A Heterotic Hermitian–Yang–Mills Equivalence
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Bibliographic record
Abstract
Abstract We consider $$N=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , $$d=4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> vacua of heterotic theories in the large radius limit in which $${{\alpha }^{\backprime }\,}\ll 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mi>‵</mml:mi> </mml:msup> <mml:mspace/> </mml:mrow> <mml:mo>≪</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . We construct a real differential operator $$\mathcal {D}= D+\bar{D}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mi>D</mml:mi> <mml:mo>+</mml:mo> <mml:mover> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> on an extension bundle $$(Q, \mathcal {D})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> with underlying topology $$Q=(T^{1,0}X)^* \oplus \textrm{End} \, E \oplus T^{1,0} X$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msup> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo>⊕</mml:mo> <mml:mtext>End</mml:mtext> <mml:mspace/> <mml:mi>E</mml:mi> <mml:mo>⊕</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msup> <mml:mi>X</mml:mi> </mml:mrow> </mml:math> whose curvature is holomorphic and Hermitian–Yang–Mills with respect to the complex structure and metric on the underlying non-Kähler complex 3-fold X if and only if the heterotic supersymmetry equations and Bianchi identity are satisfied. This is suggestive of an analogue of the Donaldson–Uhlenbeck–Yau correspondence for heterotic vacua of this type.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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