Non-abelian bosonization from factored coset models in path integrals

We present a derivation of abelian and non-abelian bosonization in a path integral setting by expressing the generating functional for current-current correlation functions as a product of a G/G-coset model, which is dynamically trivial, and a bosonic part which contains the dynamics. A BRST symmetry can be identified which leads to smooth bosonization in both the abelian and non-abelian cases.     

Surface fields on nonseparable geometries

The field on the surface of a structure having nonseparable geometry may be expanded in a set of eigenfunctions suitable for that particular geometry. The eigenfunctions are computed numerically using the boundary elements method to compute a matrix that relates the field on the surface of the structure to its normal derivative at vanishing frequency and diagonalizing the matrix. The field on the surface of a finite cylinder with hemisphical end-caps is expanded in such a set of eigenfunctions for both a simple cylinder and a cylinder containing frames. Results for the framed cylinder is compared to Fourier decomposition of the field on the cylindrical portion of the structure.     

Generalized contact geometry and T-duality

We study generalized almost contact structures on odd-dimensional manifolds. We introduce a notion of integrability and show that the class of these structures is closed under symmetries of the Courant–Dorfman bracket, including T-duality. We define a notion of geometric type for generalized almost contact structures, and study its behavior under T-duality.     

T-duality and non-local supersymmetries

We study the non-localization of extended worldsheet supersymmetry under T-duality, when the associated complex structure depends on the coordinate with respect to which duality is performed. First, the canonical transformation which implements T-duality is generalized to the supersymmetric non-linear σ-models. Then, we obtain the non-local object which replaces the complex structure in the dual theory and write down the condition it should satisfy so that the dual action is invariant under the non-local supersymmetry. For the target space, this implies that the supersymmetry transformation parameter is a non-local spinor. The analogue of the Killing equation for this non-local spinor is obtained. It is argued that in the target space the supersymmetry is no longer realized in the standard way. The string theoretic origin of this phenomenon is briefly discussed.     

Poisson-Lie T-duality and Bianchi type algebras

All Bianchi bialgebras have been obtained. By introducing a non-degenerate adjoint invariant inner product over these bialgebras the associated Drinfeld doubles have been constructed, then by calculating the coupling matrices for these bialgebras several σ-models with Poisson-Lie symmetry have been obtained. Two simple examples as prototypes of Poisson-Lie dual models have been given.     

Strings, T-duality breaking, and nonlocality without the shortest distance

T-duality of string theory suggests nonlocality manifested at the shortest possible distance. As an alternative, we suggest a nonlocal formulation of string theory that breaks T-duality at the fundamental level and does not require the shortest possible distance. Instead, the string has an objective shape in spacetime at all length scales, but different parts of the string interact in a nonlocal Bohmian manner. PACS 11.25.-w; 03.65.Ta     

Entropy of black-branes system and T-duality

A general black-branes system under the T-duality transformation could produce a smeared system with different dimensional black branes. We first use some simple examples to see that both systems have the same entropy and then present a rigorous method to prove this general property. Using the property we could easily know the entropy of some complex black-brane systems.     

High spin limits and non-abelian T-duality

The action of the non-abelian T-dual of the WZW model is related to an appropriate gauged WZW action via a limiting procedure. We extend this type of equivalence to other σ-models with non-abelian isometries and their non-abelian T-duals, focusing on Principal Chiral models. We reinforce and refine this equivalence by arguing that the non-abelian T-duals are the effective backgrounds describing states of an appropriate parent theory corresponding to divergently large highest weight representations. The proof involves carrying out a subtle limiting procedure in the group representations and relating them to appropriate limits in the corresponding backgrounds. We illustrate the general method by providing several non-trivial examples.     

Some remarks on defects and T-duality

The equations of motion for a conformal field theory in the presence of defect lines can be derived from an action that includes contributions from bibranes. For T-dual toroidal compactifications, they imply a direct relation between Poincaré line bundles and the action of T-duality on boundary conditions. We also exhibit a class of diagonal defects that induce a shift of the B-field. We finally study T-dualities for S¹$S^1$-fibrations in the example of the Wess–Zumino–Witten model on SU(2)$\mathrm{SU}(2)$ and lens spaces. Using standard techniques from D-branes, we derive from algebraic data in rational conformal field theories geometric structures familiar from Fourier–Mukai transformations.     

Non-abelian isometries and dimensional reduction

Dimensional reduction is carried out for space-times, with or without torsion, which possess non-abelian isometries. The spectra and the equations of motion of the dimensionally reduced theory are obtained directly from the higher dimensional theory. The spectra of the reduced theories are naturally given in terms of scalar fields and antisymmetric tensor field strengths. A method of studying the dependence on the extra dimensions is suggested.     

The quantum poisson-Lie T-duality and mirror symmetry

Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the quantum Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also. Zh. éksp. Teor. Fiz. 116, 11–25 (July 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Highest weight representations of the Neveu-Schwarz and Ramond algebras

We construct a family of representationsK ^,w of the Neveu-Schwarz and Ramond algebras, which generalize the Fock representations of the Virasoro algebra. We show that the representationsK ^,w are intertwined by a vertex operator.The above results are used to give the proof of the conjectured formulas for the determinant of the contravariant form on the highest weight representations of the Neveu-Schwarz and Ramond algebras. Further results on the representation theory of the latter are derived from the determinant formulas.Partially supported by the National Science Foundation through the Mathematical Sciences Research InstitutePartially supported by NSF grant MCS-8201260     

Non-abelian vortices on surfaces and their statistics

We discuss the physics of topological vortices moving on an arbitrary surface M in a YangMills-Higgs theory in which the gauge group G breaks to a finite subgroup H. We concentrate on the case where M is compact and/or non-orientable. Interesting new features arise which have no analog on the plane. The consequences for the quantum statistics of vortices are discussed, particularly when H is non-abelian.