Abstract
The partition function of four dimensional SO(4) Yang-Mills theory is rewritten in terms of variables admitting straightforward relation to the partition function of pure 4D gravity. The gauge action turns into first-order Hilbert-Palatini action for Einstein gravity with a simple extra term added. The proposed relation can be substantiated as a duality for the partition functions provided a special gauge is imposed for the gravity. The same method allows to find a closed expression for the partition function of the SO(4) gauge theory.
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