Field theories with defects and the centre functor
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Bibliographic record
Abstract
This note is intended as an introduction to the functorial formulation of quantum field theories with defects.After some remarks about models in general dimension, we restrict ourselves to two dimensions -the lowest dimension in which interesting field theories with defects exist.We study in some detail the simplest example of such a model, namely a topological field theory with defects which we describe via lattice TFT.Finally, we give an application in algebra, where the defect TFT provides us with a functorial definition of the centre of an algebra.This involves changing the target category of commutative algebras into a bicategory.Throughout this paper, we emphasise the role of higher categories -in our case bicategories -in the description of field theories with defects.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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