arXiv subjects

A. Recknagel

Publications and source records attributed to A. Recknagel.

14 recordsLinked to original sources

arXiv2001

Conformal boundary states for free bosons and fermions

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.

hep-th↗

arXiv2001

The conformal boundary states for SU(2) at level 1

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 the usual Cardy boundary states as well as their marginal deformations are consistent, the most general conformal boundary states are determined. They are found to be parametrised by group elements in SL(2,C).

hep-th↗

arXiv2000

On relevant boundary perturbations of unitary minimal models

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.

hep-th↗

arXiv2000

Brane Dynamics in Background Fluxes and Non-commutative Geometry

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.

hep-th↗

arXiv1999

Fundamental strings in Dp-Dq brane systems

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.

hep-th↗

arXiv1999

Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres

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.

hep-th↗

arXiv1999

Boundary Deformation Theory and Moduli Spaces of D-Branes

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.

hep-th↗

arXiv1998

Supersymmetric quantum theory and non-commutative geometry

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-)Kaehler 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 some detail.

math-ph↗

arXiv1998

D-branes in Gepner models

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.

hep-th↗

arXiv1997

Supersymmetric quantum theory, non-commutative geometry, and gravitation. Lecture Notes Les Houches 1995

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.

hep-th↗

arXiv1996

Supersymmetric quantum theory and (non-commutative) differential geometry

We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in algebraic data consisting of an algebra of functions on a manifold and a family of supersymmetry generators represented on a Hilbert space. We show that known types of differential geometry can be classified in terms of the supersymmetries they exhibit. Replacing commutative algebras of functions by non-commutative *-algebras of operators, while retaining supersymmetry, we arrive at a formulation of non-commutative geometry encompassing and extending Connes' original approach. We explore different types of non-commutative geometry and introduce notions of non-commutative manifolds and non-commutative phase spaces. One of the main motivations underlying our work is to construct mathematical tools for novel formulations of quantum gravity, in particular for the investigation of superstring vacua.

hep-th↗

arXiv1995

The embedding structure and the shift operator of the U(1) lattice current algebra

The structure of block-spin embeddings of the U(1) lattice current algebra is described. For an odd number of lattice sites, the inner realizations of the shift automorphism areclassified. We present a particular inner shift operator which admits a factorization involving quantum dilogarithms analogous to the results of Faddeev and Volkov.

hep-th↗

arXiv1992

Dilogarithm Identities in Conformal Field Theory

Dilogarithm identities for the central charges and conformal dimensions exist for at least large classes of rational conformally invariant quantum field theories in two dimensions. In many cases, proofs are not yet known but the numerical and structural evidence is convincing. In particular, close relations exist to fusion rules and partition identities. We describe some examples and ideas, and present some conjectures useful for the classification of conformal theories. The mathematical structures seem to be dual to Thurston's program for the classification of 3-manifolds.

hep-th↗

arXiv1992

Virasoro Representations on Fusion Graphs

For any non-unitary model with central charge c(2,q) the path spaces associated to a certain fusion graph are isomorphic to the irreducible Virasoro highest weight modules.

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