Explicit formula for dilaton profile

We use the following parametrization of :


Subsitution of into the ansatz (12) gives to the lowest order in s:


After adding some BRST-exact terms the leading term of the -expansion is proportional to:


We obtain and where:


In this formula parametrizes the bosonic space .

The expression for is more transparent in the vector notations. Let us think of as the symmetric traceless tensor of (the upper latin indices) and the symmetric traceless tensor of (the lower greek indices). We parametrize the point of as a pair of vectors , . We get:


We conclude that the dilaton profile is polynomial in the coordinates of “two-time physics”