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OpenAI reports local conformal symmetry from scale symmetry in a four-dimensional QFT class

Individual problem

Under Assumption 2.1 for a four-dimensional local, unitary, positive-energy vacuum QFT—with a physical local stress tensor and dilatation current, discrete bounded-below finite-multiplicity scaling spectrum, finite scaling support of each original field, and compatible affiliated fields in a causally commuting bounded local net—the stress tensor admits a physical dimension-two scalar improvement that is symmetric, conserved, and traceless without changing translation or Lorentz charges.

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OpenAI reports local conformal symmetry from scale symmetry in a four-dimensional QFT class

  • Mathematics
  • Theoretical Physics

Under Assumption 2.1 for a four-dimensional local, unitary, positive-energy vacuum QFT—with a physical local stress tensor and dilatation current, discrete bounded-below finite-multiplicity scaling spectrum, finite scaling support of each original field, and compatible affiliated fields in a causally commuting bounded local net—the stress tensor admits a physical dimension-two scalar improvement that is symmetric, conserved, and traceless without changing translation or Lorentz charges. Its conformal currents obey unbroken local Ward identities on the physical field algebra.

AI involvementAI-led
ImportanceNotable
Technical verificationReported
Human understandingFew

Understanding the problem

Read the background

Under Assumption 2.1 for a four-dimensional local, unitary, positive-energy vacuum QFT—with a physical local stress tensor and dilatation current, discrete bounded-below finite-multiplicity scaling spectrum, finite scaling support of each original field, and compatible affiliated fields in a causally commuting bounded local net—the stress tensor admits a physical dimension-two scalar improvement that is symmetric, conserved, and traceless without changing translation or Lorentz charges. Its conformal currents obey unbroken local Ward identities on the physical field algebra.

Why it matters

If correct, resolves the local improvement and Ward-identity problem under an explicit operational set of QFT hypotheses, including membership of the improvement scalar in the original physical theory.

What counts as progress

When does scale invariance force local conformal Ward identities in a four-dimensional QFT?

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