## On the Conformal Field Theories for Bosonic Strings in PP-Waves

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Mukhopadhyay, Partha

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Recently Kazama and Yokoi (arXiv:0801.1561 [hep-th]) have used a phase-space
method to study the Virasoro algebra of type IIB superstring theory in the
maximally supersymmetric R-R plane wave background in a semi-light-cone gauge.
Two types of normal ordering have been considered, namely "phase space normal
ordering" (PNO) and "massless normal ordering" (MNO). The second one, which is
the right one to choose in flat background, has been discarded with the
argument that the Virasoro algebra closes only in the first case. To understand
this issue better with a completely covariant treatment we consider the easiest
case of bosonic strings propagating in an arbitrary pp-wave of the simplest
kind. Using the phase-space method we show that MNO is in fact the right one to
choose because of the following reason. For both types of normal ordering the
energy-momentum tensor satisfies the desired Virasoro algebra up to anomalous
terms proportional to the space-time equation of motion of the background.
However, it is MNO which gives rise to the correct spectrum - we compute the
quadratic space-time action by restricting the string field inside a transverse
Hilbert space. This turns out to be non-diagonal. Diagonalizing this action
reproduces the spectrum directly obtained in light-cone quantization. The same
method with PNO gives rise to a spectrum with negative dimensions.

Comment: 19 pages

Comment: 19 pages

##### Keywords

High Energy Physics - Theory