Marginal deformation of N=4 SYM and Penrose limits with continuum spectrum

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We study the Penrose limit about a null geodesic with 3 equal angular momenta in the recently obtained type IIB solution dual to an exactly marginal γ-deformation of N=4 SYM. The resulting background has non-trivial NS 3-form flux as well as RR 5- and 3-form fluxes. We quantise the light-cone Green-Schwarz action and show that it exhibits a continuum spectrum. We show that this is related to the dynamics of a charged particle moving in a Landau plane with an extra interaction induced by the deformation. We interpret the results in the dual N=1 SCFT.