.d. uniform random variables taking
values in the alphabet set {1,2,...,d}. A k-superpattern is a realization of
X_1,...,X_t that contains, as an embedded subsequence, each of the
non-order-isomorphic subpatterns of length k. We focus on the non-trivial case
of d=k=3 and study the waiting time distribution of tau=inf{t>=7: X_1,...,X_t
is a superpattern}Comment: 17 page
Ga-actions of fiber type on affine T-varieties
Let X be a normal affine T-variety, where T stands for the algebraic torus.
We classify Ga-actions on X arising from homogeneous locally nilpotent
derivations of fiber type. We deduce that any variety with trivial
Makar-Limanov (ML) invariant is birationally decomposable as Y\times P^2, for
some Y. Conversely, given a variety Y, there exists an affine variety X with
trivial ML invariant birational to Y\times P^2. Finally, we introduce a new
version of the ML invariant, called the FML invariant. According to our
conjecture, the triviality of the FML invariant implies rationality. This
conjecture holds in dimension at most 3
Additive group actions on affine T-varieties of complexity one in arbitrary characteristic
Let X be a normal affine T-variety of complexity at most one over a perfect
field k, where T stands for the split algebraic torus. Our main result is a
classification of additive group actions on X that are normalized by the
T-action. This generalizes the classification given by the second author in the
particular case where k is algebraically closed and of characteristic zero.
With the assumption that the characteristic of k is positive, we introduce
the notion of rationally homogeneous locally finite iterative higher
derivations which corresponds geometrically to additive group actions on affine
T-varieties normalized up to a Frobenius map. As a preliminary result, we
provide a complete description of these additive group actions in the toric
situation.Comment: 31 page
central charge bounds from chiral algebras
We study protected correlation functions in SCFT whose
description is captured by a two-dimensional chiral algebra. Our analysis
implies a new analytic bound for the -anomaly as a function of the flavor
central charge , valid for any theory with a flavor symmetry . Combining
our result with older bounds in the literature puts strong constraints on the
parameter space of theories. In particular, it singles out a
special set of models whose value of is uniquely fixed once is given.
This set includes the canonical rank one SCFTs given by
Kodaira's classification.Comment: 12 pages, 2 figure
Automorphisms of prime order of smooth cubic n-folds
In this paper we give an effective criterion as to when a prime number p is
the order of an automorphism of a smooth cubic hypersurface of P^{n+1}, for a
fixed n > 1. We also provide a computational method to classify all such
hypersurfaces that admit an automorphism of prime order p. In particular, we
show that p<2^{n+1} and that any such hypersurface admitting an automorphism of
order p>2^n is isomorphic to the Klein n-fold. We apply our method to compute
exhaustive lists of automorphism of prime order of smooth cubic threefolds and
fourfolds. Finally, we provide an application to the moduli space of
principally polarized abelian varieties.Comment: 10 page
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