This paper explores the consistency of particle physics in metric-affine gravity through the lens of extended projective (EP) symmetry. The authors argue that while the Einstein-Hilbert action in metric-affine gravity exhibits projective invariance, this symmetry alone is insufficient to prevent inconsistencies in models, such as those involving ghosts or strong coupling. They propose that non-minimal kinetic terms of Dirac spinors suggest a new extended projective symmetry generated by a pair of vectors. The most general EP-invariant theory, at most quadratic in field strengths, is shown to be free from pathologies, featuring only the massless graviton and a single additional scalar field from the square of the Holst curvature. This scalar potential is suitable for inflation, and the model includes effective 4-Fermi interactions that can produce fermionic dark matter. An alternative double-vector symmetry is also considered, leading to a healthy theory with a propagating vector field.
The paper discusses the role of symmetries in fundamental forces, emphasizing that symmetries constrain possible theories and are essential for consistency. It highlights the importance of symmetries in the Standard Model and General Relativity, noting that diffeomorphism invariance in GR does not uniquely determine the geometry of spacetime. The paper then delves into metric-affine gravity, where the field content includes a metric and an independent affine connection, allowing for torsion and non-metricity. The authors show that allowing for these additional degrees of freedom leads to a more general formulation of gravity, but also introduces potential inconsistencies.
The paper argues that EP symmetry, generated by a pair of vectors, can bring metric-affine gravity into harmony with particle physics. It demonstrates that the most general EP-invariant theory is free from pathologies and features a unique scalar field and a massless graviton. The paper also discusses the implications of this symmetry for inflation and dark matter, showing that the model can produce fermionic dark matter through effective 4-Fermi interactions. The authors conclude that EP invariance is as relevant to metric-affine gravity as diffeomorphism invariance is to the metric formulation, and that EP-invariant gravity is a natural conclusion of metric-affine gravity.This paper explores the consistency of particle physics in metric-affine gravity through the lens of extended projective (EP) symmetry. The authors argue that while the Einstein-Hilbert action in metric-affine gravity exhibits projective invariance, this symmetry alone is insufficient to prevent inconsistencies in models, such as those involving ghosts or strong coupling. They propose that non-minimal kinetic terms of Dirac spinors suggest a new extended projective symmetry generated by a pair of vectors. The most general EP-invariant theory, at most quadratic in field strengths, is shown to be free from pathologies, featuring only the massless graviton and a single additional scalar field from the square of the Holst curvature. This scalar potential is suitable for inflation, and the model includes effective 4-Fermi interactions that can produce fermionic dark matter. An alternative double-vector symmetry is also considered, leading to a healthy theory with a propagating vector field.
The paper discusses the role of symmetries in fundamental forces, emphasizing that symmetries constrain possible theories and are essential for consistency. It highlights the importance of symmetries in the Standard Model and General Relativity, noting that diffeomorphism invariance in GR does not uniquely determine the geometry of spacetime. The paper then delves into metric-affine gravity, where the field content includes a metric and an independent affine connection, allowing for torsion and non-metricity. The authors show that allowing for these additional degrees of freedom leads to a more general formulation of gravity, but also introduces potential inconsistencies.
The paper argues that EP symmetry, generated by a pair of vectors, can bring metric-affine gravity into harmony with particle physics. It demonstrates that the most general EP-invariant theory is free from pathologies and features a unique scalar field and a massless graviton. The paper also discusses the implications of this symmetry for inflation and dark matter, showing that the model can produce fermionic dark matter through effective 4-Fermi interactions. The authors conclude that EP invariance is as relevant to metric-affine gravity as diffeomorphism invariance is to the metric formulation, and that EP-invariant gravity is a natural conclusion of metric-affine gravity.