String-loop effective action expansion ($S_{\mathrm{eff}}={\sum }_{g\ge 0}{g}_s^{2g-2}{S}_g$)

Connected oriented closed string worldsheets of genus $g$ give the spacetime effective-action term $g_s^{2g-2}{S}_g$. Each $S_g$ has a separate low-energy derivative expansion in ${\alpha }^{\prime }$. The string coupling orders quantum string loops, while ${\alpha }^{\prime }$ orders effects of finite string size.