6D trace anomalies from quantum mechanical path integrals

Dass

2001

Phys. Rev. D

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We discuss a simplified method for computing trace anomalies in dimensions d ≤ 6. It is known that in the quantum mechanical approach trace anomalies in d dimensions are given by a ( d 2 + 1)-loop computation in an auxiliary 1d sigma model with arbitrary geometry. We show how one can obtain the same information using a simpler d 2 -loop calculation on an arbitrary geometry supplemented by a ( d 2 + 1)-loop calculation on the simplified geometry of a maximally symmetric space.

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confidence: 77%

Simplified method for trace anomaly calculations ind<~6

Dass

2001

Phys. Rev. D

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“…One may use a similarity transformation to the basis of the scalar field φ and corresponding scalar regulator R = 2 − ξR to evaluate the heat kernel expansion perturbatively with covariant methods [19] (see also [25] for a review). Another useful method to compute the anomaly is to represent the Fujikawa trace as a quantum mechanical trace for a particle moving in curved space [26][27][28] (see also the book [15] for details on this method). At the end the explicit results are as follows.…”

Section: The Trace Anomaly Of a Scalar Fieldmentioning

confidence: 99%

On the trace anomaly of a Weyl fermion

Martelli

2016

J. High Energ. Phys.

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Abstract:We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa's method supplemented by a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for presenting such a calculation stems from recent studies that suggest that the trace anomaly of chiral fermions in four dimensions might contain an imaginary part proportional to the Pontryagin density. We find that the trace anomaly of a Weyl fermion is given by half the trace anomaly of a Dirac fermion, so that no imaginary part proportional to the Pontryagin density is seen to arise.

“…In the main text we use Riemann normal coordinates (for details see [44,45], and [46][47][48] for their application to nonlinear sigma models; the most accurate and explicit expansion of the metric around the origin that we are aware of may be found in [49]). On spheres the sectional curvature is positive, and we can take M = 1 a > 0.…”

Section: Discussionmentioning

confidence: 99%

On the simplified path integral on spheres

Corradini

2017

Eur. Phys. J. C

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We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the particle action. The emerging linear sigma model contains a scalar effective potential that reproduces the effects of the curvature. We present here further details of the construction, and extend its perturbative evaluation to orders high enough to read off the type-A trace anomalies of a conformal scalar in dimensions d = 14 and d = 16.