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Improved Effective Potential in Curved Spacetime and Quantum Matter - Higher Derivative Gravity Theory
High Energy Physics - Theory · Submitted 17 Oct 1994
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that, in these models, QG tends to make the scalar sector less unstable.
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The abstract, sentence by sentence
\noindent{\large\bf Abstract.} We develop a general formalism to study the renormalization group (RG) improved effective potential for renormalizable gauge theories ---including matter-$R^2$-gravity--- in curved spacetime. The result is given up to quadratic terms in curvature, and one-loop effective potentials may be easiliy obtained from it. As an example, we consider scalar QED, where dimensional transmutation in curved space and the phase structure of the potential (in particular, curvature-induced phase trnasitions), are discussed. For scalar QED with higher-derivative quantum gravity (QG), we examine the influence of QG on dimensional transmutation and calculate QG corrections to the scalar-to-vector mass ratio. The phase structure of the RG-improved effective potential is also studied in this case, and the values of the induced Newton and cosmological coupling constants at the critical point are estimated. Stability of the running scalar coupling in the Yukawa theory with conformally invariant higher-derivative QG, and in the Standard Model with the same addition, is numerically analyzed. We show that, in these models, QG tends to make the scalar sector less unstable.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | \noindent{\large\bf Abstract.} We develop a general formalism to study the renormalization group (RG) improved effective potential for renormalizable gauge theories ---including matter-$R^2$-gravity--- in curved spacetime. | contribution 1.00 | 0.96 | 0.10 | asserted 1.00 |
| s1 | The result is given up to quadratic terms in curvature, and one-loop effective potentials may be easiliy obtained from it. | result 0.59 | 0.90 | 0.09 | asserted 0.50 |
| s2 | As an example, we consider scalar QED, where dimensional transmutation in curved space and the phase structure of the potential (in particular, curvature-induced phase trnasitions), are discussed. | contribution 0.92 | 0.91 | 0.06 | asserted 0.73 |
| s3 | For scalar QED with higher-derivative quantum gravity (QG), we examine the influence of QG on dimensional transmutation and calculate QG corrections to the scalar-to-vector mass ratio. | contribution 1.00 | 0.95 | 0.07 | asserted 0.92 |
| s4 | The phase structure of the RG-improved effective potential is also studied in this case, and the values of the induced Newton and cosmological coupling constants at the critical point are estimated. | result 0.69 | 0.94 | 0.08 | asserted 0.93 |
| s5 | Stability of the running scalar coupling in the Yukawa theory with conformally invariant higher-derivative QG, and in the Standard Model with the same addition, is numerically analyzed. | contribution 0.93 | 0.95 | 0.10 | asserted 0.90 |
| s6 | We show that, in these models, QG tends to make the scalar sector less unstable. | result 0.89 | 0.95 | 0.51 | asserted 0.96 |
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Original abstract
\noindent{\large\bf Abstract.} We develop a general formalism to study the renormalization group (RG) improved effective potential for renormalizable gauge theories ---including matter-$R^2$-gravity--- in curved spacetime. The result is given up to quadratic terms in curvature, and one-loop effective potentials may be easiliy obtained from it. As an example, we consider scalar QED, where dimensional transmutation in curved space and the phase structure of the potential (in particular, curvature-induced phase trnasitions), are discussed. For scalar QED with higher-derivative quantum gravity (QG), we examine the influence of QG on dimensional transmutation and calculate QG corrections to the scalar-to-vector mass ratio. The phase structure of the RG-improved effective potential is also studied in this case, and the values of the induced Newton and cosmological coupling constants at the critical point are estimated. Stability of the running scalar coupling in the Yukawa theory with conformally invariant higher-derivative QG, and in the Standard Model with the same addition, is numerically analyzed. We show that, in these models, QG tends to make the scalar sector less unstable.
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How the literature uses it
3 arXiv papers cite this in 3 sentences
Papers citing it · 1 sentence without a confident label
Cites it as background 2 papers
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The effective evolution equation and the one-loop effective potential in curved spacetime has been well known in the literature [ref] .
Electroweak Vacuum Instability and Renormalized Vacuum Field Fluctuations in Friedmann-Lemaitre-Robertson-Walker Background · Electroweak vacuum instability in curved spacetime · 0.95
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Next, let us consider the effective potential in curved spacetime [ref] .
Cosmological Constant Problem and Renormalized Vacuum Energy Density in Curved Background · Physical interpretation of the RG running of the cosmological constant and the effective scalar potential · 0.81
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