On the Conformal Side of the Penrose Limit

Motivated by the interest in understanding the role of AdS/CFT duality in the Penrose limit, whose conformal side has received so far much less attention than the corresponding string side, we construct the pp-wave limit of N=4 superconformal mechanics with the off-shell (3,4,1) multiplet. We give the superfield and the component actions, showing that the interaction part is completely fixed by symmetry. We demonstrate that for the pp-wave case the kinetic and potential terms are invariant only when taken together, as a linear combination of the two terms, provided the value of their relative coefficient is appropriately set. We explicitly show that the passing to pp-wave limit can be achieved by keeping at most quadratic nonlinearities in the action of (super)conformal mechanics.     

Null infinity, H-space and equations of motion

We discuss the existence, arising by analogy to that in algebraically special space-times, of a unique asymptotically shear-free congruence in any asymptotically flat space-time. Associated with it is a unique complex analytic curve in H-space. The surprising potential physical significance of this curve is discussed. Fifth Award in the 2006 Essay Competition of the Gravity Research Foundation.