Polyakov action
E724408
The Polyakov action is a fundamental formulation of string theory that describes the dynamics of relativistic strings via a two-dimensional worldsheet embedded in spacetime.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Polyakov action with auxiliary worldsheet metric | 1 |
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
string theory action
ⓘ
two-dimensional field theory action ⓘ worldsheet action ⓘ |
| admitsSymmetry | 2D conformal symmetry at the quantum level (in critical dimension) ⓘ |
| advantageOver | Nambu–Goto action in quantization ⓘ |
| canIncludeTerm |
antisymmetric B-field coupling ∫ B_{μν}(X) ∂X^μ ∂X^ν
ⓘ
dilaton coupling to worldsheet curvature ⓘ |
| containsParameter |
Regge slope α′ via T = 1/(2πα′)
ⓘ
string tension T ⓘ |
| dependsOn |
inverse worldsheet metric h^{ab}
ⓘ
target-space metric G_{μν}(X) ⓘ worldsheet metric determinant √−h ⓘ |
| describes | dynamics of relativistic strings ⓘ |
| embedsWorldsheetIn | target spacetime ⓘ |
| formulatedOn | two-dimensional worldsheet ⓘ |
| hasField |
embedding coordinates X^μ(σ,τ)
ⓘ
worldsheet metric h_{ab} ⓘ |
| hasGeneralForm | S = −(T/2) ∫ d^2σ √−h h^{ab} ∂_a X^μ ∂_b X^ν G_{μν}(X) ⓘ |
| impliesBackgroundEquations | target-space field equations from beta-function conditions ⓘ |
| impliesConstraint |
Virasoro constraints after gauge fixing
ⓘ
vanishing worldsheet energy–momentum tensor ⓘ |
| inConformalGaugeBecomes | free 2D scalar fields X^μ on the worldsheet (for flat target space) ⓘ |
| introducedBy | Alexander Polyakov NERFINISHED ⓘ |
| is |
Weyl invariant at the classical level
ⓘ
locally Lorentz invariant on the worldsheet ⓘ quadratic in worldsheet derivatives of X^μ ⓘ reparametrization invariant ⓘ |
| isBasisFor | nonlinear sigma model description of strings ⓘ |
| isCentralIn | path-integral formulation of string theory ⓘ |
| isClassicallyEquivalentTo | Nambu–Goto action NERFINISHED ⓘ |
| isDefinedOn | Euclidean worldsheet in many calculations ⓘ |
| isFrameworkFor | coupling strings to background fields ⓘ |
| isGaugeFixedTo | conformal gauge ⓘ |
| isGeneralizedIn | Green–Schwarz superstring formalism with fermionic fields NERFINISHED ⓘ |
| isRelatedTo | BRST quantization of strings ⓘ |
| isStandardToolIn | string perturbation theory ⓘ |
| isUsedToDerive |
string scattering amplitudes
ⓘ
string spectrum ⓘ |
| namedAfter | Alexander Polyakov NERFINISHED ⓘ |
| quantizationLeadsTo | critical dimension D = 26 for bosonic string ⓘ |
| quantizationRequires | vanishing conformal (Weyl) anomaly ⓘ |
| usedIn |
bosonic string theory
ⓘ
conformal field theory NERFINISHED ⓘ superstring theory NERFINISHED ⓘ |
| wasIntroducedIn | late 1970s ⓘ |
| worldsheetHasCoordinates | sigma and tau ⓘ |
| yieldsEquationOfMotion | worldsheet Laplace equation for X^μ in flat space ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Polyakov action with auxiliary worldsheet metric