Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero β function as well as higher-twist effects. For example, commensurate scale relations which relate QCD observables to each other, such as the generalized Crewther relation, have no renormalization scale or scheme ambiguity and retain a convergent pe...

We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always pres...

We present explicit recursive relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four–point correlation function. The approach is based on the analytic properties of the superconformal blocks as functions of the conformal dimensions and the central charge of the superconformal algebra. The results are com...

We demonstrate the effective action scheme for the leading parton interactions and discuss the symmetry properties. The interaction kernels are particular cases of conformal symmetric two-particle kernels. There is a direct relation to the conformal symmetric rational solution of the Yang-Baxter equation .

We establish that equally spaced smectic configurations enjoy an infinite-dimensional conformal symmetry and show that there is a natural map between them and null hypersurfaces in maximally symmetric spacetimes. By choosing the appropriate conformal factor it is possible to restore additional symmetries of focal structures only found before for smectics on flat substrates.

We study global symmetries of generic 2D dilaton gravity models. Using a non-linear sigma model formulation we show that the unique theories admitting special conformal symmetries are the models with an exponential potential V ∝ e (S = 1 2π ∫ d2x √−g[Rφ+ 4λ2eβφ]), which include the model of Callan, Giddings, Harvey and Strominger (CGHS) as a particular though limiting (β = 0) case. These models...

In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occu...

We analyze the constraints of general coordinate invariance for quantum theories possessing conformal symmetry in four dimensions. The character of these constraints simplifies enormously on the Einstein universe R× S. The SO(4, 2) global conformal symmetry algebra of this space determines uniquely a finite shift in the Hamiltonian constraint from its classical value. In other words, the global...

The quantization of a free boson whose momentum satisfies a cubic constraint leads to a c = 1 2 conformal field theory with a BRST symmetry. The theory also has a W∞ symmetry in which all the generators except the stress-tensor are BRST-exact and so topological. The BRST cohomology includes states of conformal dimensions 0, 1 16 , 1 2 , together with ‘copies’ of these states obtained by acting ...