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Wish List Introduction ❖ Introduction ❖ An Organizational Principle ❖ Wilson Line Breaking ❖ More Group Theory ❖ Yet More Group Theory ❖ Wish List The Calabi-Yau The Vector Bundle A First Heterotic Standard Model Spectral Sequences A New Heterotic Standard Model Conclusion To make use of this group theory, we would like ● A Calabi-Yau threefold X with Z 3 × Z 3 fundamental group. ● ● ● The Calabi-Yau should be torus fibered. A SU(4) ⊂ E 8 instanton leaves Spin(10) unbroken, so we want a rank 4 stable holomorphic vector bundle V on X. With the “right” cohomology groups (low energy spectrum). A Heterotic Standard Model / University of North Carolina at Chapel Hill 9 / 54
Introduction The Calabi-Yau ❖ Calabi-Yau Introduction ❖ Calabi-Yau Construction ❖ Calabi-Yau Properties ❖ Group Actions on the Base I ❖ Group Actions on the Base II ❖ Invariant Cohomology ❖ Divisors on the Base ❖ Divisors on the Calabi-Yau The Calabi-Yau The Vector Bundle A First Heterotic Standard Model Spectral Sequences A New Heterotic Standard Model Conclusion A Heterotic Standard Model / University of North Carolina at Chapel Hill 10 / 54
Page 1 and 2: GoBack
Page 3 and 4: Overview Introduction The Calabi-Ya
Page 5 and 6: Introduction Introduction ❖ Intro
Page 13 and 14: An Organizational Principle Introdu
Page 15 and 16: Wilson Line Breaking Introduction
Page 17 and 18: More Group Theory Introduction ❖
Page 19 and 20: Wish List Introduction ❖ Introduc
Page 21: Wish List Introduction ❖ Introduc
Page 25 and 26: Calabi-Yau Introduction Introductio
Page 27 and 28: Calabi-Yau Construction Introductio
Page 29 and 30: Calabi-Yau Construction Introductio
Page 31 and 32: Calabi-Yau Properties Introduction
Page 33 and 34: Calabi-Yau Properties Introduction
Page 35 and 36: Group Actions on the Base I Introdu
Page 37 and 38: Group Actions on the Base II Introd
Page 39 and 40: Invariant Cohomology Introduction T
Page 41 and 42: Invariant Cohomology Introduction T
Page 43 and 44: Divisors on the Base Introduction T
Page 45 and 46: Divisors on the Calabi-Yau Introduc
Page 47 and 48: Line Bundles Introduction The Calab
Page 49 and 50: Line Bundles Introduction The Calab
Page 51 and 52: Equivariant Line Bundles I Introduc
Page 53 and 54: Equivariant Line Bundles II Introdu
Page 55 and 56: Equivariant Line Bundles II Introdu
Page 57 and 58: Notation Introduction The Calabi-Ya
Page 59 and 60: The Serre Construction Introduction
Page 61 and 62: Equivariant Vector Bundles Introduc
Page 63 and 64: Equivariant Example 0 −→ O B2 (
Page 71 and 72: Constructing Vector Bundles Introdu
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Constructing Vector Bundles Introdu
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The Gauge Bundle Introduction The C
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The Lagrangian Introduction The Cal
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The String Miracle Introduction The
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The String Miracle Introduction The
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Leray Spectral Sequence Introductio
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Leray Spectral Sequence Introductio
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Leray Degrees Introduction The Cala
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Leray Degree Table Field Cohomology
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The Superpotential The cubic terms
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More on Leray Degrees Introduction
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Introduction The Calabi-Yau The Vec
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Ideal Sheaves Introduction The Cala
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Ideal Sheaves Introduction The Cala
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Serre Construction Introduction The
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Low Energy Spectrum Introduction Th
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Low Energy Spectrum Introduction Th
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Vector Bundle Breaking Introduction
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Cohomology Introduction The Calabi-
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Doublet-Triplet Splitting Introduct
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Leray Degrees Field Cohomology Fibe
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Introduction The Calabi-Yau The Vec
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Important Lessons Introduction The
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Future Directions Introduction The
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