Complete conformal field theory solution of a chiral six-point correlation function

作者：Simmons Jacob J H^*; Kleban Peter

来源：Journal of Physics A-Mathematical and Theoretical, 2011, 44(31): 315403.

DOI：10.1088/1751-8113/44/31/315403

Using conformal field theory, we perform a complete analysis of the chiral six-point correlation function
C(z) = ,
with the four phi(1,2) operators at the corners of an arbitrary rectangle, and the point z = x + iy in the interior. We calculate this for arbitrary central charge (equivalently, SLE parameter kappa > 0). C is of physical interest because for percolation (kappa = 6) and many other two-dimensional critical points, it specifies the density at z of critical clusters conditioned to touch either or both vertical ends of the rectangle, with these ends 'wired', i.e. constrained to be in a single cluster, and the horizontal ends free. The correlation function may be written as the product of an algebraic prefactor f and a conformal block G, where f = f (x, y, m), with m a cross-ratio specified by the corners (m determines the aspect ratio of the rectangle). By appropriate choice of f and using coordinates that respect the symmetry of the problem, the conformal block G is found to be independent of either y or x, and given by an Appell function.

• 出版日期2011-8-5