A compendium of sphere path integrals

Law, Y.T. Albert

doi:10.1007/jhep12(2021)213

Title: A compendium of sphere path integrals

Journal Article · 29 December 2021 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep12(2021)213 · OSTI ID:1976603

^[1]

Columbia University, New York, NY (United States); Columbia Univ., New York, NY (United States)

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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Research Organization:: Columbia University, New York, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0011941

OSTI ID:: 1976603

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2021; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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