v 1 1 6 A ug 2 00 6 A Note on Z 2 Symmetries of the KZ Equation
نویسنده
چکیده
We continue the study of hidden Z2 symmetries of the four-point ˆ sl(2)k KnizhnikZamolodchikov equation iniciated in [1]. Here, we focus our attention on the four-point correlation function in those cases where one spectral flowed state of the sector ω = 1 is involved. We give a formula that shows how this observable can be expressed in terms of the four-point function of non spectral flowed states. This means that the formula holding for the winding violating four-string scattering processes in AdS3 has a simple expression in terms of the one for the conservative case, generalizing what is known for the case of three-point functions, where the violating and the non-violating structure constants turn out to be connected one to each other in a similar way. What makes this connection particularly simple is the fact that, unlike what one would naively expect, it is not necessary to explicitly solve the five-point function containing a single spectral flow operator to this end. Instead, non diagonal functional relations between different solutions of the KZ equation turn out to be the key point for this short path to exist. Considering such functional relation is necessary but it is not sufficient; besides, the formula also follows from the relation existing between correlators in both WZNW and Liouville conformal theories.
منابع مشابه
6 A Note on Z 2 Symmetries of the KZ Equation
We continue the study of hidden Z2 symmetries of the four-point ˆ sl(2)k KnizhnikZamolodchikov equation iniciated in [1]. Here, we focus our attention on the four-point correlation function in those cases where one spectral flowed state of the sector ω = 1 is involved. We give a formula that shows how this observable can be expressed in terms of the four-point function of non spectral flowed st...
متن کاملep - t h / 04 12 03 4 v 2 1 A ug 2 00 5 The symmetries of the Dirac – Pauli equation in two and three dimensions
We calculate all symmetries of the Dirac-Pauli equation in twodimensional and three-dimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. We construct explicitly a class of multiple zero modes with their gauge potentials. email: [email protected] email: [email protected]
متن کاملar X iv : h ep - t h / 04 12 03 4 v 2 1 A ug 2 00 5 The symmetries of the Dirac – Pauli equation in two and three dimensions
We calculate all symmetries of the Dirac-Pauli equation in twodimensional and three-dimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. We construct explicitly a class of multiple zero modes with their gauge potentials. email: [email protected] email: [email protected]
متن کاملar X iv : g r - qc / 0 31 00 91 v 2 1 4 A ug 2 00 6 Semilinear wave equations on the Schwarzschild manifold I : Local Decay Estimates
The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type inequalities.
متن کاملClassical and Nonclassical Symmetries of a Generalized Boussinesq Equation
We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Boussinesq equation, which has the classical Boussinesq equation as an special case. We study the class of functions f(u) for which this equation admit either the classical or the nonclassical method. The reductions obtained are derived. Some new exact solutions can be der...
متن کامل