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Type IIB String Backgrounds on Parallelizable PP-Waves and Conformal Liouville Theory

M. Hssaini·M. B. Sedra
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Abstract

The scope of this work concerns the adaptation of the parallelizability pp-wave (Ppp-wave) process to D=10 type IIB string backgrounds in the presence of the non-trivial anti-self dual R-R 5-form $\QTR{cal}{F}$. This is important in the sense that it gives rise to some unsuspected properties. In fact, exact solutions of type IIB string backgrounds on Ppp-waves are discussed. For the $u$-dependence of the dilaton field $Φ$, we establish explicitly a correspondence between type IIB supergravity equations of motion and 2d-conformal Liouville field theory. We show also that the corresponding conserved conformal current $T(Φ)$ coincides exactly with the trace of the symmetric matrix $μ_{ij}$ appearing in the quadratic front factor $F=μ_{ij}x^{i}x^{j}$ of the Ppp-wave. Furthermore, we consider the transverse space dependence of the dilaton $Φ$ and show that the supergravity equations are easily solved for the linear realization of the dilaton field. Other remarkable properties related to this case are also discussed.

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M. Hssaini, M. B. Sedra. 2003-09-02. Type IIB String Backgrounds on Parallelizable PP-Waves and Conformal Liouville Theory. https://arxiv.org/abs/hep-th/0308187

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