Publications (31)101.16 Total impact
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ABSTRACT: Branes and defects in topological LandauGinzburg 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.  [Show abstract] [Hide abstract]
ABSTRACT: We consider compactifications of type II string theory using exact internal CFT’s with central charge c = 9 + ϵ, ϵ ≪ 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 Dbranes. 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. KeywordsConformal Field Models in String Theory–Superstring Vacua–Flux compactifications  [Show abstract] [Hide abstract]
ABSTRACT: Starting with the SUk(2) 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 symmetrybreaking branes for other WZW models.  [Show abstract] [Hide abstract]
ABSTRACT: We study the noncommutative matrix model which arises as the lowenergy effective action of open strings in WZW models. We rederive 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 noncommutative spectral geometry that is provided by the boundary CFT data: we show that imposing invariance under extended gauge transformations singles out the stringtheoretic 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.  [Show abstract] [Hide abstract]
ABSTRACT: 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 LandauGinzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary Btype permutation branes. 
Article: Permutation Branes
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ABSTRACT: Nfold 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. Comment: 27 pages  [Show abstract] [Hide abstract]
ABSTRACT: A family of conformal boundary states for a free boson on a circle is constructed. The family contains superpositions of conventional U(1)preserving Neumann and Dirichlet branes, but for general parameter values the boundary states are fundamental and preserve only the conformal symmetry. The relative overlaps satisfy Cardy's condition, and each boundary state obeys the factorisation constraint. It is also argued that, together with the conventional Neumann and Dirichlet branes, these boundary states already account for all fundamental conformal Dbranes of the free boson theory. The results can be generalised to the situation with N=1 worldsheet supersymmetry, for which the family of boundary states interpolates between superpositions of nonBPS branes and combinations of conventional brane antibrane pairs. Comment: 32 pages, harvmac (b), 1 figure  [Show abstract] [Hide abstract]
ABSTRACT: For the case of the SU(2) WZW model at level one, the boundary states that only preserve the conformal symmetry are analysed. Under the assumption that marginal deformations of the usual Cardy boundary states are consistent, the most general conformal boundary states are determined. They are found to be parametrised by group elements in SL. 
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ABSTRACT: We consider unitary Virasoro minimal models on the disk with Cardy boundary conditions and discuss deformations by certain relevant boundary operators, analogous to tachyon condensation in string theory. Concentrating on the least relevant boundary field, we can perform a perturbative analysis of renormalization group fixed points. We find that the systems always flow towards stable fixed points which admit no further (nontrivial) relevant perturbations. The new conformal boundary conditions are in general given by superpositions of `pure' Cardy boundary conditions.  [Show abstract] [Hide abstract]
ABSTRACT: We study conformal field theory correlation functions relevant for string diagrams with open strings that stretch between several parallel branes of different dimensions. In the framework of conformal field theory, they involve boundary condition changing twist fields which intertwine between Neumann and Dirichlet conditions. A KnizhnikZamolodchikovlike differential equation for correlators of such boundary twist fields and ordinary string vertex operators is derived, and explicit integral formulas for its solutions are provided.  [Show abstract] [Hide abstract]
ABSTRACT: Branes in nontrivial backgrounds are expected to exhibit interesting dynamical properties. We use the boundary conformal field theory approach to study branes in a curved background with nonvanishing NeveuSchwarz 3form field strength. For branes on an $S^3$, the lowenergy effective action is computed to leading order in the string tension. It turns out to be a field theory on a noncommutative `fuzzy 2sphere' which consists of a YangMills and a ChernSimons term. We find a certain set of classical solutions that have no analogue for flat branes in Euclidean space. These solutions show, in particular, how a spherical brane can arise as bound state from a stack of D0branes. Comment: 25 pages  [Show abstract] [Hide abstract]
ABSTRACT: We study conformal field theory correlation functions relevant for string diagrams with open strings that stretch between several parallel branes of different dimensions. In the framework of conformal field theory, they involve boundary condition changing twist fields which intertwine between Neumann and Dirichlet conditions. A Knizhnik–Zamolodchikovlike differential equation for correlators of such boundary twist fields and ordinary string vertex operators is derived, and explicit integral formulas for its solutions are provided.  [Show abstract] [Hide abstract]
ABSTRACT: The geometry of Dbranes can be probed by open string scattering. If the background carries a nonvanishing Bfield, the worldvolume becomes noncommutative. Here we explore the quantization of worldvolume geometries in a curved background with nonzero NeveuSchwarz 3form field strength H = dB. Using exact and generally applicable methods from boundary conformal field theory, we study the example of open strings in the SU(2) WessZuminoWitten model, and establish a relation with fuzzy spheres or certain (nonassociative) deformations thereof. These findings could be of direct relevance for Dbranes in the presence of NeveuSchwarz 5branes; more importantly, they provide insight into a completely new class of worldvolume geometries.  [Show abstract] [Hide abstract]
ABSTRACT: Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate noncommutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes' noncommutative spin geometry encompassing noncommutative Riemannian, symplectic, complexHermitian and (Hyper) Kähler geometry. A general framework for noncommutative geometry is developed from the point of view of supersymmetry and illustrated in terms of examples. In particular, the noncommutative torus and the noncommutative 3sphere are studied in some detail.  [Show abstract] [Hide abstract]
ABSTRACT: Dbranes 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.  [Show abstract] [Hide abstract]
ABSTRACT: Boundary conformal field theory is the suitable framework for a microscopic treatment of Dbranes in arbitrary CFT backgrounds. In this work, we develop boundary deformation theory in order to study the changes of boundary conditions generated by marginal boundary fields. The deformation parameters may be regarded as continuous moduli of Dbranes. We identify a large class of boundary fields which are shown to be truly marginal, and we derive closed formulas describing the associated deformations to all orders in perturbation theory. This allows us to study the global topology properties of the moduli space rather than local aspects only. As an example, we analyse in detail the moduli space of c = 1 theories, which displays various stringy phenomena. 
Article: Dbranes in Gepner models
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ABSTRACT: We discuss Dbranes from a conformal field theory point of view. In this approach, branes are described by boundary states providing sources for closed string modes, independently of classical notions. The boundary states must satisfy constraints which fall into two classes. The first consists of gluing conditions between left and rightmoving Virasoro or further symmetry generators, whereas the second encompasses nonlinear consistency conditions from worldsheet duality, which severely restrict the allowed boundary states. We exploit these conditions to give explicit formulas for boundary states in Gepner models, thereby computing excitation spectra of brane configurations. From the boundary states, brane tensions and RR charges can also be read off directly.  [Show abstract] [Hide abstract]
ABSTRACT: This is an expanded version of the notes to a course taught by the first author at the 1995 Les Houches Summer School. Constraints on a tentative reconciliation of quantum theory and general relativity are reviewed. It is explained what supersymmetric quantum theory teaches us about differential topology and geometry. Noncommutative differential topology and geometry are developed in some detail. As an example, the noncommutative torus is studied. An introduction to string theory and $M$(atrix) models is provided, and it is outlined how tools of noncommutative geometry can be used to explore the geometry of string theory and conformal field theory.  [Show abstract] [Hide abstract]
ABSTRACT: 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.
Publication Stats
2k  Citations  
101.16  Total Impact Points  
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Institutions

20012011

King's College London
 Department of Mathematics
Londinium, England, United Kingdom


2008

ICL
Londinium, England, United Kingdom


19992000

Max Planck Institute for Gravitational Physics (AlbertEinsteinInstitute)
Potsdam, Brandenburg, Germany 
Harvard University
 Department of Mathematics
Cambridge, Massachusetts, United States


1998

Max Planck Institute for Mathematics
Bonn, North RhineWestphalia, Germany 
Institut des Hautes Études Scientifiques
BuresOrsay, ÎledeFrance, France


1997

ETH Zurich
 Institute for Theoretical Physics
Zürich, Zurich, Switzerland 
Universität Hamburg
 II. Institut für Theoretische Physik
Hamburg, Hamburg, Germany


1991

University of Bonn
 Physics Institute
Bonn, North RhineWestphalia, Germany
