Counting Surfaces by Bertrand Eynard

Author:Bertrand Eynard
Language: eng
Format: epub
Publisher: Springer Basel, Basel

5.4.2 String Equation

The KdV minimal model ( p, 2) with p = 2m + 1, coupled to gravity, was formulated in terms of a “string equation” by Douglas and Shenker in 1990 [27]. Let P, Q two differential operators of respective orders p and 2, satisfying the so-called “string equation”:

(5.4.1)

is a redundant parameter, which can be absorbed by a redefinition of s and u, but we prefer to keep it to play the role of a scaling parameter which can be sent to zero to get the “classical limit”.

In all this chapter, we shall denote with a dot the derivative with respect to s: in order to shorten notations. The prime will be reserved to derivatives with respect to the spectral parameter df∕dx = f′.

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