We present a novel theory of the very early universe which addresses the traditional horizon and flatness problems of big bang cosmology and predicts a scale invariant spectrum of perturbations. Unlike inflation, this scenario requires no exponential accelerated expansion of space-time. Instead, the early universe is described by a conformal field theory minimally coupled to gravity. The confor...

We present three types of non-conformal symmetries for a wide class of 2D dilaton-gravity models. For the particular CGHS, or string-inspired model a linear combination of these symmetries is conformal and turns out to be the well-known symmetry which allows to construct the exactly solvable semiclassical RST and BPP models. We show that one of these non-conformal symmetries can be converted in...

Some years ago, Polyakov [1] proposed constructing all conformally invariant quan tum field theories by using the constraint of conformal invariance to make concrete the fundamental principles of quantum field theory. This is the conformal boots t rap program. Conformal field theories describe the universality classes of critical phenomena, or equivalently the short distance limits of quantum f...

A flow invariant is a quantity depending only on the UV and IR conformal fixed points and not on the flow connecting them. Typically, its value is related to the central charges a and c. In classically-conformal field theories scale invariance is broken by quantum effects and the flow invariant aUV − aIR is measured by the area of the graph of the beta function between the fixed points. There e...

For a hypersurface V n−1 of a conformal space, we introduce a conformal differential invariant I = h 2 g , where g and h are the first and the second fundamental forms of V n−1 connected by the apolarity condition. This invariant is called the conformal quadratic element of V n−1. The solution of the problem of conformal rigidity is presented in the framework of conformal differential geometry ...

The anomalous conformal transformation law of the generalized entropy is found for dilaton gravity coupled to a 1+1 conformal matter sector with central charges c = c̃. (When c 6= c̃ the generalized entropy is not invariant under local Lorentz boosts.) It is shown that a certain second null derivative of the entropy, S′′ gen + (6/c)(S ′ out) , is primary, and therefore retains its sign under a ge...

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection-diffusion equations for potential flows, and...

The problem of maintaining scale and conformal invariance in Maxwell and general N-form gauge theories away from their critical dimension d c = 2(N +1) is analyzed. We first exhibit the underlying group-theoretical clash between locality, gauge, Lorentz and conformal invariance requirements. " Improved "-traceless-stress tensors are then constructed; each violates one of the above criteria. How...

This work presents a novel rotational invariant quadrature filter approach called the conformal monogenic signal for analyzing i(ntrinsic)1D and i2D local features of any curved 2D signal such as lines, edges, corners and junctions without the use of steering. The conformal monogenic signal contains the monogenic signal as a special case for i1D signals and combines monogenic scale space, phase...

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Extending previous work on two-and three-point functions, we study the four-point function and its conformal block ...