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Trace Anomaly in Metric-Affine gravity
General Relativity and Quantum Cosmology · Submitted 9 Sep 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We identify a new anomaly related to hypermomentum, arising from the dilation part mediated by the Weyl component of nonmetricity.
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The abstract, sentence by sentence
We explore the trace (Weyl) anomaly within a general metric-affine geometry that includes both torsion and nonmetricity. Using the Heat Kernel method and Seeley's algorithm, we compute the Minakshisundaram coefficients for arbitrary spacetimes within this framework, incorporating the effects of the nonmetricity and torsion tensors for the first time. We then determine the corrections to the trace anomaly at one loop for the matter sector in theories invariant under conformal transformation, frame rescaling transformation, and projective transformation. We identify a new anomaly related to hypermomentum, arising from the dilation part mediated by the Weyl component of nonmetricity. As particular cases, we analyze the spin $0$ and spin $1/2$ cases, considering various couplings between matter and the gravitational sector. We demonstrate that invariance under the frame rescaling transformation results in an anomaly in the relationship between the hypermomentum and the stress-energy tensor. In contrast, under the projective transformation, no anomaly is present; specifically, there is no non-zero trace of the hypermomentum tensor in any of our concrete examples.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We explore the trace (Weyl) anomaly within a general metric-affine geometry that includes both torsion and nonmetricity. | contribution 0.85 | 0.80 | 0.05 | asserted 0.77 |
| s1 | Using the Heat Kernel method and Seeley's algorithm, we compute the Minakshisundaram coefficients for arbitrary spacetimes within this framework, incorporating the effects of the nonmetricity and torsion tensors for the first time. | method 0.93 | 0.96 | 0.06 | asserted 1.00 |
| s2 | We then determine the corrections to the trace anomaly at one loop for the matter sector in theories invariant under conformal transformation, frame rescaling transformation, and projective transformation. | contribution 0.69 | 0.96 | 0.14 | asserted 1.00 |
| s3 | We identify a new anomaly related to hypermomentum, arising from the dilation part mediated by the Weyl component of nonmetricity. | result 0.98 | 0.96 | 0.39 | asserted 1.00 |
| s4 | As particular cases, we analyze the spin $0$ and spin $1/2$ cases, considering various couplings between matter and the gravitational sector. | contribution 0.89 | 0.94 | 0.04 | asserted 0.88 |
| s5 | We demonstrate that invariance under the frame rescaling transformation results in an anomaly in the relationship between the hypermomentum and the stress-energy tensor. | result 0.98 | 0.94 | 0.21 | asserted 1.00 |
| s6 | In contrast, under the projective transformation, no anomaly is present; specifically, there is no non-zero trace of the hypermomentum tensor in any of our concrete examples. | result 1.00 | 0.94 | 0.16 | asserted 1.00 |
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The paper
Original abstract
We explore the trace (Weyl) anomaly within a general metric-affine geometry that includes both torsion and nonmetricity. Using the Heat Kernel method and Seeley's algorithm, we compute the Minakshisundaram coefficients for arbitrary spacetimes within this framework, incorporating the effects of the nonmetricity and torsion tensors for the first time. We then determine the corrections to the trace anomaly at one loop for the matter sector in theories invariant under conformal transformation, frame rescaling transformation, and projective transformation. We identify a new anomaly related to hypermomentum, arising from the dilation part mediated by the Weyl component of nonmetricity. As particular cases, we analyze the spin $0$ and spin $1/2$ cases, considering various couplings between matter and the gravitational sector. We demonstrate that invariance under the frame rescaling transformation results in an anomaly in the relationship between the hypermomentum and the stress-energy tensor. In contrast, under the projective transformation, no anomaly is present; specifically, there is no non-zero trace of the hypermomentum tensor in any of our concrete examples.
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References
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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We remind here that in addition to torsion and curvature tensors, generalized differential geometries, known as metric-affine geometries [ref] , are also characterized by the non-metricity tensor, which has been recently employed in an extensive way in quantum field theory in curved spacetime [ref] , gravity [ref] and cosmology [ref] .
Weyl Geometry in Weyl Semimetals · Introduction · 0.98
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It would also be worthwhile to explore whether the affine-lift approach can shed new light on quantum aspects of conserved currents, including trace and gravitational anomalies as in [ref] , and on the role of hypermomentum in generalized gravitational theories.
Belinfante-Rosenfeld Symmetrization from Metric-Affine Conservation Laws: Hypermomentum as the Improvement Term -- The Cases of QED and QCD · conclusions · 0.82
What it cites · 53 sentences without a confident label
Cites as background 12 papers
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We should note that the group where the gauge approach of MAG is constructed is the so-called General Linear group $GL(4,R)$ that is an infinite dimensional gauge group [ref] .
Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance · The asymptotic expansion for the symbol of resolvent · 0.80
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For example, the form of the anomaly in the Riemann-Cartan case has been discussed by several authors [ref] , while in the more general case of MAG, particularly regarding the effects of nonmetricity, it has not yet been thoroughly explored, to the best of our knowledge.
Conformal symmetry, anomaly and effective action for metric-scalar gravity with torsion · Introduction · 0.82
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For example, the form of the anomaly in the Riemann-Cartan case has been discussed by several authors [ref] , while in the more general case of MAG, particularly regarding the effects of nonmetricity, it has not yet been thoroughly explored, to the best of our knowledge.
Weyl cohomology and the conformal anomaly in the presence of torsion · Introduction · 0.82
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