Muti-instanton Amplitudes in Type IIB String Theory

Abstract

We compute the normalization of the multiple D-instanton amplitudes in type IIB string theory and show that the result agrees with the prediction of S-duality due to Green and Gutperle.

D-instanton Effects in Type IIB String Theory

“…The open+closed string field theory approach developed in [16][17][18][19][20][21] is free of the afore mentioned regularization ambiguity. In Section 6, we will analyze various pieces of the string field theoretic computation of (1.11) and argue that the SFT result can at most differ from the naive on-shell computation by the constant term C 1 .…”

“…In this case, the integrand appearing on the RHS (1.2) is singular along the loci where D-instantons collide, and the naive on-shell open string perturbation theory breaks down. This is already apparent in the low energy limit, where for suitable observables, the open string field theory reduces to the IKKT matrix model [21,29,30], which does not admit a perturbative expansion [31][32][33].…”

“…On the other hand, it is known to fail when there are singularities in the D-instanton moduli space, which occurs in M (n,0) for n ≥ 2. Such singularities are due to the appearance of new "massless" open string modes, and may be resolved in the open+closed string field theory approach [21].…”

“…The worldsheet formalism is also known to capture certain non-perturbative effects, known as D-instantons, by including worldsheets with boundaries subject to suitable Dirichlet-type boundary conditions [4]. While D-instanton effects are fundamental to the dynamics of string theory [5,6], and have been determined in some cases by a combination of on-shell worldsheet methods and string dualities [7][8][9][10][11][12][13][14][15], a systematic framework for computing them has been lacking until recent work of Sen [16][17][18][19][20][21] based on open+closed string field theory [22].…”

Snowmass White Paper: Bootstrapping String Theory

“…In string theory, the worldsheet formalism produces, in principle, the complete perturbative expansion of closed string amplitudes [1][2][3][4][5][6][7][8][9][10][11], in particular of the gravitons and their superpartners, and it also captures certain non-perturbative corrections [12]. In practice, however, explicit results of string amplitudes are only available up to two-loop order in perturbation theory [13][14][15][16][17][18][19][20], with the exception of certain supersymmetry-protected terms, 2 along with pieces of D-instanton corrections up to next-to-leading order [26][27][28][29][30][31][32][33][34][35]. Moreover, the effective gravitational coupling is expected to become strong at the Planck scale, obscuring the interpolation from perturbation theory at low energies to effective descriptions of very high-energy excitations as spacetime geometry with horizons.…”