Two AdS2 branes in the Euclidean AdS3

We compute the density of open strings stretching between AdS2 branes in the Euclidean AdS3. This is done by solving the factorization constraint of a degenerate boundary field, and the result is checked by a Cardy-type computation. We mention applications to branes in the Minkowskian AdS3 and its cigar coset.Comment: 5 pages, some arguments clarified, version published in JHE

D3-branes in NS5-brane backgrounds

We study D3-branes in an NS5-branes background defined by an arbitrary 4d harmonic function. Using a gauge-invariant formulation of Born-Infeld dynamics as well as the supersymmetry condition, we find the general solution for the $\omega$-field. We propose an interpretation in terms of the Myers effect.Comment: 7 pages, 1 figure, version published in JHE

Boundary three-point function on AdS2 D-branes

Using the H3+-Liouville relation, I explicitly compute the boundary three-point function on AdS2 D-branes in H3+, and check that it exhibits the expected symmetry properties and has the correct geometrical limit. I then find a simple relation between this boundary three-point function and certain fusing matrix elements, which suggests a formal correspondence between the AdS2 D-branes and discrete representations of the symmetry group. Concluding speculations deal with the fuzzy geometry of AdS2 D-branes, strings in the Minkowskian AdS3, and the hypothetical existence of new D-branes in H3+.Comment: 27 pages, v2: significant clarifications added in sections 4.3 and

Lax matrix solution of c=1 Conformal Field Theory

To a correlation function in a two-dimensional conformal field theory with the central charge $c=1$, we associate a matrix differential equation $\Psi' = L \Psi$, where the Lax matrix $L$ is a matrix square root of the energy-momentum tensor. Then local conformal symmetry implies that the differential equation is isomonodromic. This provides a justification for the recently observed relation between four-point conformal blocks and solutions of the Painlev\'e VI equation. This also provides a direct way to compute the three-point function of Runkel-Watts theory -- the common $c\rightarrow 1$ limit of Minimal Models and Liouville theory.Comment: 20 pages, v3: Corrected sign mistakes in eqs. (4.35), (4.37), (4.42), (4.45) and (4.52). Conclusions unchange

Four Point Functions in the SL(2,R) WZW Model

We consider winding conserving four point functions in the SL(2,R) WZW model for states in arbitrary spectral flow sectors. We compute the leading order contribution to the expansion of the amplitudes in powers of the cross ratio of the four points on the worldsheet, both in the m- and x-basis, with at least one state in the spectral flow image of the highest weight discrete representation. We also perform certain consistency check on the winding conserving three point functions.Comment: 15 pages, Late

A conformal bootstrap approach to critical percolation in two dimensions

We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the Virasoro algebra. Based on this ansatz, we compute four-point functions using a numerical conformal bootstrap approach. The results agree with Monte-Carlo computations of connectivities of random clusters.Comment: 16 pages, Python code available at https://github.com/ribault/bootstrap-2d-Python, v2: some clarifications and minor improvement