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arXiv · 1611.02507

A note on sphere free energy of $p$-form gauge theory and Hodge duality

Himanshu Raj
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Abstract

We consider a free $p$-form gauge theory on a $d$-dimensional sphere of radius $R$ and calculate its free energy. We perform the calculation for generic values of $p$ and obtain the free energy as a function of $d, p$ and $R$. The result contains a $\log R$ term with coefficient proportional to $\left(2p+2-d \right)$, which is consistent with lack of conformal invariance for $p$ form theories in dimensions other than $2p+2$. We also compare the result for $p$-form and $(d-p-2)$-form theory which are classically Hodge dual to each other in $d$ dimensions and find that they agree for odd values of $d$. Instead, for even $d$, we find that the results disagree by an amount that is consistent with the reported values in the literature.

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Himanshu Raj. 2017-11-23. A note on sphere free energy of $p$-form gauge theory and Hodge duality. https://doi.org/10.1088/1361-6382%2Faa8cfd

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