Hypothetical framework in which elementary particles are one-dimensional strings whose vibrational modes yield the particle spectrum (including massless spin-2 states interpretable as gravitons). Internally consistent only in 10 dimensions…
string-theory
Bosonic string action
Nambu–Goto action S = –T ∫ d²σ √(–det h_ab) with induced worldsheet metric h_ab = ∂_aX^μ∂_bX_μ (Polyakov form introduces auxiliary…
Superstring theory
Worldsheet supersymmetry (or spacetime SUSY via GSO projection) eliminates the tachyon and drops critical dimension from 26 to 10. Five…
M-theory
11-dimensional theory whose strong-coupling limits yield the five 10D superstring theories via compactification/dualities. Fundamental…
Compactification
Six of the 10 spatial dimensions wrapped on a compact internal manifold (Calabi–Yau threefold for N=1 SUSY preservation). Shape/size moduli…
Calabi–Yau manifold
Compact Ricci-flat Kähler manifold with trivial canonical bundle and holonomy SU(n). The 6-D three-fold case is the preferred internal…
AdS/CFT correspondence
Maldacena's conjecture: type IIB string theory on AdS₅×S⁵ is dual to N=4 SU(N) super Yang–Mills in four dimensions. First concrete…
T-duality
Compactifying a closed string on a circle of radius R is physically equivalent to compactifying on radius α'/R, exchanging momentum and…
String landscape
Discretuum of metastable vacua arising from flux compactifications of type IIB on Calabi–Yau orientifolds (KKLT). Estimated cardinality…
Calabi–Yau quintic threefold (string-theory compactification)
String-theory application of L0 Hodge theory and projective varieties. The generic smooth degree-5 hypersurface X ⊂ ℙ⁴ is the prototypical…
Mirror symmetry Hodge-diamond swap (string-theory duality)
String-theory application of L0 sheaf cohomology and moduli spaces. Mirror symmetry posits, for every Calabi–Yau n-fold X, a mirror…
Monstrous moonshine: j-function coefficients as Monster irreducible dimensions (string-theory)
String-theory application of L0 modular-form and Euler-product. The Klein j-function j(τ) is the fundamental SL(2,ℤ)-invariant modular…
K3 elliptic genus and Mathieu-M₂₄ moonshine (string-theory)
String-theory application of L0 elliptic-curve and Dirichlet-L-function. The elliptic genus of the K3 complex surface, φ_{K3}(τ, z), is a…