Witten index

In quantum field theory/statistical mechanics, the Witten index at the inverse temperature β is defined as a modification of the standard partition function:

Tr[( − 1)^Fe ^{− βH}]

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Note the (-1)^F operator. This is what makes it different from the ordinary partition function.

In a supersymmetric theory, each nonzero energy eigenvalue contains an equal number of bosonic and fermionic states. Because of this, the Witten index is independent of the temperature and gives the number of bosonic vacuum states minus the number of fermionic vacuum states.