The free Schrödinger theory in d space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in particular for the |Φ|-theory in d = 2. We compute the full quantum corrections to the 4-point function to show that the symmetry is broken by an anomalous contribu...

We study the relation between the (generalized) conformal quantum mechanics of 0branes and the two-dimensional dilaton gravity. The two-dimensional actions obtained from the supergravity effective actions for the (dilatonic) 0-branes through the compactification on a sphere are related to known two-dimensional dilaton gravity models. The SL(2,R) symmetry of the (generalized) conformal quantum m...

The form of realistic space-time supersymmetry is fixed, by HaagLopuszanski-Sohnius theorem, either to the familiar form of Poincare supersymmetry or, in massless case, to that of conformal supersymmetry. We question necessity for such strict restriction in the context of theories with broken symmetries. In particular, we consider parabose N = 4 algebra as an extension of conformal supersymmetr...

Conformal algebra on R × S derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess-Zumino action managing non-perturbative dynamics of the conformal factor in the metric field. It is shown that the residual diff...

It is well known that classical conservation laws of energy, momentum, angular momentum and center-of-energy movement of the electromagnetic field are the consequences of the Maxwell equations invariance with respect to Poincare transformations. However, the relativistic invariance does not exhaust all symmetry properties of these equations. A natural question arises whether there exist any oth...

We derive a boundary action of N = 2 super-Liouville theory which preserves both N = 2 supersymmetry and conformal symmetry by imposing explicitly T = T and G = G. The resulting boundary action shows a new duality symmetry.

We derive a boundary action of N = 2 super-Liouville theory which preserves both N = 2 supersymmetry and conformal symmetry by imposing explicitly T = T and G = G. The resulting boundary action shows a new duality symmetry.

We study N = 1 global and local supersymmetric theories with a continuous global U(1)R symmetry. We discuss conditions for supersymmetry (SUSY) breaking and vacuum structures of R-symmetric SUSY models. Especially we find the conditions for R-symmetry breaking and runway vacua in global supersymmetric theories. We introduce explicit R-symmetry breaking terms into such models in global and local...

Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply a Verlinde formula for non-simply connected groups like PGL(n, C). We then explain how conformal blocks enter in the construction of conformal field theories...

We study N = 1 global and local supersymmetric theories with a continuous global U(1)R symmetry. We discuss conditions for supersymmetry (SUSY) breaking and vacuum structures of R-symmetric SUSY models. Especially we find the conditions for R-symmetry breaking and runway vacua in global supersymmetric theories. We introduce explicit R-symmetry breaking terms into such models in global and local...