Frederik Denef のレビュー “Les Houches Lectures on Constructing String Vacua” に沿って、それを読むための超弦理論の基本的事項を随時解説しながら、超弦理論による現実的な素粒子模型や初期宇宙模型の構成に必要となる理論的知識を習得していただく。特に、古くから知られているにも関わらず我が国にあっては理解が非常に遅れている、超対称性を部分的に保つフラックスコンパクト化とその理解に必要な代数幾何学的知識、特にトーリック幾何の取り扱いについての入門的講義を行う。（平成２９年度は授業は英語で行われました。）

1. Preliminaries
   1-1 Basics of superstring theory
   Why superstrings  in TEN dimensions?
   How can strings be a theory of particles?
   Five superstrings: TypeIIA,TypeIIB,TypeI,Heterotic E8xE8/SO(32)1-2 Basics of differential geometry
   Topological space   Tangent space   Tangent bundle   Vector bundle   Differential form   Exterior derivative   De Rham cohomology   Simplicial homology

   1-3 Local symmetry, gauge theory and vector bundles
   Transition function of a vector bundle   Ex. Dirac monopole
   Chern classes   Chern’s theorem   Characteristic classes

2. Type IIB theory and M-theory
   2-1 Type IIB theory
   Almost correct action   Scalar part:SL(2,Z)/U(1) sigma model2-2 M-theory
   11D supergravity   Black M2/M5 solutions   Near horizon limit of M5/M2    Anomalies on M5 brane   Anomaly polynomials and anomaly inflow mechanism

   2-3 Type IIB/M-theory  duality
   Dimensional reduction to D=9

   2-4 M-theory and type IIA theory
   Dimensional reduction from D=11 to 10   string/Einstein frames   M-theory as a strong coupling limit

3. Flux compactifications
   3-1 Why flux compactification?
   Why flux?   Historical remarks on flux compactifications3-2 SUSY compactifications without fluxes: Calabi-Yau compactifications
   Killing spinor equation   6d gamma matrices   Holonomy

   3-3 Complex, Kahler and Ricci-flat manifolds
   SUSY→complex manifolds Fierz transformation   Complex  manifold   Almost complex structure   Nijenhuis tensor   Newlander-Nirenberg’s theorem   Kahler manifold

   3-4 Examples of Kahler manifolds
   CP1   CPn   Fubini-Study metric   Kahler potential   Properties of Kahler manifolds

   3-5 Introduction to moduli stabilizations and flux compactifications
   Supergravity superpotential formula   Holomorphic 3-/4-forms   Gukov-Vafa-Witten superpotential

   3-6 Toric varieties
   Definition   Fans   Divisors   Stanley-Reisner ideal   SUSY nonlinear sigma model
   Intersection number of divisors   Kahler cone   Divisor volume   Swiss-Cheese Calabi-Yau