arXiv subjects
Publications and source records attributed to Stefan Fredenhagen.
The conical defect solutions in higher-spin gauge theories on 2+1 dimensional space-times with AdS-asymptotics are conjectured to correspond to certain primary fields in the dual conformal field theory on the boundary. In this note we prove that indeed all higher-spin charges match.
We consider the limit of two-dimensional N=(2,2) superconformal minimal models when the central charge approaches c=3. Starting from a geometric description as non-linear sigma models, we show that one can obtain two different limit theories. One is the free theory of two bosons and two fermions, the other one is a continuous orbifold thereof. We substantiate this claim by detailed conformal field theory computations.
The limit of families of two-dimensional conformal field theories has recently attracted attention in the context of AdS/CFT dualities. In our work we analyse the limit of N=(2,2) superconformal minimal models when the central charge approaches c=3. The limiting theory is a non-rational N=(2,2) superconformal theory, in which there is a continuum of chiral primary fields. We determine the spectrum of the theory, the three-point functions on the sphere, and the disc one-point functions.
We investigate defects between supersymmetric Landau-Ginzburg models whose superpotentials are related by a variable transformation. It turns out that there is one natural defect, which can then be used to relate boundary conditions and defects in the different models. In particular this defect can be used to relate Grassmannian Kazama-Suzuki models and minimal models, and one can generate rational boundary conditions in the Kazama-Suzuki models from those in minimal models. The defects that appear here are closely related to the defects that are used in Khovanov-Rozansky link homology.
We discuss how to systematically compute the asymptotic symmetry algebras of generic three-dimensional bosonic higher-spin gauge theories in backgrounds that are asymptotically AdS. We apply these techniques to a one-parameter family of higher-spin gauge theories that can be considered as large N limits of SL(N) x SL(N) Chern-Simons theories, and we provide a closed formula for the structure constants of the resulting infinite-dimensional non-linear W-algebras. Along the way we provide a closed formula for the structure constants of all classical W_N algebras. In both examples the higher-spin generators of the W-algebras are Virasoro primaries. We eventually discuss how to relate our basis to a non-primary quadratic basis that was previously discussed in literature.
We show that the disc bulk one-point functions in a sl(n) Toda conformal field theory have a well-defined limit for the central charge c=n-1, and that their limiting values can be obtained from a limit of bulk one-point functions in the W_n minimal models. This comparison leads to a proposal for one-point functions for twisted boundary conditions in Toda theory.
We discuss the emergence of W-algebras as asymptotic symmetries of higher-spin gauge theories coupled to three-dimensional Einstein gravity with a negative cosmological constant. We focus on models involving a finite number of bosonic higher-spin fields, and especially on the example provided by the coupling of a spin-3 field to gravity. It is described by a SL(3) \times SL(3) Chern-Simons theory and its asymptotic symmetry algebra is given by two copies of the classical W_3-algebra with central charge the one computed by Brown and Henneaux in pure gravity with negative cosmological constant.
Matrix factorisations describe B-type boundary conditions in N=2 supersymmetric Landau-Ginzburg models. At the infrared fixed point, they correspond to superconformal boundary states. We investigate the relation between boundary states and matrix factorisations in the Grassmannian Kazama-Suzuki coset models. For the first non-minimal series, i.e. for the models of type SU(3)_k/U(2), we identify matrix factorisations for a subset of the maximally symmetric boundary states. This set provides a basis for the RR charge lattice, and can be used to generate (presumably all) other boundary states by tachyon condensation.
We propose a new class of non-factorising D-branes in the product group GxG where the fluxes and metrics on the two factors do not necessarily coincide. They generalise the maximally symmetric permutation branes which are known to exist when the fluxes agree, but break the symmetry down to the diagonal current algebra in the generic case. Evidence for the existence of these branes comes from a Lagrangian description for the open string world-sheet and from effective Dirac-Born-Infeld theory. We state the geometry, gauge fields and, in the case of SU(2)xSU(2), tensions and partial results on the open string spectrum. In the latter case the generalised permutation branes provide a natural and complete explanation for the charges predicted by K-theory including their torsion.
The behaviour of boundary conditions under relevant bulk perturbations is studied for the Virasoro minimal models. In particular, we consider the bulk deformation by the least relevant bulk field which interpolates between the mth and (m-1)st unitary minimal model. In the presence of a boundary this bulk flow induces an RG flow on the boundary, which ensures that the resulting boundary condition is conformal in the (m-1)st model. By combining perturbative RG techniques with insights from defects and results about non-perturbative boundary flows, we determine the endpoint of the flow, i.e. the boundary condition to which an arbitrary boundary condition of the mth theory flows to.
We investigate D-branes on the product GxG of two group manifolds described as Wess-Zumino-Novikov-Witten models. When the levels of the two groups coincide, it is well known that there exist permutation D-branes which are twisted by the automorphism exchanging the two factors. When the levels are different, the D-brane charge group demands that there should be generalisations of these permutation D-branes, and a geometric construction for them was proposed in hep-th/0509153. We give further evidence for this proposal by showing that the generalised permutation D-branes satisfy the Dirac-Born-Infeld equations of motion for arbitrary compact, simply connected and simple Lie groups G.
The symmetries of perturbed conformal field theories are analysed. We explain which generators of the chiral algebras of a bulk theory survive a perturbation by an exactly marginal bulk field. We also study the behaviour of D-branes under current-current bulk deformations. We find that the branes always continue to preserve as much symmetry as they possibly can, i.e. as much as is preserved in the bulk. We illustrate these findings with several examples, including permutation branes in WZW models and B-type D-branes in Gepner models.
In this paper we prove a formula for fusion coefficients of affine Kac-Moody algebras first conjectured by Walton [Wal2], and rediscovered in [Fe]. It is a reformulation of the Frenkel-Zhu affine fusion rule theorem [FZ], written so that it can be seen as a beautiful generalization of the classical Parasarathy-Ranga Rao-Varadarajan tensor product theorem [PRV].
We show that N=1 supersymmetric Liouville theory can be continued to central charge c=3/2, and that the limiting non-rational superconformal field theory can also be obtained as a limit of supersymmetric minimal models. This generalises a result known for the non-supersymmetric case. We present explicit expressions for the three-point functions of bulk fields, as well as a set of superconformal boundary states. The main technical ingredient to take the limit of minimal models consists in determining analytic expressions for the structure constants. In the appendix we show in detail how the structure constants of supersymmetric and Virasoro minimal models can be rewritten in terms of Barnes' double gamma functions.
The influence of closed string moduli on the D-brane moduli space is studied from a worldsheet point of view. Whenever a D-brane cannot be adjusted to an infinitesimal change of the closed string background, the corresponding exactly marginal bulk operator ceases to be exactly marginal in the presence of the brane. The bulk perturbation then induces a renormalisation group flow on the boundary whose end-point describes a conformal D-brane of the perturbed theory. We derive the relevant RG equations in general and illustrate the phenomenon with a number of examples, in particular the radius deformation of a free boson on a circle. At the self-dual radius we can give closed formulae for the induced boundary flows which are exact in the boundary coupling constants.
Generalised permutation branes in products of N=2 minimal models play an important role in accounting for all RR charges of Gepner models. In this paper an explicit conformal field theory construction of these generalised permutation branes for one simple class of examples is given. We also comment on how this may be generalised to the other cases.
It is shown that the RR charges of Gepner models are not all accounted for by the usual tensor product and permutation branes. In order to characterise the missing D-branes we study the matrix factorisation approach to the description of D-branes for Gepner models. For each of the A-type models we identify a set of matrix factorisations whose charges generate the full lattice of quantised charges. The additional factorisations that are required correspond to generalised permutation branes.
In this letter we discuss charges of D-branes on the group manifold SO(3). Our discussion will be based on a conformal field theory analysis of boundary states in a Z_2-orbifold of SU(2). This orbifold differs from the one recently discussed by Gaberdiel and Gannon in its action on the fermions and leads to a drastically different charge group. We shall consider maximally symmetric branes as well as branes with less symmetry, and find perfect agreement with a recent computation of the corresponding K-theory groups.