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A compendium of sphere path integrals

Law, Y.T. Albert
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Abstract

We study the manifestly covariant and local 1-loop path integrals on S d+1 for general massive, shift-symmetric and (partially) massless totally symmetric tensor fields of arbitrary spin s ≥ 0 in any dimensions d ≥ 2. After reviewing the cases of massless fields with spin s = 1, 2, we provide a detailed derivation for path integrals of massless fields of arbitrary integer spins s ≥ 1. Following the standard procedure of Wick-rotating the negative conformal modes, we find a higher spin analog of Polchinski’s phase for any integer spin s ≥ 2. The derivations for low-spin (s = 0, 1, 2) massive, shift-symmetric and partially massless fields are also carried out explicitly. Finally, we provide general prescriptions for general massive and shift-symmetric fields of arbitrary integer spins and partially massless fields of arbitrary integer spins and depths.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSfield theories in higher dimensionshigher spin symmetry, models of quantum gravity

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Law, Y.T. Albert. 2021-12-29. A compendium of sphere path integrals. https://doi.org/10.1007/jhep12(2021)213

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