Search results for "Conformal"

Phragmén-Lindelöf's and Lindelöf's theorems

1985

Scattering Amplitudes from Superconformal Ward Identities

2018

We consider finite superamplitudes of N=1 matter, and use superconformal symmetry to derive powerful first-order differential equations for them. Because of on-shell collinear singularities, the Ward identities have an anomaly, which is obtained from lower-loop information. We show that in the five-particle case, the solution to the equations is uniquely fixed by the expected analytic behavior. We apply the method to a nonplanar two-loop five-particle integral. We consider finite superamplitudes of N=1 matter, and use superconformal symmetry to derive powerful first-order differential equations for them. Due to on-shell collinear singularities, the Ward identities have an anomaly, which is …

Cohomology of Lie algebras

1995

This chapter is devoted to studying some concepts that will be extensively used in the last chapters, namely the cohomology of Lie algebras with values in a vector space, the Whitehead lemmas and Lie algebra extensions (which are related to second cohomology groups). The same three different cases of extensions of chapter 5 as well as the ℱ( M )-valued version of cohomology will be considered. In fact, the relation between Lie group and Lie algebra cohomology will be explored here, first with the simple example of central extensions of groups and algebras (governed by twococycles), and then in the higher order case, providing explicit formulae for obtaining Lie algebra cocycles from Lie gro…

Can conformal Transformations change the fate of 2D black holes?

1998

By using a classical Liouville-type model of two dimensional dilaton gravity we show that the one-loop theory implies that the fate of a black hole depends on the conformal frame. There is one frame for which the evaporation process never stops and another one leading to a complete disappearance of the black hole. This can be seen as a consequence of the fact that thermodynamic variables are not conformally invariant. In the second case the evaporation always produces the same static and regular end-point geometry, irrespective of the initial state.

Intra--Galactic thin shell wormhole and its stability

2013

In this paper, we construct an intra-galactic thin shell wormhole joining two copies of identical galactic space times described by the Mannheim-Kazanas de Sitter solution in conformal gravity and study its stability under spherical perturbations. We assume the thin shell material as a Chaplygin gas and discuss in detail the values of the relevant parameters under which the wormhole is stable. We study the stability following the method by Eiroa and we also qualitatively analyze the dynamics through the method of Weierstrass. We find that the wormhole is generally unstable but there is a small interval in radius for which the wormhole is stable.

Three physical quantum manifolds from the conformal group

1987

Massless Spectra and Gauge Couplings at One-Loop on Non-Factorisable Toroidal Orientifolds

2018

So-called `non-factorisable' toroidal orbifolds can be rewritten in a factorised form as a product of three two-tori by imposing an additional shift symmetry. This finding of Blaszczyk et al., arXiv:1111.5852, provides a new avenue to Conformal Field Theory methods, by which the vector-like massless matter spectrum - and thereby the type of gauge group enhancement on orientifold invariant fractional D6-branes - and the one-loop corrections to the gauge couplings in Type IIA orientifold theories can be computed in addition to the well-established chiral matter spectrum derived from topological intersection numbers among three-cycles. We demonstrate this framework for the $\mathbb{Z}_4 \times…

Fully Covariant and Conformal Formulation of the Z4 System Compared to the BSSN Formulation in Spherical Symmetry

2014

We have generalized a covariant and conformal version of the Z4 system of the Einstein equations by adopting a reference metric approach, that we denote as fCCZ4, well suited for curvilinear as well as Cartesian coordinates. We implement this formalism in spherical polar coordinates under the assumption of spherical symmetry using a partially-implicit Runge-Kutta (PIRK) method, without using any regularization scheme, and show that our code can evolve both vacuum and non-vacuum spacetimes without encountering instabilities. We have performed several tests and compared the Hamiltonian constraint violations of the fCCZ4 system, for different choices of certain free parameters, with these of B…

Singularities in L^p-quasidisks

2021

We study planar domains with exemplary boundary singularities of the form of cusps. A natural question is how much elastic energy is needed to flatten these cusps; that is, to remove singularities. We give, in a connection of quasidisks, a sharp integrability condition for the distortion function to answer this question. peerReviewed

Solving the Balitsky-Kovchegov equation at next to leading order accuracy

2016

We solve the Balitsky-Kovchegov small-x evolution equation in coordinate space. We find that the solution to the equation is unstable when using an initial condition relevant for phenomenological applications at leading order. The problematic behavior is shown to be due to a large double logarithmic contribution. The same problem is found when the evolution of the “conformal dipole” is solved, even though the double logarithmic term is then absent from the evolution equation.