In mathematics, and in particular, in the mathematical background of string theory, the Goddard–Thorn theorem (also called the no-ghost theorem) is a theorem about certain vector spaces. It is named after Peter Goddard and Charles Thorn. The name "no-ghost theorem" stems from the fact that in the original statement of the theorem, the vector space inner product is positive definite. Thus, there were no vectors of negative norm for r ≠ 0. The name "no-ghost theorem" is also a word play on the phrase no-go theorem.