Annulus Amplitudes and ZZ Branes in Minimal String Theory

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Abstract
We study the annulus amplitudes of (p,q) minimal string theory and their geometrical interpretation in terms of the Riemann surface M_{p,q} that emerges from the FZZT branes. Focusing on the ZZ-FZZT annulus amplitude as a target-space probe of the ZZ brane, we use it to confirm that the ZZ branes are localized in the strong-coupling region. We also show that the deformation to M_{p,q} due to the presence of background ZZ branes is measured by the annulus amplitude, and we find that these deformations diagonalize the A-cycles of the surface. Finally, based on our study of the annulus amplitudes and the deformations of M_{p,q}, we argue that the ZZ branes can be regarded as "wrong-branch" tachyons which violate the bound \alpha<Q/2.

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