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S-wave absorption of scalars by noncommutative D3-branes

On the supergravity side, we study the propagation of the RR scalar and the dilaton in the D3-branes with NS $B$-field. To obtain the noncommutative effect, we consider the case of $B\to \infty(θ\toπ/2)$. We approximate this as the smeared D1-brane background with $F_5=H=0$. In this background, the RR scalar induces an instability of the near-horizon geometry. However, it turns out that the RR scalar is nonpropagating, while the dilaton is a physically propagating mode. We calculate the s-wave absorption cross section of the dilaton. One finds $σ_0^ϕ|_{B\to\infty} \sim (\tilde ω\tilde R_{π\over 2})^{8.9} / ω^5$ in the leading-order while $σ_0^ϕ|_{B=0} \sim (\tilde ωR_0)^{8}/ω^5$ in the D3-branes without $B$-field. This means that although the dilaton belongs to a minimally coupled scalar in the absence of $B$-field, it becomes a sort of fixed scalar in the limit of $B \to \infty$.