worldsheet

In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. The term was coined by Leonard Susskind as a direct generalization of the world line concept for a point particle in special and general relativity. The type of string, the geometry of the spacetime in which it propagates, and the presence of long-range background fields (such as gauge fields) are encoded in a two-dimensional conformal field theory defined on the worldsheet. For example, the bosonic string in 26 dimensions has a worldsheet conformal field theory consisting of 26 free scalar bosons. Meanwhile, a superstring worldsheet theory in 10 dimensions consists of 10 free scalar fields and their fermionic superpartners.

In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. The term was coined by Leonard Susskind as a direct generalization of the world line concept for a point particle in special and general relativity. The type of string, the geometry of the spacetime in which it propagates, and the presence of long-range background fields (such as gauge fields) are encoded in a two-dimensional conformal field theory defined on the worldsheet. For example, the bosonic string in 26 dimensions has a worldsheet conformal field theory consisting of 26 free scalar bosons. Meanwhile, a superstring worldsheet theory in 10 dimensions consists of 10 free scalar fields and their fermionic superpartners. Strings are further classified into open and closed. The topology of the worldsheet of an open string is \mathbb{R}\times I , where I := [0,1] , a closed interval, and admits a global coordinate chart (\tau, \sigma) with -\infty and 0 \leq \sigma \leq 1 . Meanwhile the topology of the worldsheet of a closed string is \mathbb{R}\times S^1 , and admits 'coordinates' (\tau, \sigma) with -\infty and \sigma \in \mathbb{R}/2\pi\mathbb{Z} . That is, \sigma is a periodic coordinate with the identification \sigma \sim \sigma + 2\pi . The redundant description (using quotients) can be removed by choosing a representative 0 \leq \sigma .

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