The $g$-function and defect changing operators from wavefunction overlap on a fuzzy sphere
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Bibliographic record
Abstract
Defects are common in physical systems with boundaries, impurities or extensive measurements. The interaction between bulk and defect can lead to rich physical phenomena. Defects in gapless phases of matter with conformal symmetry usually flow to a defect conformal field theory (dCFT). Understanding the universal properties of dCFTs is a challenging task. In this paper, we propose a computational strategy applicable to a line defect in arbitrary dimensions. Our main assumption is that the defect has a UV description in terms of a local modification of the Hamiltonian so that we can compute the overlap between low-energy eigenstates of a system with or without the defect insertion. We argue that these overlaps contain a wealth of conformal data, including the g <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>g</mml:mi> </mml:math> -function, which is an RG monotonic quantity that distinguishes different dCFTs, the scaling dimensions of defect creation operators \Delta^{+0}_\alpha <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msubsup> <mml:mi>Δ</mml:mi> <mml:mi>α</mml:mi> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and changing operators \Delta^{+-}_\alpha <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msubsup> <mml:mi>Δ</mml:mi> <mml:mi>α</mml:mi> <mml:mrow> <mml:mo>+</mml:mo> <mml:mo>−</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> that live on the intersection of different types of line defects, and various OPE coefficients. We apply this method to the fuzzy sphere regularization of 3D CFTs and study the magnetic line defect of the 3D Ising CFT. Using exact diagonalization and DMRG, we report the non-perturbative results g=0.602(2),\Delta^{+0}_0=0.108(5) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.602</mml:mn> <mml:mrow> <mml:mo stretchy="true" form="prefix">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="true" form="postfix">)</mml:mo> </mml:mrow> <mml:mo>,</mml:mo> <mml:msubsup> <mml:mi>Δ</mml:mi> <mml:mn>0</mml:mn> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>0.108</mml:mn> <mml:mrow> <mml:mo stretchy="true" form="prefix">(</mml:mo> <mml:mn>5</mml:mn> <mml:mo stretchy="true" form="postfix">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and \Delta^{+-}_0=0.84(5) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msubsup> <mml:mi>Δ</mml:mi> <mml:mn>0</mml:mn> <mml:mrow> <mml:mo>+</mml:mo> <mml:mo>−</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>0.84</mml:mn> <mml:mrow> <mml:mo stretchy="true" form="prefix">(</mml:mo> <mml:mn>5</mml:mn> <mml:mo stretchy="true" form="postfix">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> for the first time. We also obtain other OPE coefficients and scaling dimensions. Our results have significant physical implications. For example, they constrain the possible occurrence of spontaneous symmetry breaking at line defects of the 3D Ising CFT. Our method can be potentially applied to various other dCFTs, such as plane defects and Wilson lines in gauge theories.
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Full frame distilled prediction
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it