Permutation Orbifolds Research Articles

The operator algebra and twisted KZ equations of WZW orbifolds

We obtain the operator algebra of each twisted sector of all WZW orbifolds, including the general twisted current algebra and the algebra of the twisted currents with the twisted affine primary fields. Surprisingly, the twisted right and left mover current algebras are not a priori copies of each other. Using the operator algebra we also derive world-sheet differential equations for the twisted affine primary fields of all WZW orbifolds. Finally we include ground state properties to obtain the twisted Knizhnik-Zamolodchikov equations of the WZW permutation orbifolds and the inner-automorphic WZW orbifolds.

MORE ABOUT ALL CURRENT-ALGEBRAIC ORBIFOLDS

Recently a construction was given for the stress tensors of all sectors of the general current-algebraic orbifold A(H)/H, where A(H) is any current-algebraic conformal field theory with a finite symmetry group H. Here we extend and further analyze this construction to obtain the mode formulation of each sector of each orbifold A(H)/H, including the twisted current algebra, the Virasoro generators, the orbifold adjoint operation and the commutator of the Virasoro generators with the modes of the twisted currents. As applications, general expressions are obtained for the twisted current–current correlator and ground state conformal weight of each twisted sector of any permutation orbifold A(H)/H, H⊂SN. Systematics are also outlined for the orbifolds A(Lie h(H))/H of the (H and Lie h)-invariant conformal field theories, which include the general WZW orbifold and the general coset orbifold. Finally, two new large examples are worked out in further detail: the general SNpermutation orbifold A(SN)/SNand the general inner-automorphic orbifold A(H(d))/H(d).

Orbifoldization, Covering Surfaces and Uniformization Theory

The connection between the theory of permutation orbifolds, covering surfaces, and uniformization is investigated, and the higher genus partition functions of an arbitrary permutation orbifold are expressed in terms of those of the original theory.

The torus and the Klein bottle amplitude of permutation orbifolds

The torus and the Klein bottle amplitude coefficients are computed in permutation orbifolds of RCFT's in terms of the same quantities in the original theory and the twist group. An explicit expression is presented for the number of self conjugate primaries in the orbifold as a polynomial of the total number of primaries and the number of self conjugate ones in the parent theory. The formulae in the Z 2 orbifold illustrate the general results.

NEW DUALITY TRANSFORMATIONS IN ORBIFOLD THEORY

We find new duality transformations which allow us to construct the stress tensors of all the twisted sectors of any orbifold A(H)/H, where A(H) is the set of all current-algebraic conformal field theories with a finite symmetry group H⊂ Aut (g). The permutation orbifolds with H=ℤλ and H=S3 are worked out in full as illustrations but the general formalism includes both simple and semisimple g. The motivation for this development is the recently-discovered orbifold Virasoro master equation, whose solutions are identified by the duality transformations as sectors of the permutation orbifolds [Formula: see text].

New Duality Transformations in Orbifold Theory

We find new duality transformations which allow us to construct the stress tensors of all the twisted sectors of any orbifold A(H)/H, where A(H) is the set of all current-algebraic conformal field theories with a finite symmetry group H \subset Aut(g). The permutation orbifolds with H = Z_\lambda and H = S_3 are worked out in full as illustrations but the general formalism includes both simple and semisimple g. The motivation for this development is the recently-discovered orbifold Virasoro master equation, whose solutions are identified by the duality transformations as sectors of the permutation orbifolds A(D_\lambda)/Z_\lambda.

Characters and modular properties of permutation orbifolds

Explicit formulae describing the genus one characters and modular transformation properties of permutation orbifolds of arbitrary Rational Conformal Field Theories are presented, and their relation to the theory of covering surfaces is investigated.