Finite volume QCD at fixed topological charge

In finite volume the partition function of QCD with a given θ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume $1/V$. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of a $1/V$ expansion. Applying this formula, we propose a class of methods to determine the topological susceptibility in QCD from various correlation functions calculated in a fixed topological sector.