# Contents

## Idea

In a sigma-model quantum field theory a field configuration is a morphism $\phi : \Sigma \to X$ for $\Sigma$ an $n$-dimensional manifold or similar. One is to think of this as being the trajectory of an $(n-1)$-brane propagating in the target space $X$.

For the case $n = 1$ (for instance the relativistic particle, a 0-brane) the term worldline for $\Sigma$ has a long tradition. Accordingly one calls $\Sigma$ the worldvolume of the given $(n-1)$-brane when $n \gt 1$. For the case $n=2$ (the case of relevance in string theory) one also says worldsheet.

Revised on April 9, 2014 10:31:05 by Urs Schreiber (77.251.114.72)