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# Title: Two-loop renormalization of multiflavor $φ^3$ theory in six dimensions and the trace anomaly

Abstract: We use the background-field method and the heat kernel to obtain all counterterms to two-loop order of conformally-coupled multiflavor $\phi^3$ theory in six spacetime dimensions, defined in curved spacetime and with spacetime-dependent couplings. We also include spacetime-dependent mass terms for completeness. We use these results to write a general expression for the trace anomaly. With the use of Weyl consistency conditions we are able to show that the strong $a$-theorem for a certain natural candidate quantity $\tilde{a}$ is violated in this theory, and obtain a three-loop expression for the coefficient $a$ of the Euler term in the anomaly.
 Comments: 31 pages. v2: Equation (4.16) corrected. The discussion in sections 3 and 6 contains errors that have been addressed in arXiv:1604.01782 Subjects: High Energy Physics - Theory (hep-th) Journal reference: Phys. Rev. D 92, 045013 (2015) DOI: 10.1103/PhysRevD.92.045013 Cite as: arXiv:1504.05959 [hep-th] (or arXiv:1504.05959v2 [hep-th] for this version)

## Submission history

From: Andreas Stergiou [view email]
[v1] Wed, 22 Apr 2015 20:00:41 GMT (284kb)
[v2] Thu, 21 Apr 2016 15:15:51 GMT (284kb)
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