# Worldsheet

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String Theory
Prior to the First Superstring Revolution
Early History S-Matrix Theory
Regge Trajectory
Bosonic String Theory Worldsheet
String
Bosonic String Theory
String Perturbation Theory
Tachyon Condensation
Supersymmetric Revolution Supersymmetry
RNS Formalism
GS Formalism
BPS
Superstring Revolutions
First Superstring Revolution GSO Projection
Type II String Theory
Type IIB String Theory
Type IIA String Theory
Type I String Theory
Type H String Theory
Type HO String Theory
Type HE String Theory
Second Superstring Revolution T-Duality
D-Brane
S-Duality
Horava-Witten String Theory
M-Theory
Holographic Principle
N=4 Super-Yang-Mills Theory
BFSS Matrix Theory
Matrix String Theory
(2,0) Theory
Twistor String Theory
F-Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
Phenomenology String Theory Landscape
Minimal Supersymmetric Standard Model
String Phenomenology

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In String Theory, a Worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. [1] The term was coined by Leonard Susskind around 1967 as a direct generalization of the Worldline 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 and the Spacetime Metric) are encoded in a Conformal Field Theory defined on the worldsheet. [2] For example, the Bosonic String in 26-dimensional Minkowski spacetime has a worldsheet conformal field theory consisting of 26 free scalar fields. Meanwhile, a superstring worldsheet theory in 10 dimensions consists of 10 free scalar fields and their fermionic superpartners.

A String Theory can be almost entirely formulated in terms of a Lagrangian Density across a worldsheet.

In Bosonic String Theory, the Lagrangian Density across the worldsheet is given by the Polyakov Lagrangian Density. [3]

$\mathcal{L_P} = {\frac{T }{2}}h^{ab} \partial_a X^\mu \partial_b X^\nu g_{\mu \nu}$

In Type IIB String Theory, Type IIA String Theory and Type I String Theory, the Lagrangian Density across the worldsheet is the Ramond Neveu-Schwarz Lagrangian Density.[3]

$\mathcal{L_{RNS}} = {\frac{T }{2}}h^{ab} \left(\partial_a X^\mu \partial_b X^\nu - i\hbar c_0\bar{\psi_\mu }\not\partial\psi^\mu \right)g_{\mu \nu}$

In the Type HE String Theory and the Type HO String Theory is given by the Hetrotic Lagrangian Density.[3]

${{\mathsf{\mathcal{L}}}_{\mathsf{\mathcal{H}}}}=\frac{T}{2}{{h}^{ab}}\left( {{\partial }_{a}}{{X}^{\mu }}{{\partial }_{b}}{{X}^{\nu }}- \sum\limits_{k=1}^{32}{\left( i\hbar c_0 \bar{\lambda_{\mu}} \not\partial \lambda ^\mu \right)}-\left( i\hbar c_0\bar{\psi_{\mu }} \not\partial\psi^\mu \right) \right){{g}_{\mu \nu }}$

## ReferencesEdit this section

1. 3.0 3.1 3.2 McMohan, David (2009). String theory DeMystified. Chicago: McGrawHill. ISBN 978-0071498708.