nLab
vacuum

under construction

Idea

In quantum field theory

In the perturbation theory of a quantum field theory defined by an action functional $S:\mathrm{Conf}\to ℝ$, a vacuum of the theory is a classical solution: a configuration ${\varphi }_0\in \mathrm{Conf}$ that solves the Euler-Lagrange equations of $S$.

Because in the perturbative quantum dynamics around ${\varphi }_0$ quanta? are small deviations from a classical solution. Hence the absence of any quanta, hence the “vacuum”, is the solution ${\varphi }_0$ 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 .

Related concepts

• false vacuum

• topological defects due to spontaneous symmetry breaking

  • domain wall, cosmic string, monopole

• Yang-Mills instanton

  • BPTS instanton

  • instanton in QCD, QCD vacuum