Search results for "Conformal"

Adiabatic expansions for Dirac fields, renormalization, and anomalies

2018

11 pags.

Quantum Backreaction on Three-Dimensional Black Holes and Naked Singularities

2016

We analytically investigate backreaction by a quantum scalar field on two rotating Ba\~nados-Teitelboim-Zanelli (BTZ) geometries: that of a black hole and that of a naked singularity. In the former case, we explore the quantum effects on various regions of relevance for a rotating black hole space-time. We find that the quantum effects lead to a growth of both the event horizon and the radius of the ergosphere, and to a reduction of the angular velocity, compared to the unperturbed values. Furthermore, they give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the case of a naked singularity, we f…

Yangian Symmetry for Fishnet Feynman Graphs

2017

Various classes of fishnet Feynman graphs are shown to feature a Yangian symmetry over the conformal algebra. We explicitly discuss scalar graphs in three, four and six spacetime dimensions as well as the inclusion of fermions in four dimensions. The Yangian symmetry results in novel differential equations for these families of largely unsolved Feynman integrals. Notably, the considered fishnet graphs in three and four dimensions dominate the correlation functions and scattering amplitudes in specific double scaling limits of planar, gamma-twisted N=4 super Yang-Mills or ABJM theory. Consequently, the study of fishnet graphs allows us to get deep insights into the integrability of the plana…

Integrating over quiver variety and BPS/CFT correspondence

2019

We show the vertex operator formalism for the quiver gauge theory partition function and the $qq$-character of highest-weight module on quiver, both associated with the integral over the quiver variety.

Improved Hölder regularity for strongly elliptic PDEs

2019

We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of H\"older regularity, higher than what is given by the classical exponent $1/K$.

Planar Quasiconformal Mappings; Deformations and Interactions

1998

The theory of quasiconformal mappings divides traditionally into two branches, the mappings in the plane and the case of higher dimensions. Basically, this is not due to the history of the topic but rather since planar quasiconformal mappings admit flexible methods (so far) not available in space. In this expository paper we wish to describe some recent trends and activities in quasiconformal theory peculiar to the plane. It is obvious, though, that not all topics can be covered no matter which point of view is taken; many important advances and connections must necessarily be bypassed. Therefore we concentrate on a specific theme, a property that singles out the difference between mappings…

Intrinsic Hardy–Orlicz spaces of conformal mappings

2014

We define a new type of Hardy-Orlicz spaces of conformal mappings on the unit disk where in place of the value |f(x)| we consider the intrinsic path distance between f(x) and f(0) in the image domain. We show that if the Orlicz function is doubling then these two spaces are actually the same, and we give an example when the intrinsic Hardy-Orlicz space is strictly smaller.

Boundary regularity and the uniform convergence of quasiconformal mappings

1979

Uniform continuity of quasiconformal mappings and conformal deformations

2008

We prove that quasiconformal maps onto domains satisfying a suitable growth condition on the quasihyperbolic metric are uniformly continuous even when both domains are equipped with internal metric. The improvement over previous results is that the internal metric can be used also in the image domain. We also extend this result for conformal deformations of the euclidean metric on the unit ball of R n \mathbb {R}^n .

Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds

2022

In this article we study the linearized anisotropic Calderon problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a complete set. We assume that the manifold is transversally anisotropic and that the transversal manifold is real analytic and satisfies a geometric condition related to the geometry of pairs of intersecting geodesics. In this case, we solve the linearized anisotropic Calderon problem. The geometric condition does not involve the injectivity of the geodesic X-ray transform. Crucial ingredients in the proof of our result are the construction of Gaussian beam quasimodes on the tra…