Polyakov action in string theory

E724407

action functional in theoretical physics string theory formalism

The Polyakov action in string theory is a reformulation of the string’s dynamics that treats the worldsheet metric as an independent field, providing a convenient starting point for quantizing strings and analyzing their conformal symmetry.

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Observed surface forms (1)

Surface form	Occurrences
Polyakov action for path-integral quantization	1

Statements (48)

Predicate	Object
instanceOf	action functional in theoretical physics ⓘ string theory formalism ⓘ
afterGaugeFixingLeadsTo	free 2D scalar fields plus ghosts in flat background ⓘ
allows	gauge fixing to conformal gauge ⓘ
betaFunctionsCorrespondTo	target-space equations of motion ⓘ
canCoupleTo	antisymmetric B-field background ⓘ dilaton background ⓘ
centralTo	modern covariant string perturbation theory ⓘ
couplesTo	target-space metric background ⓘ
dependsOn	embedding coordinates of the string in target spacetime ⓘ string tension ⓘ worldsheet metric ⓘ
describes	dynamics of relativistic strings ⓘ
exhibits	Weyl invariance at the classical level ⓘ two-dimensional diffeomorphism invariance ⓘ worldsheet conformal invariance ⓘ
field	string theory ⓘ
formulatedIn	Euclidean worldsheet signature ⓘ Lorentzian worldsheet signature ⓘ
frameworkFor	deriving low-energy effective field equations from string theory ⓘ
generalizedBy	nonlinear sigma model with background fields ⓘ
hasDomain	two-dimensional worldsheet ⓘ
implies	critical dimension 10 for superstring (with supersymmetric extension) ⓘ critical dimension 26 for bosonic string ⓘ
introducedIn	late 1970s ⓘ
involves	pullback of target-space metric to the worldsheet ⓘ two-dimensional scalar curvature term (topological in 2D) ⓘ worldsheet area element ⓘ
isClassicallyEquivalentTo	Nambu–Goto action NERFINISHED ⓘ
isMoreConvenientThan	Nambu–Goto action for quantization ⓘ
leadsTo	conformal field theory on the worldsheet ⓘ
mathematicallyFormulatedAs	two-dimensional nonlinear sigma model ⓘ
namedAfter	Alexander Polyakov NERFINISHED ⓘ
quantizationRequires	cancellation of conformal (Weyl) anomaly ⓘ
reformulates	Nambu–Goto action NERFINISHED ⓘ
treatsAsIndependentField	worldsheet metric ⓘ
usedFor	analysis of conformal symmetry on the worldsheet ⓘ covariant quantization of strings ⓘ derivation of Virasoro constraints ⓘ path integral quantization of strings ⓘ study of critical dimensions of string theory ⓘ
usedIn	bosonic string theory NERFINISHED ⓘ heterotic string theory NERFINISHED ⓘ superstring theory (with fermionic generalizations) ⓘ type I string theory NERFINISHED ⓘ type II string theories ⓘ
variationWithRespectTo	embedding coordinates gives string equations of motion ⓘ worldsheet metric gives energy–momentum tensor constraints ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Alexander Polyakov → knownFor → Polyakov action in string theory ⓘ

Nambu–Goto action → oftenReplacedBy → Polyakov action in string theory ⓘ

this entity surface form: Polyakov action for path-integral quantization