Motivated by the recent discussions of the Penrose limit of ${\mathrm{AdS}}_5\times {\mathrm{S}}^5,$ we examine a more general class of supersymmetric pp-wave solutions of the type IIB theory, with a larger number of nonvanishing structures in the self-dual 5-form. One of the pp-wave solutions can be obtained as a Penrose limit of a D3-D3 intersection. In addition to 16 standard supersymmetries these backgrounds always allow for supernumerary supersymmetries. The latter are in one-to-one correspondence with the linearly realized world-sheet supersymmetries of the corresponding exactly solvable type IIB string action. The pp-waves provide new examples where supersymmetries will survive in a T-duality transformation on the $x^{+}$ coordinate. The T-dual solutions can be lifted to give supersymmetric deformed M2-branes in $D=11.\mathrm{}$ The deformed M2-brane is dual to a three-dimensional field theory whose renormalization group flow runs from the conformal fixed point in the infrared regime to a nonconformal theory as the energy increases. At a certain intermediate energy scale there is a phase transition associated with a naked singularity of the M2-brane. In the ultraviolet limit the theory is related by T duality to an exactly solvable massive type IIB string theory.

• Received 6 August 2003

DOI:https://doi.org/10.1103/PhysRevD.69.046003