Branes in the WZNW model (original) (raw)

Journal of Geometry and Physics, 2000

The structures in target space geometry that correspond to conformally invariant boundary conditions in WZW theories are determined both by studying the scattering of closed string states and by investigating the algebra of open string vertex operators. In the limit of large level, we find branes whose world volume is a regular conjugacy class or, in the case of symmetry breaking boundary conditions, a 'twined' version thereof. In particular, in this limit one recovers the commutative algebra of functions over the brane world volume, and open strings connecting different branes disappear. At finite level, the branes get smeared out, yet their approximate localization at (twined) conjugacy classes can be detected unambiguously.

D-branes in N=2 WZW models

Physics Letters B, 2003

We briefly review the construction of N=2 WZW models in terms of Manin triples. We analyse the restrictions which should be imposed on the gluing conditions of the affine currents in order to preserve half of the bulk supersymmetry. In analogy with the Kähler case there are two types of D-branes, A-and B-types which have a nice algebraic interpretation in terms of the Manin triple.

On the unitarity of gauged non-compact world-sheet supersymmetric WZNW models

Nuclear Physics B, 2009

In this paper we generalize our investigation of the unitarity of non-compact WZNW models connected to Hermitian symmetric spaces to the N=1 world-sheet supersymmetric extension of these models. We will prove that these models have a unitary spectrum in a BRST approach for antidominant highest weight representations if the level and weights of the gauged subalgebra are integers. We will find new critical string theories in 7 and 9 space-time dimensions.

A matrix model for branes on WZW simple current orbifolds

Nuclear Physics B, 2005

An algebraic formulation of the stringy geometry on simple current orbifolds of the WZW models of type A N is developed within the framework of Reflection Equation Algebras, REA q (A N ). It is demonstrated that REA q (A N ) has the same set of outer automorphisms as the corresponding current algebra A (1) N which is crucial for the orbifold construction. The CFT monodromy charge is naturally identified within the algebraic framework. The ensuing orbifold matrix models are shown to yield results on brane tensions and the algebra of functions in agreement with the exact BCFT data.

Superconformal boundary conditions for the WZW model

Journal of High Energy Physics, 2003

We review the most general, local, superconformal boundary conditions for the two-dimensional N = 1 and N = 2 non-linear sigma models, and analyse them for the N = 1 and N = 2 supersymmetric WZW models. We find that the gluing map between the left and right affine currents is generalised in a very specific way as compared to the constant Lie algebra automorphisms that are known.

On symmetric simplicial (super)string backgrounds, (super-)WZW defect fusion and the Chern-Simons theory

2022

The super-σ-model of dynamics of the super-charged loop in an ambient supermanifold in the presence of worldsheet defects of arbitrary topology is formalised within Gawȩdzki's highercohomological approach, drawing inspiration from the precursor Ref. [RS09]. A distinguished class of the corresponding backgrounds (supertargets with additional bicategorial supergeometric data), organised into simplicial hierarchies, is considered. To these, configurational (super)symmetry of the bulk field theory is lifted coherently, whereby the notion of a maximally (super)symmetric background, and in particular that of a simplicial Lie background, arises as the target structure requisite for the definition of the super-σ-model with defects fully transmissive to the currents of the bulk (super)symmetry. The formal concepts are illustrated in two settings of physical relevance: that of the WZW σ-model of the bosonic string in a compact simple 1-connected Lie group and that of the GS super-σ-model of the superstring in the Minkowski super-space. In the former setting, the structure of the background is fixed through a combination of simplicial, symmetry(-reducibility) and cohomological arguments, and a novel link between fusion of the maximally symmetric WZW defects of Fuchs et al. and the 3d CS theory with timelike Wilson lines with fixed holonomy is established. Moreover, a purely geometric interpretation of the Verlinde fusion rules is proposed. In the latter setting, a multiplicative structure compatible with supersymmetry is shown to exist on the GS super-1-gerbe of hep-th/1706.05682, and subsequently used in a novel construction of a class of maximally (rigidly) supersymmetric bi-branes whose elementary fusion is also studied. Contents Part 2. The maximally symmetric WZW defects and the CS theory 4. The geometry of the un-graded maximally symmetric WZW defect 5. The higher geometry of the WZW background Part 3. Candidate maximally supersymmetric defects in the flat GS model 6. The Green-Schwarz super-WZW-model and its super-1-gerbe 7. A multiplicative structure on the Green-Schwarz super-1-gerbe 8. Some supersymmetric G GS-(bi-)branes 9. Supersymmetric G GS-bi-brane fusion and elementary G GS-inter-bi-branes

Boundary conditions in rational conformal field theories

Nuclear Physics B, 2000

We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph G to each RCFT such that the conformal boundary conditions are labelled by the nodes of G. This approach is carried to completion for sl(2) theories leading to complete sets of conformal boundary conditions, their associated cylinder partition functions and the A-D-E classification. We also review the current status for WZW sl(3) theories. Finally, a systematic generalization of the formalism of Cardy-Lewellen is developed to allow for multiplicities arising from more general representations of the Verlinde algebra. We obtain information on the bulk-boundary coefficients and reproduce the relevant algebraic structures from the sewing constraints. 2

Superspace conformal field theory

Journal of Physics A: Mathematical and Theoretical, 2013

Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.

On D-branes in the Nappi-Witten and GMM gauged WZW models

Journal of High Energy Physics, 2003

We construct D-branes in the Nappi-Witten (NW) and Guadagnini-Martellini-Mintchev (GMM) gauged WZW models. For the SL(2, R) × SU (2)/U (1) × U (1) NW and SU (2) × SU (2)/U (1) GMM models we present the explicit equations describing the D-brane hypersurfaces in their target spaces. In the latter case we show that the D-branes are classified according to the Cardy theorem. We also present the semiclassical mass computation and find its agreement with the CFT predictions.

Branes in the WZNW model (original) (raw)

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