[Show abstract][Hide abstract]ABSTRACT: 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.
Preview · Article · Dec 2011 · Journal of High Energy Physics
[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 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.
KeywordsConformal Field Models in String Theory–Superstring Vacua–Flux compactifications
Preview · Article · Feb 2011 · Journal of High Energy Physics
[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 symmetry-breaking branes for other WZW models.
[Show abstract][Hide abstract]ABSTRACT: 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.
Full-text · Article · Feb 2008 · Journal of High Energy Physics
[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 Landau-Ginzburg potentials. In
this paper we identify the matrix factorisations associated to
arbitrary B-type permutation branes.
Full-text · Article · Aug 2005 · Journal of High Energy Physics
[Show abstract][Hide abstract]ABSTRACT: 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. Comment: 27 pages
Preview · Article · Aug 2002 · Journal of High Energy Physics
[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 D-branes of the free boson theory. The results can be generalised to the situation with N=1 world-sheet supersymmetry, for which the family of boundary states interpolates between superpositions of non-BPS branes and combinations of conventional brane anti-brane pairs. Comment: 32 pages, harvmac (b), 1 figure
Preview · Article · Aug 2001 · Journal of High Energy Physics
[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.
[Show abstract][Hide abstract]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 (non-trivial) relevant perturbations. The new conformal boundary conditions are in general given by superpositions of `pure' Cardy boundary conditions.
Full-text · Article · Nov 2000 · Nuclear Physics B
[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-Zamolodchikov-like 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 non-trivial backgrounds are expected to exhibit interesting dynamical properties. We use the boundary conformal field theory approach to study branes in a curved background with non-vanishing Neveu-Schwarz 3-form field strength. For branes on an $S^3$, the low-energy effective action is computed to leading order in the string tension. It turns out to be a field theory on a non-commutative `fuzzy 2-sphere' which consists of a Yang-Mills and a Chern-Simons 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 D0-branes. Comment: 25 pages
Preview · Article · Mar 2000 · Journal of High Energy Physics
[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–Zamolodchikov-like 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.
Full-text · Article · Dec 1999 · Nuclear Physics B
[Show abstract][Hide abstract]ABSTRACT: The geometry of D-branes can be probed by open string scattering. If the background carries a non-vanishing B-field, the world-volume becomes non-commutative. Here we explore the quantization of world-volume geometries in a curved background with non-zero Neveu-Schwarz 3-form 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) Wess-Zumino-Witten model, and establish a relation with fuzzy spheres or certain (non-associative) deformations thereof. These findings could be of direct relevance for D-branes in the presence of Neveu-Schwarz 5-branes; more importantly, they provide insight into a completely new class of world-volume geometries.
Preview · Article · Sep 1999 · Journal of High Energy Physics
[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 non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations
of Connes' non-commutative spin geometry encompassing non-commutative Riemannian, symplectic, complex-Hermitian and (Hyper-)
Kähler geometry. A general framework for non-commutative geometry is developed from the point of view of supersymmetry and
illustrated in terms of examples. In particular, the non-commutative torus and the non-commutative 3-sphere are studied in
[Show abstract][Hide abstract]ABSTRACT: 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.
Preview · Article · Mar 1999 · Fortschritte der Physik
[Show abstract][Hide abstract]ABSTRACT: Boundary conformal field theory is the suitable framework for a microscopic treatment of D-branes 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 D-branes. 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.
[Show abstract][Hide abstract]ABSTRACT: We discuss D-branes 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 right-moving Virasoro or further symmetry generators, whereas the second encompasses non-linear consistency conditions from world-sheet 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. Non-commutative differential topology and geometry are developed in some detail. As an example, the non-commutative torus is studied. An introduction to string theory and $M$(atrix) models is provided, and it is outlined how tools of non-commutative 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.
Preview · Article · Jun 1997 · Letters in Mathematical Physics