Abstract
Abstract Three-point correlation function in perturbed conformal field theory coupled to two-dimensional quantum gravity (perturbed Liouville gravity) is explicitly computed by using the free field approach. The representation considered here is the one recently proposed in [G. Giribet, Nucl. Phys. B 737 (2006) 209] to describe the string theory in AdS 3 space. Consequently, this computation extends previous results which presented free field calculations of particular cases of string amplitudes, and confirms that the free field approach leads to the exact result. Remarkably, this representation allows to compute winding violating three-point functions without making use of the spectral flow operator.
Highlights
In a recent paper [1], a new free field representation of string theory in AdSy was introduced in order to realize the explicit iden tities that, according to what was proven in [2], turn out to connect the correlation functions in both Liouville and SL(2)g WZNW theories
Such representation corresponds to a perturbed conformal field theory coupled to two-dimensional quantum gravity
It is known that the free field approach and the Coulomb gas-like prescription were previously employed to this end [3]; the computation here regards those cases that were not worked out in previous free field calculations
Summary
In a recent paper [1], a new free field representation of string theory in AdSy was introduced in order to realize the explicit iden tities that, according to what was proven in [2], turn out to connect the correlation functions in both Liouville and SL(2)g WZNW theories Such representation corresponds to a perturbed conformal field theory coupled to two-dimensional quantum gravity (per turbed Liouville gravity). Previous free field computations considered particular relations between left-moving m and right-moving m momenta, imposing in such a way certain constraints on the angular momentum of the interacting strings We relax such assumptions and calculate the generic "winding violating” three-point amplitude in AdSy within the framework of the Coulomb gas-like prescription. We do this in detail, by emphasizing the steps through the calculation
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