arXiv subjects

I. T. Todorov

Publications and source records attributed to I. T. Todorov.

21 records · Page 2Linked to original sources

arXiv1995

A QFT approach to W_{1+infty}

W_{1+infty} is defined as an infinite dimensional Lie algebra spanned by the unit operator and the Laurent modes of a series of local quasiprimary chiral fields V^l(z) of dimension l+1 (l=0,1,2,...). These fields are neutral with respect to the u(1) current J(z)=V^0(z); as a result the (l+2)-fold commutator of J with V^l vanishes. We outline a construction of rational conformal field theories with stress energy tensor T(z)=V^1(z) whose chiral algebras include all V^l's. It is pointed out that earlier work on local extensions of the u(1) current algebra solves the problem of classifying all such theories for Virasoro central charge c=1.

hep-th↗

arXiv1994

Characterizing Invariants for Local Extensions of Current Algebras

Pairs $å\subset \bb$ of local quantum field theories are studied, where $å$ is a chiral conformal \qft and $\bb$ is a local extension, either chiral or two-dimensional. The local correlation functions of fields from $\bb$ have an expansion with respect to $å$ into \cfb s, which are non-local in general. Two methods of computing characteristic invariant ratios of structure constants in these expansions are compared: $(a)$ by constructing the monodromy \rep of the braid group in the space of solutions of the Knizhnik-Zamolodchikov differential equation, and $(b)$ by an analysis of the local subfactors associated with the extension with methods from operator algebra (Jones theory) and algebraic quantum field theory. Both approaches apply also to the reverse problem: the characterization and (in principle) classification of local extensions of a given theory.

hep-th↗

arXiv1994

$SU_3$ coherent state operators and invariant correlation functions and their quantum group counterparts

Coherent state operators (CSO) are defined as operator valued functions on G=SL(n,C), homogeneous with respect to right multiplication by lower triangular matrices. They act on a model space containing all holomorphic finite dimensional representations of G with multiplicity 1. CSO provide an analytic tool for studying G invariant 2- and 3-point functions, which are written down in the case of $SU_3$. The quantum group deformation of the construction gives rise to a non-commutative coset space. We introduce a "standard" polynomial basis in this space (related to but not identical with the Lusztig canonical basis) which is appropriate for writing down $U_q(sl_3)$ invariant 2-point functions for representaions of the type $(λ,0)$ and $(0,λ)$. General invariant 2-point functions are written down in a mixed Poincaré-Birkhoff-Witt type basis.

hep-th↗