Renormalizing (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>theory in curved space-time

Kodaira, Jiro; Okada, J.

doi:10.1103/physrevd.33.2875

Cited by 6 publications

(6 citation statements)

References 19 publications

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“…Eq. ( 11) generalizes the single field result of [23] (see also [20,21,24,25]) to the multi-field case, and agrees with the results of [22,26,27]. The first contribution to ( 12) is non-planar.…”

Section: Results From the Effective Potentialsupporting

confidence: 86%

Challenge to theaTheorem in Six Dimensions

et al. 2014

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The possibility of a strong a theorem in six dimensions is examined in multiflavor ϕ^{3} theory. Contrary to the case in two and four dimensions, we find that, in perturbation theory, the relevant quantity a[over ˜] increases monotonically along flows away from the trivial fixed point. a[over ˜] is a natural extension of the coefficient a of the Euler term in the trace anomaly, and it arises in any even spacetime dimension from an analysis based on Weyl consistency conditions. We also obtain the anomalous dimensions and beta functions of multiflavor ϕ^{3} theory to two loops. Our results suggest that some new intuition about the a theorem is in order.

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Section: Results From the Effective Potentialsupporting

confidence: 86%

Challenge to theaTheorem in Six Dimensions

et al. 2014

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“…Eq. (5.6) reproduces the result of [32] (see also [19][20][21]33]) in the case of a single field φ. In that case β (1) has a negative sign, and hence the corresponding theory is asymptotically-free.…”

Section: Beta Functions and Anomalous Dimensionssupporting

confidence: 75%

“…In the single-field case (5.8) reproduces the result of [32] (see also [19][20][21] 11 ), which, just like β (1) , is also negative.…”

Section: Beta Functions and Anomalous Dimensionssupporting

confidence: 55%

“…For the case of a single field φ our results (5.2) and (5.4) reduce to the results of [32] (see also [19][20][21]33]).…”

Section: Beta Functions and Anomalous Dimensionssupporting

confidence: 54%

“…The main ingredients are the background field method and the heat kernel in dimensional regularization. In φ 3 theory in six dimensions with a single scalar field and with spacetime-independent couplings, results for the two-loop effective action have been obtained in [19][20][21]; we have checked our results for some quantities against those listed in these references.…”

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confidence: 99%

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Two-loop renormalization of multiflavorϕ3theory in six dimensions and the trace anomaly

et al. 2015

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We use the background-field method and the heat kernel to obtain all counterterms to two-loop order of conformally-coupled multiflavor φ 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 quantityã is violated in this theory, and obtain a three-loop expression for the coefficient a of the Euler term in the anomaly. *

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Partition function of massless scalar field in Schwarzschild background

Sanyal

2014

Quantum Stud.: Math. Found.

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Using thermal value of zeta function instead of zero temperature, the partition function of quantized fields in arbitrary stationary backgrounds was found to be independent of undetermined regularization constant in even-dimension and the long drawn problem associated with the trace anomaly effect had been removed. Here, we explicitly calculate the expression for the coincidence limit so that the technique may be applied in some specific problems. A particular problem dealt with here is to calculate the partition function of massless scalar field in Schwarzschild background.

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Renormalizing (φ3)6theory in curved space-time

Cited by 6 publications

References 19 publications

Challenge to theaTheorem in Six Dimensions

Challenge to theaTheorem in Six Dimensions

Two-loop renormalization of multiflavorϕ3theory in six dimensions and the trace anomaly

Partition function of massless scalar field in Schwarzschild background

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