arXiv subjects

Andreas Recknagel

Publications and source records attributed to Andreas Recknagel.

11 recordsLinked to original sources

arXiv2017

Orbifold equivalence: structure and new examples

Orbifold equivalence is a notion of symmetry that does not rely on group actions. Among other applications, it leads to surprising connections between hitherto unrelated singularities. While the concept can be defined in a very general category-theoretic language, we focus on the most explicit setting in terms of matrix factorisations, where orbifold equivalences arise from defects with special properties. Examples are relatively difficult to construct, but we uncover some structural features that distinguish orbifold equivalences -- most notably a finite perturbation expansion. We use those properties to devise a search algorithm, then present some new examples including Arnold singularities.

math.QA↗

arXiv2011

Algorithmic deformation of matrix factorisations

Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these algorithms and apply them to several examples. Apart from explicit results in concrete cases, this leads to a novel way to generate new matrix factorisations via nilpotent substitutions, and to criteria whether boundary obstructions can be lifted by bulk deformations.

hep-th↗

arXiv2010

Moduli Stabilisation on the Worldsheet

We consider compactifications of type II string theory using exact internal CFT's with central charge $c=9+ε$, $|ε| \ll 1$, leading to an effective potential for the dilaton. For $ε>0$ the potential is positive and the dilaton is ultimately driven to weak coupling. For $ε<0$ the dilaton is driven to strong coupling, but we can stabilise the background by including D-branes. The resulting minimum admits an $AdS_4$ solution where the cosmological constant is of the order $ε^3$ and the string coupling constant is of order $ε$. Furthermore these CFT's typically do not possess any massless or tachyonic modes. Thus these vacua provide exact CFT descriptions of moduli stabilisation in weakly coupled string theory.

hep-th↗

arXiv2007

Non-commutative Weitzenboeck geometry, gerbe modules, and WZW branes

We study the non-commutative matrix model which arises as the low-energy effective action of open strings in WZW models. We re-derive this fuzzy effective gauge dynamics in two different ways, without recourse to conformal field theory. The first method starts from a linearised version of the WZW sigma model, which is classically equivalent to an action of Schild type, which in turn can be quantised in a natural way to yield the matrix model. The second method relies on purely geometric symmetry principles -- albeit within the non-commutative spectral geometry that is provided by the boundary CFT data: we show that imposing invariance under extended gauge transformations singles out the string-theoretic action up to the relevant order in the gauge field. The extension of ordinary gauge transformations by tangential shifts is motivated by the gerbe structure underlying the classical WZW model and standard within Weitzenboeck geometry -- which is a natural reformulation of geometry to use when describing strings in targets with torsion.

hep-th↗

arXiv2007

Symmetry-breaking boundary states for WZW models

Starting with the SU(2)_k WZW model, we construct boundary states that generically preserve only a parafermion times Virasoro subalgebra of the full affine Lie algebra symmetry of the bulk model. The boundary states come in families: intervals for generic k, quotients of SU(2) by discrete groups if k is a square. In that case, special members of the families can be viewed as superpositions of rotated Cardy branes. Using embeddings of SU(2) into higher groups, the new boundary states can be lifted to symmetry-breaking branes for other WZW models.

hep-th↗

arXiv2005

Permutation branes and linear matrix factorisations

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.

hep-th↗

arXiv2002

Permutation Branes

N-fold tensor products of a rational CFT carry an action of the permutation group S_N. These automorphisms can be used as gluing conditions in the study of boundary conditions for tensor product theories. We present an ansatz for such permutation boundary states and check that it satisfies the cluster condition and Cardy's constraints. For a particularly simple case, we also investigate associativity of the boundary OPE, and find an intriguing connection with the bulk OPE. In the second part of the paper, the constructions are slightly extended for application to Gepner models. We give permutation branes for the quintic, together with some formulae for their intersections.

hep-th↗

arXiv2001

Open Strings and Non-commutative Geometry of Branes on Group Manifolds

In this contribution we review some recent work on the non-commutative geometry of branes on group manifolds. In particular, we show how fuzzy spaces arise in this context from an exact world-sheet description and we sketch the construction of a low-energy effective action for massless open string modes. The latter is given by a combination of a Yang-Mills and a Chern-Simons like functional on the fuzzy world-volume. It can be used to study condensation on various brane configurations in curved backgrounds.

hep-th↗

arXiv1999

Moduli Spaces of D-branes in CFT-backgrounds

D-branes in curved backgrounds can be treated with techniques of boundary conformal field theory. We discuss the influence of scalar condensates on such branes, i.e. perturbations of boundary conditions by marginal boundary operators. A general criterion is presented that guarantees a boundary perturbation to be truly marginal in all orders of perturbation theory. Our results on boundary deformations have several interesting applications which are sketched at the end of this note.

hep-th↗

arXiv1996

From path representations to global morphisms for a class of minimal models

We construct global observable algebras and global DHR morphisms for the Virasoro minimal models with central charge c(2,q), q odd. To this end, we pass {}from the irreducible highest weight modules to path representations, which involve fusion graphs of the c(2,q) models. The paths have an interpretation in terms of quasi-particles which capture some structure of non-conformal perturbations of the c(2,q) models. The path algebras associated to the path spaces serve as algebras of bounded observables. Global morphisms which implement the superselection sectors are constructed using quantum symmetries: We argue that there is a canonical semi-simple quantum symmetry algebra for each quasi-rational CFT, in particular for the c(2,q) models. These symmetry algebras act naturally on the path spaces, which allows to define a global field algebra and covariant multiplets therein.

hep-th↗

arXiv1996

Generalization of the Knizhnik-Zamolodchikov-Equations

In this letter we introduce a generalization of the Knizhnik- Zamolodchikov equations from affine Lie algebras to a wide class of conformal field theories (not necessarily rational). The new equations describe correlations functions of primary fields and of a finite number of their descendents. Our proposal is based on Nahm's concept of small spaces which provide adequate substitutes for the lowest energy subspaces in modules of affine Lie algebras. We explain how to construct the first order differential equations and investigate properties of the associated connections, thereby preparing the grounds for an analysis of quantum symmetries. The general considerations are illustrated in examples of Virasoro minimal models.

hep-th↗