We use the conformal group to study non-local operators in conformal field theories. A plane or a sphere (of any dimension) is mapped to itself by some subgroup of the conformal group, hence operators confined to that submanifold may be classified in representations of this subgroup. For local operators this gives the usual definition of conformal dimension and spin, but some conformal field th...

Article history: Received 27 May 2014 Accepted 17 April 2015 Available online 20 April 2015 Editor: S. Dodelson We examine the role of using symmetry and effective field theory in inflationary model building. We describe the standard formulation of starting with an approximate shift symmetry for a scalar field, and then introducing corrections systematically in order to maintain control over th...

Abstract: The invariance under unitary representations of the conformal group SL(2,R) of a quantum particle is rigorously investigated in two-dimensional spacetimes containing Killing horizons using de Alfaro-Fubini-Furlan’s model. The limit of the near-horizon approximation is considered. If the Killing horizon is bifurcate (Schwarzschild-like near horizon limit), the conformal symmetry is hid...

1 Kasner, "Algebraic Potential Curves," BuO. Am. Math. Soc., 1901. 2 Kasner, "Conformal Geometry," Proc. Fifth Internat. Cong. of Math., 2, 81 (1912). 3 Kasner, "Geometry of Conformal Symmetry (Schwarzian Reflection)," Ann. Math., 38, 873 (1937). 4 Comenetz, "Conformal Geometry on a Surface," Ibid., 39, 863 (1938). I wish to thank J. De Cicco, Aida Kailish, F. Supnik and C. Vlucay for assistanc...

Using conformal Ward identities, the influence of the conformal symmetry breaking on the evolution of the flavor-nonsinglet quark-antiquark distribution amplitude is investigated in dimensional regularization and a minimal subtracted scheme. It is found that a conformal consistency relation provides some simplification for construction of the distribution amplitude. Both the evolution in next-t...

In this paper we show that the worldline reparametrization for particles with higher derivative interactions appears as a higher dimensional symmetry on the phase space. In the limit of infinite order time dervatives, the fields on the worldline get naturally promoted to those living on a two dimensional space, and the reparametrization symmetry is locally the same as the conformal symmetry.