Polyakov Action - Equations of Motion

Equations of Motion

Using diffeomorphisms and Weyl transformation, with a Minkowskian target space, one can transform the action into the following form:

where

Keeping in mind that one can derive the constraints:

.

Substituting one obtains:

And consequently:

With the boundary conditions in order to satisfy the second part of the variation of the action.

• Closed strings

Periodic boundary conditions:

• Open strings

(i) Neumann boundary conditions:

(ii) Dirichlet boundary conditions: