Two-loop superstrings and S-duality

Abstract

The two-loop contribution to the Type IIB low energy effective action term $D^4 R^4$, predicted by SL(2,Z) duality, is compared with that of the two-loop 4-point function derived recently in superstring perturbation theory through the method of projection onto super period matrices. For this, the precise overall normalization of the 4-point function is determined through factorization. The resulting contributions to $D^4 R^4$ match exactly, thus providing an indirect check of SL(2,Z) duality. The two-loop Heterotic low energy term $D^2F^4$ is evaluated in string perturbation theory; its form is closely related to the $D^4 R^4$ term in Type II, although its significance to duality is an open issue.Comment: 44 pages, LaTeX, epsfig, 1 figur

D6ℛ4 amplitudes in various dimensions

“…arise in dimensions where ultraviolet divergences in supergravity set in [20]. Moreover, the asymptotic expansion of the Eisenstein series at weak coupling regime reproduces the known perturbative corrections [21][22][23], along with an infinite series of non-perturbative contributions coming from Euclidean D-branes wrapping cycles of the internal manifold, preserving the expected number of supersymmetries [17,19]. In the limit where the radius of one circle in T d becomes infinite, E…”

“…At weak coupling, this produces the expected tree-level, one-loop (vanishing) and two-loop corrections [21,22], along with an infinite series of D-instanton corrections,…”

“…In defining these divergent integrals we use the renormalization prescription of [42,43], and normalize the integration measure dµ h as in [34]. At two-loop, the corrections to R 4 couplings vanish, but the corrections to D 4 R 4 and D 6 R 4 are given by modular integrals over the fundamental domain F 2 of the Siegel upper-half plane of degree 2, which parametrizes genus 2 Riemann surfaces, [22,33],…”

Recursion relations from space-time supersymmetry

“…Most of the analysis involves the first few terms in the α ′ expansion of the effective action; for a selection of papers, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Of particular interest to us are interactions in ten-dimensional type IIB Here E s (τ,τ ) is the non-holomorphic Eisenstein series given in Appendix B.…”

Factorization of the two loop four-particle amplitude in superstring theory revisited

“…Note added: Recently the 2-loop 4-particle amplitude in superstring theory was also obtained in [28,29] and its factorization was studied by D'Hoker, Gutperle and Phong in [30].…”