Path integral and moduli space of Riemann surfaces

\(Z=\sum_{g=0}^{\infty} g_{s}^{-\chi(\Sigma_{g})}Z_{g}=\frac{1}{g_{s}^2}Z_{0}+g_{s}^{0}Z_{1}+g_{s}^2Z_{2}+\cdtos\)

classical

\(\frac{1}{g_{s}^2}Z_{0}\)

other terms : loo (=quantum ) corrections

 

Scattering amplitude

\(Z(V_1,\cdots, V_{s},V_{s+1},\cdots, V_{s+p})=\sum_{g=0}^{\infty} g_{s}^{-\chi(\Sigma_{g})}Z_{g}(V_1,\cdots, V_{s},V_{s+1},\cdots, V_{s+p})\)

 

 

 

Polchinski I,5