Effective action of conformal spins on spheres with multiplicative and conformal anomalies

Abstract

Two multiplicative anomalies are evaluated for the determinant of the conformal higher spin propagating operator on spheres given by Tseytlin. One holds for the decomposition of the higher derivative product into its individual second order factors and the other applies to its complete linear factorisation. Using this last factorisation, I also calculate the determinants explicitly in terms of the Riemann ζfunction, for both even and odd dimensions. In the latter case there is, of course no multiplicative anomaly. The conformal anomaly is also found for arbitrary spin and dimension. 1

On higher spin partition functions

“…(A.9) 32 In this Appendix we add hats to Laplacian operators not to confuse them with dimension parameter ∆. 33 Let us note that [14] considered the case of a generic massive AdS d+1 scalar with non-integer r = m 2 + d 2 4 when the associated induced boundary theory is non-local: the kinetic operator is inverse of…”

“…(A.9) 32 In this Appendix we add hats to Laplacian operators not to confuse them with dimension parameter ∆. 33 Let us note that [14] considered the case of a generic massive AdS d+1 scalar with non-integer r =…”

Form factors and non-local multiplicative anomaly for fermions with background torsion

“…It is worth mentioning that this non-local MA is different from what is investigated by many authors in previous papers [4][5][6][7], by using the ζ -regularization (see also [8] for MA analysis of the Dirac fields with vector and axial vector in Minkowski spacetime). In those works, the MA can be related to the ambiguity of the choice of μ itself [6,7]. One can say that the MA which we are considering is a non-local version of earlier MA.…”

“…This kind of ambiguity, coming from what is called the non-local multiplicative anomaly (MA), was treated in recent papers, where different examples were studied: (i) finite one-loop quantum corrections from massive fermionic fields in an electromagnetic background in curved space, [2]; and (ii) finite oneloop quantum corrections from massive fermionic fields in the Yukawa model (also in curved space), [3]. It is worth mentioning that this non-local MA is different from what is investigated by many authors in previous papers [4][5][6][7], by using the ζ -regularization (see also [8] for MA analysis of the Dirac fields with vector and axial vector in Minkowski spacetime). In those works, the MA can be related to the ambiguity of the choice of μ itself [6,7].…”

Non-relativistic limit of thermodynamics of Bose field in a static space-time and Bose–Einstein condensation

“…(32) Let us remark that alternative factorizations of the quartic term in (31) lead to multiplicative anomalies in the functional determinant [14][15][16]. However as shown in [16] at least in the Minkowski spacetime the factorization (31) is the one which yields the same result as that obtained by the canonical method, and therefore will be the one used in this work.…”