Volume Stabilization via $\alpha^\prime$ Corrections in Type IIB Theory with Fluxes

We consider the Type IIB string theory in the presence of various extra $7/\bar 7$-brane pairs compactified on a warped Calabi-Yau threefold that admits a conifold singularity. We demonstrate that the volume modulus can be stabilized perturbatively at a non-supersymmetric $AdS_4/dS_4$ vacuum by the effective potential that includes the stringy $(\alpha^\prime)^3$ correction obtained by Becker {\it et al.} together with a combination of positive tension and anomalous negative tension terms generated by the additional 7-brane-antibrane pairs.