String embedding map ( $X^{μ} (σ, τ)$ )

The string embedding map

X : Σ \to M

assigns each worldsheet point its position in target spacetime.

Table of contents
- Induced worldsheet metric String embedding map
  - Nambu–Goto action Induced worldsheet metric

Induced worldsheet metric ( $γ_{α β}$ )

The induced worldsheet metric is the pullback of the target-space metric:

γ_{α β} = \partial_{α} X^{μ} \partial_{β} X^{ν} η_{μν} .

Nambu–Goto action

The Nambu–Goto action

S_{NG} = - T \int_{Σ} d^{2} σ - det γ

is minus the string tension times the Lorentzian area of the worldsheet.

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