M5/D4 brane partition function on a circle bundle

Understand

We consider Abelian M5 brane on a six-manifold which we take as a circle bundle over a five-manifold $M$.

• We compute the zero mode part of the M5 brane partition function using Chern-Simons theory and Hamiltonian formulation respectively and find an agreement.
• We also show that the D4 brane on $M$ shares exactly the same zero mode partition function again using the Hamiltonian formulation.
• For the oscillator modes we find that KK modes associated with the circle compactification are missing from the D4 brane.