D-branes and complex curves in c=1 string theory

Abstract

We give a geometric interpretation for D-branes in the c=1 string theory. The geometric description is provided by complex curves which arise in both CFT and matrix model formulations. On the CFT side the complex curve appears from the partition function on the disk with Neumann boundary conditions on the Liouville field (FZZ brane). In the matrix model formulation the curve is associated with the profile of the Fermi sea of free fermions. These two curves are not the same. The latter can be seen as a certain reduction of the former. In particular, it describes only (m,1) ZZ branes, whereas the curve coming from the FZZ partition function encompasses all (m,n) branes. In fact, one can construct a set of reductions, one for each fixed n. But only the first one has a physical interpretation in the corresponding matrix model. Since in the linear dilaton background the singularities associated with the ZZ branes degenerate, we study the c=1 matrix model perturbed by a tachyon potential where the degeneracy disappears. From the curve of the perturbed model we give a prediction how D-branes flow with the perturbation and derive the two-point bulk correlation function on the disk with the FZZ boundary conditions.

28 pages, 6 figures; references added; minor corrections

References in corpus (8)

• Liouville Field Theory -- A decade after the revolution
• Branes, Rings and Matrix Models in Minimal (Super)string Theory
• The Annular Report on Non-Critical String Theory
• Matrix Quantum Mechanics and Two-dimensional String Theory in Non-trivial Backgrounds
• Boundary Ground Ring in 2D String Theory
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Cited by in corpus (10)

• Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
• Annulus Amplitudes and ZZ Branes in Minimal String Theory
• Flux-vacua in Two Dimensional String Theory
• Probing the fuzzy sphere regularisation in simulations of the 3d λϕ^4 model
• Instantons in sine-Liouville theory
• c=1 from c<1: Bulk and boundary correlators
• c-map as c=1 string
• Complex curves and non-perturbative effects in c=1 string theory
• A Note on Tachyon Moduli and Closed Strings
• Multi-instantons in 2d string theory