On partition function and Weyl anomaly of conformal higher spin fields

Sep 3, 2013
34 pages
Published in:
  • Nucl.Phys.B 877 (2013) 598-631
  • Published: Dec 11, 2013
e-Print:
Report number:
  • IMPERIAL-TP-AT-2013-4

Citations per year

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Abstract: (Elsevier)
We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s ) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative “partially massless” spin s fields, generalizing the previously known expression for the 1-loop Weyl graviton ( s=2 ) partition function. We compute the corresponding spin s Weyl anomaly coefficients as and cs . Our result for as reproduces the expression found recently in arXiv:1306.5242 by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S4 to a ratio of known partition functions of massless higher-spin field in AdS 5 with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A)dS background is given by the product of squares of “partially massless” spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in arXiv:1306.5242 that the sum of the bosonic as coefficients over all s is zero when computed using the ζ -function regularization, and we observe that the same property is true also in the fermionic case.
Note:
  • 36 pages. v2: misprints corrected, references added; v3: comments on D greater than 4 generalization and appendix B on conformal higher derivative scalar operator added; v4: a minor comment in section 3.1 and references added
  • spin: high
  • anomaly: Weyl
  • field theory: conformal
  • gravitation: conformal
  • anomaly: conformal
  • derivative: high
  • regularization: zeta function
  • partition function
  • AdS/CFT correspondence
  • graviton