Duality and higher derivative terms in M theory

By M. Green, Pierre Vanhove. 2005

214 citations recorded by the source corpus.

Dualities of M-theory are used to determine the exact dependence on the coupling constant of the D6 4 interaction of the IIA and IIB superstring effective action. Upon lifting to eleven dimensions this determines the coefficient of the D6 4 interaction in eleven-dimensional M-theory. These results are obtained by considering the four-graviton two-loop scattering amplitude in eleven-dimensional supergravity compactified on a circle and on a two-torus — extending earlier results concerning lower-derivative interactions. The torus compactification leads to an interesting SL(2,)-invariant function of the complex structure of the torus (the IIB string coupling) that satisfies a Laplace equation with a source term on the fundamental domain of moduli space. The structure of this equation is in accord with general supersymmetry considerations and immediately determines tree-level and one-loop contributions to D64 in perturbative IIB string theory that agree with explicit string calculations, and two-loop and three-loop contributions that have yet to be obtained in string theory. The complete solution of the Laplace equation contains infinite series' of single D-instanton and double D-instanton contributions, in addition to the perturbative terms. General considerations of the higher loop diagrams of eleven-dimensional supergravity suggest extensions of these results to interactions of higher order in the low energy expansion.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0c16fad9e2baef05bd993e96d06720258462a636

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$$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization (2019, background): “The τs dependence of the analytic terms f̃R4(s, t), f̃D4R4(s, t) and f̃D6R4(s, t) are captured by certain SL(2,Z) invariants that involve non-holomorphic Eisenstein series [51–54], whose expansion at small gs give a finite number of perturbative contributions and also infinite non-perturbative contr”
Automorphic properties of low energy string amplitudes in various dimensions (2010, methodology): “The expression for the scalar box function is, I (D−d−1) 4 (S, T ) = π D−d−1 2 Vd+1 ∫ ∞ Λ−2 dt t t d−D+9 2 ∫ TST 3 ∏ r=1 dωr ∑ mI∈Zd+1 e−π t g IJmImJ+π tQ4(S,T ) , (G.1) where D = 11 + 2ǫ, TST = {0 ≤ ω1 ≤ ω2 ≤ ω3 ≤ 1}, and the function Q4(S, T ) is defined by [7] Q4(S, T ) = −Sω1(ω3 − ω2)− T (ω2 − ω”