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:

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