Higher twisted sector couplings of ZN orbifolds (original) (raw)
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Physics Letters B, 1990
R du',dity in simple orbifold models at arbitrary orders in string perturbation theory. It is shown that duality involves certain linear relations among twist correlators at dual radii. We derive gener',d expressions for the coefficients of these relations and show that they can be expressed in terms of functions of the orbifold cosets obeying an algebra bearing a striking resemblance to Verlinde's fusion rule algebra. Finally, we study the behavior of the coefficients under fac'torization, in particular their dependence on the genus. A few examples are worked out.
An operator formulation of orbifold conformal field theory
Communications in Mathematical Physics, 1990
In 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.
Correlation Functions for M N / S N Orbifolds
Communications in Mathematical Physics, 2001
We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M N /S N , where M is an arbitrary manifold. The path integral with twist operators is replaced by a path integral on a covering space with no operator insertions. Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms of partition functions on Riemann surfaces with a finite range of genus g. For large N, this genus expansion coincides with a 1/N expansion. The contribution from the covering space of genus zero is 'universal' in the sense that it depends only on the central charge of the CFT. For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contributions. The condition for the genus zero contribution to the 3-point functions to be non-vanishing is similar to the fusion rules for an SU(2) WZW model. We observe that the 3-point coupling becomes small compared to its large N limit when the orders of the twist operators become comparable to the square root of Nthis is a manifestation of the stringy exclusion principle.
Modular invariance of trace functions in orbifold theory
The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of rational orbifold conformal field theory, in other words the theory of rational vertex operator algebras and their automorphisms. Under a certain finiteness condition on a rational vertex operator algebra V which holds in all known examples, we determine the precise numbers of g-twisted sectors for any automorphism g of V of finite order. We prove that the trace functions and correlations functions associated with such twisted sectors are holomorphic functions in the upper half-plane and, under suitable conditions, afford a representations of the modular group of the type prescribed in string theory. We establish the rationality of conformal weights and central charge. In addition to conformal field theory itself, where our conclusions are required on physical grounds, there are applications to the generalized Moonshine conjectures of Conway-Norton-Queen and to equivariant elliptic...
Correlation functions for orbifolds of the type MN/SN
Nuclear Physics B - Proceedings Supplements, 2001
The D1-D5 system, which arises in black hole physics, gives rise to a 2-d CFT which is the low energy limit of a sigma model with target space an orbifold (1~14)N/s N. (M4 is a 4-d manifold which can be T 4 or K3, and S N is the permutation group on N elements). With this motivation, we develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds MN/sN, where M is an arbitrary manifold. We find intriguing relations between the CFT correlators and the gravity theory that is conjectured to be dual to the D1-D5 system. Science B.V.
Journal of High Energy Physics, 2005
We study closed N = 2 strings on orbifolds of the form T 4 /Z 2 and C 2 /Z 2. We compute the torus partition function and prove its modular invariance. We analyze the BRST cohomology of the theory, construct the vertex operators, and compute three and four point amplitudes of twisted and untwisted states. We introduce a background of D-branes, and compute twist states correlators.
The nonperturbative analysis of background duality in orbifold conformal field theory
Nuclear Physics B, 1991
We study duality in simple two-dimensional orbifold models with metric and axionic backgrounds at arbitrary orders in string perturbation theory. It is shown that duality involves certain linear relations among twist correlators at dual backgrounds which are independent of the perturbative order. Relying on methods of harmonic analysis, a nonperturbative representation (in the sense of string field theory) of a class of S-matrix elements is obtained in terms of a universal background-independent spectral distribution and non_holomomhic mndiOlar vertar functions of the background parameters. At the same time, we find new realizations of the Verlinde algebra and of hypergroups characterizing the S-matrix nonperturbatively. Various examples and calculations are worked out.