PostulateStatement: Literature-sourcedProof: Not applicablePipeline-generatedprecheck passjudge pass (gpt-6-luna)‡ sources checked 2026-11-04

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Type Iia Two Derivative Supergravity Action

Physical scope

Adopted source-free, massless, leading tree-level, two-derivative type IIA bosonic effective action in string frame on a smooth oriented ten-dimensional Lorentzian manifold. Fermions, localized sources, Romans mass, loop and alpha-prime corrections are omitted. This is a model premise, not a derivation from string theory or a claim that every string background solves its Euler–Lagrange equations.

Postulate

Adopt $S_{I I A} = S_{N S} - \frac{1}{4 κ_{0}^{2}} \int_{M^{10}} d^{10} x \sqrt{- g_{s}} (∣ G_{2} ∣_{s}^{2} + ∣ {\tilde{G}}_{4} ∣_{s}^{2}) - \frac{1}{4 κ_{0}^{2}} \int_{M^{10}} B_{2} \land G_{4} \land G_{4},$ where $S_{N S} = (2 κ_{0}^{2})^{- 1} \int \sqrt{- g_{s}} e^{- 2 Φ} (R_{s} + 4 ∣ d Φ ∣_{s}^{2} - \frac{1}{2} ∣ H_{3} ∣_{s}^{2}) d^{10} x$ is the adopted local NS–NS action. The fields are a string-frame Lorentzian metric $g_{s}$ , real scalar dilaton $Φ$ , local potentials $B_{2}, C_{1}, C_{3}$ , and $H_{3} = d B_{2}, G_{2} = d C_{1}, G_{4} = d C_{3}, {\tilde{G}}_{4} = G_{4} - C_{1} \land H_{3} .$ For this item write $g_{s} : = G^{(s)}$ for the string-frame metric; it is distinct from the dimensionless string coupling $g_{s t r}$ . The coefficient convention is $2 κ_{0}^{2} = (2 π)^{7} α^{' 4}$ , the signature is $(- + \dots +)$ , and $∣ F_{p} ∣^{2} = F_{M_{1} \dots M_{p}} F^{M_{1} \dots M_{p}} / p!$ , as fixed by the adopted supergravity conventions. Use natural units $ℏ = c = 1$ , length-valued target coordinates, dimensionless metric and dilaton components, and dimensionless coordinate components of $B_{2}, C_{1}, C_{3}$ ; then $H_{3}, G_{2}, G_{4}, {\tilde{G}}_{4}$ have component dimension length $^{- 1}$ , $κ_{0}^{2}$ has dimension length $^{8}$ , and every displayed action term is dimensionless. The mass parameter is $F_{0} = 0$ . This postulate applies locally where the potentials are defined and $d H_{3} = 0$ ; there are no magnetic or localized sources. It includes neither a fermion action nor a supersymmetry transformation law.

Postulate references

M. J. D. Hamilton, §6.1, Definition 6.1

Joseph Polchinski, §12.1

Ten Dimensional NS NS Supergravity Action

Supergravity Conventions And Normalizations

Remarks

The current convention definition and NS–NS postulate carriers and their current ready Step 1 records were inspected; their exact interfaces match this action. This postulate remains a source-reported low-energy model input, not a derivation from string theory.

Type Iia Two Derivative Supergravity Action

Postulate

Postulate references

Remarks

Depends on

Dependency tree · 2 levels

Sources