An action functional for sigma models with target space a pseudo-Riemannian manifold.
The Polyakov action is classically equivalent to the Nambu-Goto action.
The Polyakov action was introduced in
Quantum geometry of bosonic strings , Phys. Lett. B103 (1981) 207;
Quantum geometry of fermionic strings , Phys. Lett. B103 (1981) 211