---
title: "Trace anomaly"
type: "entity"
entity_kind: "concept"
status: "hub"
canonical_name: "Trace anomaly"
aliases: ["conformal anomaly"]
first_seen: "2026-10-11T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["renormalization (quantum field theory)","semiclassical gravity","Weyl/conformal invariance","Hadamard parametrix","gravitational stress-energy tensor"]
seek_code_commit: "d40ee39"
---


The trace (or conformal) anomaly is what happens when a classically
scale-invariant quantum field is renormalized on a curved background: the
procedure needed to make sense of the field's quantum stress-energy tensor
forces in a fixed, state-independent, purely geometric term where the
classical theory's trace would have vanished exactly. The field's classical
Weyl invariance — the symmetry that made the stress-energy tensor traceless
in the first place — does not survive quantization intact; the anomaly is
the residue it leaves behind.

The vault met this concept through Antonio Ferreiro and Andrea Cavallaro's
2026 preprint (arXiv:2610.10588), where it is the single
mechanical fact doing all the philosophical work: the anomaly breaks the
dimensional ("weight-zero") condition that [[entity-erik-curiel|Curiel]]'s
classical non-existence proof depended on
([[claim-ferreiro-cavallaro-2026-qft-renormalization-yields-gravitational-stress-energy-tensor]]),
and the same underlying quantity (up to a fixed factor, the coincidence-limit
Hadamard coefficient used to renormalize the stress-energy operator) is read
as simultaneously geometric and material in
[[claim-ferreiro-cavallaro-2026-metric-gains-material-significance-egalitarian-reading]].

## References
- [[claim-ferreiro-cavallaro-2026-qft-renormalization-yields-gravitational-stress-energy-tensor]]
- [[claim-ferreiro-cavallaro-2026-metric-gains-material-significance-egalitarian-reading]]
- Capture: 10-inbox/raw/2026-10-09-outside-arxiv261010588-when-quantum-field-theory-kicks-in.md

## Log
- 2026-10-11: Page created on promotion of the arXiv:2610.10588 capture. The anomaly is the single mechanism the captured paper's central technical and philosophical claims both turn on.