The Polyakov action introduces an independent worldsheet metric :Its metric equation makes conformal to the induced worldsheet metric, reducing it classically to the Nambu–Goto action.
A worldsheet diffeomorphism is a smooth reparameterization of the worldsheet coordinates under which is a scalar and is a rank-two tensor.
Static gauge identifies selected target-space coordinates with worldvolume coordinates, such as for a string.
A Weyl transformation rescales the worldsheet metric locally, , without changing . The classical Polyakov action is Weyl invariant.
After conformal gauge fixing, independent reparameterizations and remain, accompanied by a compensating Weyl transformation.
Light-cone gauge uses residual conformal transformations to make the target-space coordinate linear in worldsheet time. The Virasoro constraints then determine from the transverse fields.
The worldsheet metric equation in conformal gauge sets the stress tensor to zero, . In oscillator language these are the Virasoro constraints.
Gauge fixing worldsheet diffeomorphism and Weyl symmetry introduces an anticommuting vector ghost and a symmetric traceless antighost . In complex coordinates they form holomorphic and antiholomorphic systems.
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The Polyakov action is an important concept in theoretical physics, particularly in the context of string theory. It is a two-dimensional field theory that describes the dynamics of strings in spacetime. Named after the physicist Alexander Polyakov, the action provides a framework to model how strings propagate and interact in a background spacetime.