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Wilson Line Breaking 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 Spin(10) ⊃ SU(3)×SU(2)×U(1)×U(1)×Z 3 × Z 3 16 = χ 2 1χ 2 ( 3, 2, 1, 1 ) ⊕ χ 2 1 ( 1, 1, 6, 3 ) ⊕ ⊕ χ 2 1 χ2 2( 3, 1, −4, −1 ) ⊕ χ 2 2 ( 3, 1, 2, −1 ) ⊕ ⊕ ( 1, 2, −3, −3 ) ⊕ χ 1 ( 1, 1, 0, 3 ) ( ) ( ) 10 = χ 1 1, 2, 3, 0 ⊕ χ1 χ 2 3, 1, −2, −2 ⊕ ) ( ) ⊕ χ1( 2 1, 2, −3, 0 ⊕ χ 2 1 χ 2 2 3, 1, 2, 2 Right-handed Neutrino A Heterotic Standard Model / University of North Carolina at Chapel Hill 6 / 54
More Group Theory 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 G = Z 3 × Z 3 = G 1 × G 2 Fix generators g 1 and g 2 . Characters (=1-d representations): Denote generators by χ 1 and χ 2 , where (ω = e 2πi 3 ) χ 1 (g 1 ) = ω χ 1 (g 2 ) = 1 χ 2 (g 1 ) = 1 χ 2 (g 2 ) = ω . All other characters are products of χ 1 and χ 2 . A Heterotic Standard Model / University of North Carolina at Chapel Hill 7 / 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: Wilson Line Breaking Introduction
Page 19 and 20: Wish List Introduction ❖ Introduc
Page 21 and 22: Wish List Introduction ❖ Introduc
Page 23 and 24: Introduction The Calabi-Yau ❖ Cal
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 65 and 66: Equivariant Example 0 −→ O B2 (
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Equivariant Example 0 −→ O B2 (
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Equivariant Example 0 −→ O B2 (
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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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