Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 306 / 1 / 4

Table of contents
- Solution 4

Solution

Changing the target metric by

δ G_{μν} = ϵ_{μν}

changes the action by

δ S = - \frac{1}{4 π α ^{'}} \int_{Σ} d^{2} σ ∣ h ∣ h^{ab} ϵ_{μν} \partial_{a} X^{μ} \partial_{b} X^{ν} .

Since the path-integral weight is

e^{i S}

, the leading change is the insertion

δ ⟨ ϕ_{1} \dots ϕ_{n} ⟩ = \int_{Σ} d^{2} σ ⟨ O (σ, τ) ϕ_{1} \dots ϕ_{n} ⟩_{conn},

where

O = - \frac{i}{4 π α ^{'}} ∣ h ∣ h^{ab} ϵ_{μν} \partial_{a} X^{μ} \partial_{b} X^{ν} .

A change of worldsheet metric within a gauge orbit changes only the redundant description and cannot alter gauge-invariant observables. The target-space metric is instead a physical coupling of the string nonlinear sigma model, so changing it changes the theory and its correlation functions.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version