Sylvain Ribault

Some remarks on anti-de Sitter D-branes

We present some preliminary investigations about the AdS2 × S2 D3-branes in AdS3 × S3. We analyse the quadratic fluctuations of the Dirac-Born- Infeld action around a given semi-classical D-brane configuration and compare them with results obtained by using conformal-field-theory techniques. We finally study classical motions of open strings attached to those D-branes and analyse the role of the spectral flow in this context.

Flux stabilization in compact groups

We consider the Born-Infeld action for symmetry-preserving, orientable D-branes in compact group manifolds. We find classical solutions that obey the flux quantization condition. They correspond to conformally invariant boundary conditions on the world sheet. We compute the spectrum of quadratic fluctuations and find agreement with the predictions of conformal field theory, up to a missing level-dependent truncation. Our results extend to D-branes with the geometry of twined conjugacy classes; they illustrate the mechanism of flux stabilization of D-branes.

Solution of the H+3 model on a disc

We determine all the correlators of the H+3 model on a disc with AdS2-brane boundary conditions in terms of correlators of Liouville theory on a disc with FZZT-brane boundary conditions. We argue that the Cardy-Lewellen constraints are weaker in the H+3 model than in rational conformal field theories due to extra singularities of the correlators, but strong enough to uniquely determine the bulk two-point function on a disc. We confirm our results by detailed analyses of the bulk-boundary two-point function and of the boundary two-point function. In particular we find that, although the target space symmetry preserved by AdS2-branes is the group SL(2,), the open string states between two distinct parallel AdS2-branes belong to representations of the universal covering group.

Liouville theory with a central charge less than one

A bstractWe determine the spectrum and correlation functions of Liouville theory with a central charge less than (or equal) one. This completes the definition of Liouville theory for all complex values of the central charge. The spectrum is always spacelike, and there is no consistent timelike Liouville theory. We also study the non-analytic conformal field theories that exist at rational values of the central charge. Our claims are supported by numerical checks of crossing symmetry. We provide Python code for computing Virasoro conformal blocks, and correlation functions in Liouville theory and (generalized) minimal models.

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 ω-field. We propose an interpretation in terms of the Myers effect.

Discrete D-branes in AdS 3 and in the 2d black hole

I show how the AdS2 D-branes in the Euclidean AdS3 string theory are related to the continuous D-branes in Liouville theory. I then propose new discrete D-branes in the Euclidean AdS3 which correspond to the discrete D-branes in Liouville theory. These new D-branes satisfy the appropriate shift equations. They give rise to two families of discrete D-branes in the 2d black hole, which preserve different symmetries.

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.

On sℓ3 Knizhnik-Zamolodchikov equations and 3 null-vector equations

Starting from Sklyanins separation of variables for the sl3 Yangian model, we derive the separation of variables for the quantum sl3 Gaudin model. We use the resulting new variables for rewriting the sl3 Knizhnik-Zamolodchikov equations, and comparing them with certain null-vector equations in conformal field theories with W3-algebra symmetry. The two sets of equations are remarkably similar, but become identical only in the critical level limit. This is in contrast to the sl2 Knizhnik-Zamolodchikov equations, which are known to be equivalent to Belavin-Polyakov-Zamolodchikov equations for all values of the level.

A family of solvable non-rational conformal field theories

We find non-rational conformal field theories in two dimensions, which are solvable due to their correlators being related to correlators of Liouville theory. Their symmetry algebra consists of the dimension-two stress-energy tensor, and two dimension-one fields. The theories come in a family with two parameters: the central charge c and a complex number m. The special case m = 0 corresponds to Liouville theory (plus two free bosons), and m = 1 corresponds to the H3+ model. In the case m = 2 we show that the correlators obey third-order differential equations, which are associated to a subsingular vector of the symmetry algebra.

Lax matrix solution of c = 1 conformal field theory

A bstractTo a correlation function in a two-dimensional conformal field theory with the central charge c = 1, we associate a matrix differential equation Ψ′ = LΨ, 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 Painlevé VI equation. This also provides a direct way to compute the three-point function of Runkel-Watts theory — the common c → 1 limit of Minimal Models and Liouville theory.