Graded parafermions

A graded generalization of the Z_k parafermionic current algebra is constructed. This symmetry is realized in the osp(1|2)/U(1) coset conformal field theory. The structure of the parafermionic highest-weight modules is analyzed and the dimensions of the fields of the theory are determined. A free field realization of the graded parafermionic system is obtained and the structure constants of the current algebra are found. Although the theory is not unitary, it presents good reducibility properties.     

Nonabelian parafermions and their dimensions

We propose a generalization of the Zamolodchikov–Fateev parafermions which are abelian, to nonabelian groups. The fusion rules are given by the tensor product of representations of the group. Using Vafa equations we get the allowed dimensions of the parafermions. We find for simple groups that the dimensions are integers. For cover groups of simple groups, we find, for n.G.m$n.G.m$, that the dimensions are the same as Zn$Z_n$ parafermions. Examples of integral parafermionic systems are studied in detail.     

Nonstandard parafermions and string compactification

Nonstandard parafermions are built and their central charges and dimensions are calculated. We then construct new N=2 superconformal field theories by tensoring the parafermions with a free boson. We study the spectrum and modular transformations of these theories. Superstring and heterotic strings in four dimensions are then obtained by tensoring the new superconformal field theories along with some minimal models. The generations and antigenerations are studied. We give an example of the ¹²(5,7) theory which is shown to have two net generations.     

Graded parafermions: standard and quasiparticle bases

Two bases of states are presented for modules of the graded parafermionic conformal field theory associated to the coset . The first one is formulated in terms of the two fundamental (i.e., lowest-dimensional) parafermionic modes. In that basis, one can identify the completely reducible representations, i.e., those whose modules contain an infinite number of singular vectors; the explicit form of these vectors is also given. The second basis is a quasiparticle basis, determined in terms of a modified version of the exclusion principle. A novel feature of this model is that none of its bases are fully ordered and this reflects a hidden structural exclusion principle.     

Parabosons,parafermions, and explicit representations of infinite-dimensional algebras

The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so(∞) and of the Lie superalgebra osp(1|∞). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labeled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. Alternatively, the basis vectors can be expressed as semi-standard Young tableaux.     

A(2)2 parafermions: a new conformal field theory

A new parafermionic algebra associated with the homogeneous space A⁽²⁾₂/U(1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A⁽²⁾₂ parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy–momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a W-algebra type primary field with spin two.     

Twisted vortex state

We study a twisted vortex bundle where quantized vortices form helices circling around the axis of the bundle in a "force-free" configuration. Such a state is created by injecting vortices into a rotating vortex-free superfluid. Using continuum theory we determine the structure and the relaxation of the twisted state. This is confirmed by numerical calculations. We also present experimental evidence of the twisted vortex state in superfluid 3He-B.     

Twisted Heisenberg Doubles

We introduce a twisted version of the Heisenberg double, constructed from a twisted Hopf algebra and a twisted pairing. We state a Stone–von Neumann type theorem for a natural Fock space representation of this twisted Heisenberg double and deduce the effect on the algebra of shifting the product and coproduct of the original twisted Hopf algebra. We conclude by showing that the quantum Weyl algebra, quantum Heisenberg algebras, and lattice Heisenberg algebras are all examples of the general construction.     

Twisted Gauge Theories

Gauge theories on a space-time that is deformed by the Moyal–Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is used to construct gauge invariant quantities. The connection will be enveloping algebra valued in a particular representation of the Lie algebra. This gives rise to additional fields, which couple only weakly via the deformation parameter θ and reduce in the commutative limit to free fields. Consistent field equations that lead to conservation laws are derived and some properties of such theories are discussed.     

Twisted Orbifold K-Theory

 We use equivariant methods to define and study the orbifold K-theory of an orbifold X. Adapting techniques from equivariant K-theory, we construct a Chern character and exhibit a multiplicative decomposition for K ^* _orb (X)⊗ℚ, in particular showing that it is additively isomorphic to the orbifold cohomology of X. A number of examples are provided. We then use the theory of projective representations to define the notion of twisted orbifold K–theory in the presence of discrete torsion. An explicit expression for this is obtained in the case of a global quotient. Received: 21 August 2001 / Accepted: 27 January 2003 Published online: 13 May 2003 RID="*" ID="*" Both authors were partially supported by the NSF RID="*" ID="*" Both authors were partially supported by the NSF Communicated by R.H. Dijkgraaf     

Twisted reduced chiral model

The idea of twisted reduction of space-time degrees of freedom recently proposed by the present authors is applied to the matrix chiral model. The equivalence of our reduced model and the usual chiral model is established by comparing the Schwinger-Dyson equations and weak coupling expansions and by performing the Monte Carlo simulation.     

Twisted group algebras I

A generalization of the group algebra of a locally compact group is studied, by expressing the group algebra of a central group extension as the direct sum of closed *-ideals each one of which is isomorphic to such a twisted group algebra. In particular, the representation theory of such algebras is associated with the theory of projective representations by studying the representations of the group algebra of the group extension and the associated unitary representations of the group extension.     

Twisted group algebras II

Wendel showed that norm non-increasing isomorphisms between the group algebras of locally compact groups could be expressed in terms of group characters and topological isomorphisms. His results are extended to twisted group algebras. In particular, by applying a generalisation ofWendel's main result to twisted group algebras over the same group, it is shown that the number of such algebras is equal to the number of orbits in a 2-cohomology group overG under the action of the automorphism group ofG. An application to the twisted group algebra defined byWeyl's form of the canonical commutation relations is considered.     

Twisted classical phase space

We consider relativistic phase space constructed by the twist procedure from the translation sector of the standard, nondeformed Poincaré algebra. Using the concept of cross product algebra we derive two kinds of phase space with noncommuting configuration space. The generalized uncertainty relations are formulated.     

Twisted K Theory Invariants

An invariant for twisted K theory classes on a 3-manifold is introduced. The invariant is then applied to the twisted equivariant classes arising from the supersymmetric Wess–Zumino–Witten model based on the group SU(2). It is shown that the classes defined by different highest weight representations of the loop group LSU(2) are inequivalent. The results are compatible with Freed–Hopkins–Teleman identification of twisted equivariant K theory as the Verlinde algebra.