Correlation functions in conformal Toda field theory I
Abstract
Twodimensional {sl}(n) quantum Toda field theory on a sphere is considered. This theory provides an important example of conformal field theory with higher spin symmetry. We derive the threepoint correlation functions of the exponential fields if one of the three fields has a special form. In this case it is possible to write down and solve explicitly the differential equation for the fourpoint correlation function if the fourth field is completely degenerate. We give also expressions for the threepoint correlation functions in the cases, when they can be expressed in terms of known functions. The semiclassical and minisuperspace approaches in the conformal Toda field theory are studied and the results coming from these approaches are compared with the proposed analytical expression for the threepoint correlation function. We show, that in the framework of semiclassical and minisuperspace approaches general threepoint correlation function can be reduced to the finitedimensional integral.
 Publication:

Journal of High Energy Physics
 Pub Date:
 November 2007
 DOI:
 10.1088/11266708/2007/11/002
 arXiv:
 arXiv:0709.3806
 Bibcode:
 2007JHEP...11..002F
 Keywords:

 High Energy Physics  Theory
 EPrint:
 54 pages, JHEP style