Breakdown Of Conformal Invariance Research Articles

Gravity as the breakdown of conformal invariance

In this paper, we propose that at the beginning of the universe gravity existed in a limbo either because it was switched off or because it was only conformally coupled to all particles. This picture can be reverse-engineered from the requirement that the cosmological perturbations be (nearly) scale-invariant without the need for inflation. It also finds support in recent results in quantum gravity suggesting that spacetime becomes two-dimensional at super-Planckian energies. We advocate a novel top-down approach to cosmology based on the idea that gravity and the Big Bang Universe are relics from the mechanism responsible for breaking the fundamental conformal invariance. Such a mechanism should leave clear signatures in departures from scale-invariance in the primordial power spectrum and the level of gravity waves generated.

Non-conformality of -deformed \U0001d4a9 = 4 SYM theory

We show that the γi-deformation, which was proposed as candidate gauge theory for a non-supersymmetric three-parameter deformation of the anti-de Sitter / conformal field theory correspondence, is not conformally invariant due to a running double-trace coupling—not even in the ’t Hooft limit. Moreover, this non-conformality cannot be cured when we extend the theory by adding at tree-level arbitrary multi-trace couplings that obey certain minimal consistency requirements. Our findings suggest a possible connection between this breakdown of conformal invariance and a puzzling divergence recently encountered in the integrability-based descriptions of two-loop finite-size corrections for the single-trace operator of two identical chiral fields. We propose a test to clarify this.

Breakdown of conformal invariance at strongly random critical points

We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a strongly random critical point. The average correlation functions of this system demonstrate a breakdown of conformal invariance, while the typical correlation functions demonstrate a breakdown of scale invariance. The breakdown of conformal invariance is due to the vanishing of the correlation functions at the infinite disorder fixed point, causing the critical correlation functions to be controlled by a dangerously irrelevant operator describing the approach to the fixed point. We relate the computation of average correlation functions to a problem of persistence in the RG flow.

Conformal invariance in N = 4 supersymmetric Yang-Mills theory

It is shown, by consideration of anomaly multiplets, that the maximally extended supersymmetric Yang-Mills theory is conformally invariant, assuming that the theory is supersymmetric and O(4)-invariant and that the structure of anomalies is given by the breakdown of conformal invariance in its coupling to supergravity.

Remarks on the spontaneous breakdown of conformal invariance

where D is the di la ta t ion operator . Equa t i on (1) contradic ts the wel l -known s ta temen t (~) t ha t a genera tor does not annihi la te the vacuum if the corresponding symmet ry is v io la t ed spontaneously. He has then concluded t h a t conformal invar ianee canno t be v io la ted by the vacuum. In this note we examine a s imple a -model (3) to show tha t his conclusion is not well founded and there is no inconsis tency in the theory of spontaneous breakdown of conformal invar iance . Consider the Lagrang ian