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At VIII. Disscussion, p. 36:

"Our main result is the formula (53) for the inner product in Hj1,...,jn in terms of a holomorphic integral over the space of “shapes” parametrized by the cross-ratio coordinates Zi. In the “tetrahedral” n = 4 case there is a single cross-ratio Z. Somewhat unexpectedly, we have found that the integration kernel ˆK (Zi, ¯ Zi) is

**given by the n-point function of the bulk/boundary dualities of string theory**, and this fact allowed to give to ˆK (Zi, ¯ Zi) an interpretation that related them to the Kahler potential on the space of “shapes”."