Related papers: Holography, Fractals and the Weyl Anomaly

Weyl semimetals are 3D condensed matter systems characterized by a degenerate Fermi surface, consisting of a pair of `Weyl nodes'. Correspondingly, in the infrared limit, these systems behave effectively as Weyl fermions in $3+1$…

We consider an intrinsic entropy associated with a local conformal net A by the coefficients in the expansion of the logarithm of the trace of the ``heat kernel'' semigroup. In analogy with Weyl theorem on the asymptotic density…

We propose a recipe - arguably the simplest - to compute the holographic type-B Weyl anomaly for general higher-derivative gravity in asymptotically AdS spacetimes. In 5 and 7 dimensions we identify a suitable basis of curvature invariants…

We study the interior metric of 4D spherically symmetric static black holes by using the semi-classical Einstein equation and find a consistent class of geometries with large curvatures. We approximate the matter fields by conformal fields…

Using the path integral formulation in Euclidean space, we extended the calculation of the abelian chiral anomalies in the case of Lorentz violating theories by considering a new fermionic correction term provided by the standard model…

Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and…

Weyl fermions1 do not appear in nature as elementary particles, but they are now found to exist as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have…

We perform a detailed analysis of holographic entanglement R\'enyi entropy in some modified theories of gravity with four dimensional conformal field theory duals. First, we construct perturbative black hole solutions in a recently proposed…

Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX…

We present a method of constructing discrete integrable systems with crystallographic reflection group (Weyl) symmetries, thus clarifying the relationship between different discrete integrable systems in terms of their symmetry groups.…

A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl's electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the…

We study Weyl symmetry for non-relativistic conformal filed theories on curved spatial spaces, and calculate it's quantum anomaly. We show that there is no geometric anomaly, and the non-relativistic Weyl anomaly can appear only due to…

Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and…

We study inflation in Weyl gravity. The original Weyl quadratic gravity, based on Weyl conformal geometry, is a theory invariant under Weyl symmetry of (gauged) local scale transformations. In this theory Planck scale ($M$) emerges as the…

Weyl semimetals are one kind of three-dimensional gapless semimetal with nontrivial topology in the momentum space. The chiral anomaly in Weyl semimetals manifests as a charge imbalance between the Weyl nodes of opposite chiralities induced…

We compute the trace, diffeomorphism and Lorentz anomalies of a free Weyl fermion in a gravitational background field by path integral methods. This is achieved by regularising the variation of the determinant of the Weyl operator building…

This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by…

We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed G-manifold M, where G is a compact, connected Lie group acting effectively and isometrically on M. Using resolution of singularities, we…

In this work we study the asymptotic behavior of the curves of the Fu{\v{c}}{\'{\i}}k spectrum for weighted second order linear ordinary differential equations. We prove a Weyl type asymptotic behavior of the hyperbolic type curves in the…

This work addresses problems on simultaneous Diophantine approximation on fractals, motivated by a long standing problem of Mahler regarding Cantor's middle $1/3$ set. We obtain the first instances where a complete analogue of Khintchine's…