1,721,016 research outputs found
An operator formulation of orbifold conformal field theory
No full textIn many applications of conformal field theory one encounters twisted conformal fields, i.e. fields which have branch cut singularities on the relevant Riemann surfaces. We present a geometrical framework describing twisted conformal fields on Riemann surfaces of arbitrary genus which is alternative to the standard method of coverings. We further illustrate the theory of twisted Grassmannians and its relation with the representation theory of the twisted oscillator algebras. As an application of the above, we expound an operator formalism for orbifold strings. © 1990 Springer-Verlag
Abelian Duality and Abelian Wilson Loops
No full textWe consider a pure U (1) quantum gauge field theory on a general Riemannian compact four manifold. We compute the partition function with Abelian Wilson loop insertions. We find its duality covariance properties and derive topological selection rules. Finally, we show that, to have manifest duality, one must assume the existence of twisted topological sectors besides the standard untwisted one
Light cone Wn geometry and its symmetries and projective field theory
No full textIt is shown that the generalized Beltrami differentials and projective connections which appear naturally in induced light cone Wn gravity are geometrical fields parametrizing in one-to-one fashion generalized projective structures on a fixed base Riemann surface. It is also shown that Wn symmetries are nothing but gauge transformations of the flat SL(n,c) vector bundles canonically associated with the generalized projective structures. This provides an original formulation of classical light cone W n geometry. From the knowledge of the symmetries, the full BRS algebra is derived. Inspired by the results of literature, it is argued that quantum Wn gravity may be formulated as an induced gauge theory of generalized projective connections. This leads to projective field theory. The possible anomalies arising at the quantum level are analysed by solving Wess-Zumino consistency conditions. The implications for induced covariant Wn gravity are briefly discussed. The results presented, valid for arbitrary n, reproduce those obtained for n=2,3 by different methods
A Polyakov action on Riemann surfaces (II)
No full textWe continue the model independent study of the Polyakov action on an arbitrary compact surface without boundary of genus larger than 2 as the general solution of the relevant conformal Ward identity. A general formula for the Polyakov action and an explicit calculation of the energy-momentum tensor density is provided. It is further shown how Polyakov's SL(2,C) symmetry emerges in a curved base surface. © 1993 Springer-Verlag
Tomonaga-Dirac-Schwinger formulation of the fermionic string
No full textWe present the Tomonaga-Dirac-Schwinger formulation of the fermionic string. The constraint algebra of the classical theory reproduces upon suitable quantization the superconformal algebra of the BRST formalism. The supergeometrodynamic degrees of freedom are related to the ghost and superghost variables in a simple manner. © 1987
A Krichever-Novikov formulation of classical W algebras on Riemann surfaces
No full textIt is shown how the theory of classical W-algebras can be formulated on a higher genus Riemann surface in the spirit of Krichever and Novikov. An intriguing relation between the theory of A1 embeddings into simple Lie algebras and the holomorphic geometry of Riemann surfaces is exhibited. © 1994
On the Polyakov theory of open string off-shell green functions
No full textA Polyakov theory of oriented open-bosonic-string off-shell Green functions is illustrated. It is shown that the relevant world sheets are manifolds with corners. The structure of the gauge group in relation to the corners is investigated. In particular, it is shown that the mapping-class group factorizes into the semidirect product of the subgroup of all mapping-classes which leave the corners fixed with a finite group whose definition and properties are explicitly given. The gauge volume of the latter is divided out, leading to a simplified starting expression. Further, it is shown that the final expression is an integral over an extended moduli space, defined as the quotient of the space of all admissible metrics by the semidirect product of the Weyl group with the subgroup of all diffeomorphisms which leave the corners fixed. © 1988
A Polyakov action on Riemann surfaces
No full textWe present a calculation of the effective action for induced conformal gravity on higher genus Rieman surfaces. Our expression, generalizing Polyakov's formula, depends holomorphically on the Beltrami differential and integrates the diffeomorphism anomaly. © 1991
A geometrical framework for twisted conformal field theory on Riemann surfaces
No full textIn twisted conformal field theory the basic fields have branch cut singularities on the relevant Riemann surfaces. We present a geometrical framework describing these fields which is alternative to the standard method of coverings. This leads to a non-trivial generalization of the Serre and Riemann-Roch theory. We further introduce the notion of twisted grassmanians and define the appropriate generalization of the Krichever map in this setting. © 1989
Target space equivariant cohomological structure of the Poisson sigma model
No full textWe study a formulation of the standard Poisson sigma model in which the target space Poisson manifold carries the Hamilton action of some finite-dimensional Lie algebra. We show that the structure of the action and the properties of the gauge invariant observables can be understood in terms of the associated target space equivariant cohomology. We use a de Rham superfield formalism to efficiently explore the implications of the Batalin-Vilkoviski master equation. © 2003 Elsevier Science B.V. All rights reserved
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