Euclidean quantum M5 brane theory on $S^1 \times S^5$

We consider Euclidean quantum M5 brane theory on $S^1\times S^5$. Dimensional reduction along $S^1$ gives a 5d SYM on $S^5$. We derive this 5d SYM theory from a classical Lorentzian M5 brane Lagrangian on $S^1 \times S^5$, where $S^1$ is a timelike circle of radius $T$, by performing a Scherk-Schwarz reduction along $S^1$ followed by Wick rotation of $T$.

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