Definitions
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 n. A twodimensional manifold which describes the embedding of a string in spacetime, a direct generalization of the worldline of a particle in special and general relativity.
Etymologies
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Examples

The mechanism is completely different from the usual string paradigm: spacetime is not introduced ab initio as a target, but emerges as the space of degree 1 worldsheet instantons in the twistor space target.

The fact that it is consistent, in not really a big point in its favor, because all the consistency is really coming from the two dimensional conformal field theory of the worldsheet.

Afterwards it was discovered that the existence of fermions (something we see every day) required that the string worldsheet have supersymmetry.

Any possibility that the worldsheet bosons and fermions of string theory are related to the spin networks of LQG?

For example, in the bosonic string there are 26 bosonic fields which ‘live’ on the string worldsheet which are interpreted as dimensions.

As strings move through time, they trace out a worldsheet similar to the worldlines of point theory.

Simple bosonic strings can be described by a field theory defined on the string worldsheet where the action is dependent upon the metric h_ {mn} on the worldsheet, the 2curvature R_ {2} of the worldsheet, and a dilaton \phi (a scalar field on the worldsheet).

If we demand that the worldsheet field theory is conformally invariant (scale invariant), then the socalled beta functions must vanish (this is necessary for us to gaugefix the metric to the conformal gauge).

If the background is curved, then it has a metric which enters the field theory on the worldsheet as a set of couplings between the string coordinates.

Why do you demand that the worldsheet field theory is conformally invariant on the quantum level?
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