$C_T$ for monodromy defects of fields on odd dimensional spheres for higher derivative propagation

The central charge $C_T$ is computed for scalar and Dirac fields propagating according to GJMS-type kinetic operators acting on odd $d$-dimensional spheres in the presence of a spherical monodromy. The relation of $C_T$ to the derivatives of the free energy on the conically deformed sphere via the Perlmutter factor leads to a numerical quadrature. The variation of $C_T$ with the monodromy flux, $δ$, displays sign changes, exactly as in even dimensions. Closed forms for $C_T$ are derived when $δ$ equals 0 or 1/2 with the derivative order either even or odd and shown to agree with existing, even $d$ expressions. The infinite $d$ limits are also derived in these special cases.

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