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In quantum field theory

In the perturbation theory of a quantum field theory defined by an action functional S:ConfS : Conf \to \mathbb{R}, a vacuum of the theory is a classical solution: a configuration ϕ 0Conf\phi_0 \in Conf that solves the Euler-Lagrange equations of SS.

Because in the perturbative quantum dynamics around ϕ 0\phi_0 quanta are small deviations from a classical solution. Hence the absence of any quanta, hence the “vacuum”, is the solution ϕ 0\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 (