# nLab vacuum

## Surveys, textbooks and lecture notes

under construction

# Contents

## Idea

### In quantum field theory

In the perturbation theory of a quantum field theory defined by an action functional $S : Conf \to \mathbb{R}$, a vacuum of the theory is a classical solution: a configuration $\phi_0 \in Conf$ that solves the Euler-Lagrange equations of $S$.

Because in the perturbative quantum dynamics around $\phi_0$ quanta are small deviations from a classical solution. Hence the absence of any quanta, hence the “vacuum”, is the solution $\phi_0$ itself.

(…)

### In string theory

In string theory the vacua of the effective background QFT are at the same time identified with certain 2-dimensional CFTs – namely the string sigma-models which have the given effective QFT as their second quantization.

Perturbative string theory is defined as the string perturbation series of these sigma-models about these vacua.

The moduli space of these vacua – which is hardly understood – has come to be called the landscape of string theory vacua .

Revised on March 24, 2014 01:55:59 by Urs Schreiber (89.204.137.20)