Let G be an inner form of a general linear group over a non-archimedean local field. We prove that the local Langlands correspondence for G preserves depths. We also show that the local Langlands correspondence for inner forms of special linear groups preserves the depths of essentially tame Langlands parameters.

Progress in Mathematics

We propose a duality between the 2d ${\mathcal{W}}_{N}$ minimal models in the large $N$ 't Hooft limit, and a family of higher spin theories on ${\mathrm{AdS}}_{3}$. The 2d conformal field theories (CFTs) can be described as Wess-Zumino-Witten coset models, and include, for $N=2$, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the 't Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the 't Hooft coupling. We also show that the renormalization group flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an ${\mathrm{AdS}}_{4}$ dual for the singlet sector of large $N$ vector models.

An AdS_3 Dual for Minimal Model CFTs

In this review we describe our current understanding of the properties of open string tachyons on an unstable D-brane or brane–antibrane system in string theory. The various string theoretic methods used for this study include techniques of two-dimensional conformal field theory, open string field theory, boundary string field theory, noncommutative solitons, etc. We also describe various attempts to understand these results using field theoretic methods. These field theory models include toy models like singular potential models and p-adic string theory, as well as more realistic version of the tachyon effective action based on Dirac–Born–Infeld type action. Finally we study closed string background produced by the "decaying" unstable D-branes, both in the critical string theory and in the two-dimensional string theory, and describe the open string completeness conjecture that emerges out of this study. According to this conjecture the quantum dynamics of an unstable D-brane system is described by an int...

Tachyon Dynamics in Open String Theory

We show that one can construct D-branes in parafermionic and WZW theories (and their orbifolds) which have very natural geometrical interpretations, and yet are not automatically included in the standard Cardy construction of D-branes in rational conformal field theory. The relation between these theories and their T-dual description leads to an analogy between these D-branes and the familiar A-branes and B-branes of N=2 theories.

Geometrical interpretation of D-branes in gauged WZW models

We show that one can construct D-branes in parafermionic and WZW theories (and their orbifolds) which have very natural geometrical interpretations, and yet are not automatically included in the standard Cardy construction of D-branes in rational conformal field theory. The relation between these theories and their T-dual description leads to an analogy between these D-branes and the familiar A-branes and B-branes of N = 2 theories.

http://iopscience.iop.org/article/10.1088/1126-6708/2001/07/046/pdf

We propose defect lines as a useful tool in the study of bulk perturbations of conformal field theory, in particular in the analysis of the induced renormalisation group flows of boundary conditions. As a concrete example we study bulk perturbations of N = 2 supersymmetric minimal models. To these perturbations we associate a special class of defects between the respective UV and IR theories, whose fusion with boundary conditions indeed reproduces the behaviour of the latter under the corresponding RG flows.

http://iopscience.iop.org/article/10.1088/1126-6708/2008/04/001/pdf

Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds

We consider Landau-Ginzburg models with possibly different superpotentials glued together along one-dimensional defect lines. Defects preserving B-type supersymmetry can be represented by matrix factorisations of the difference of the superpotentials. The composition of these defects and their action on B-type boundary conditions is described in this framework. The cases of Landau-Ginzburg models with superpotential W = Xd and W = Xd+Z2 are analysed in detail, and the results are compared to the CFT treatment of defects in N = 2 superconformal minimal models to which these Landau-Ginzburg models flow in the IR.

B-type defects in Landau-Ginzburg models

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.

Permutation branes and linear matrix factorisations

Moduli spaces of conformal field theories corresponding to current-current deformations are discussed. For WZW models, CFT and sigma model considerations are compared. It is shown that current-current deformed WZW models have WZW-like sigma model descriptions with non-bi-invariant metrics, additional B-fields and a non-trivial dilaton.

https://iopscience.iop.org/article/10.1088/1126-6708/2003/05/071/pdf

Daniel Roggenkamp

Papers

Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds

B-type defects in Landau-Ginzburg models

Permutation branes and linear matrix factorisations

Current-current deformations of conformal field theories, and WZW models

On relevant boundary perturbations of unitary minimal models