Interconnections between type II superstrings, M theory and N=4 Yang-Mills

Abstract

These lecture notes 1 begin with a review of the first nonleading contributions to the derivative expansion of the M theory effective action compactified on a two-torus. The form of these higher-derivative interactions is shown to follow from ten-dimensional type IIB supersymmetry as well as from one-loop quantum corrections to classical eleven-dimensional supergravity. The detailed information concerning D-instanton effects encoded in these terms is related to the problem of evaluating the Witten index for N D-particles in the type IIA theory. Using the AdS/CFT conjecture, it also leads to very specific predictions of multi-instanton contributions in N = 4 supersymmetric SU (N ) Yang-Mills theory in the limit of strong 't Hooft coupling.

Recursion relations from space-time supersymmetry

“…For a review, see [19]. Let us recall the U(1) charge assignment to the various fields and parameters of type IIB supergravity given by [20,21], Supersymmetry naturally constrains the coupling containing the most fermions which determines f (12,−12) as shown in [8] extending the arguments of [22][23][24].…”

Non-perturbative contributions to the plane-wave string mass matrix

“…The factor g 7/2 s can be extracted from the form of certain higher derivative interactions that enter into the type IIB effective action at O(1/α ′ ) [14] 1 . Although (1.3) is exponentially small, it is the leading contribution with the phase factor e 2πiC (0) .…”

Local renormalization group functions from quantum renormalization group and holographic bulk locality

“…In passing, we also note that in type IIB superstring theory, the higher derivative corrections start at O(R 4 ) and the difference between N 2 and N 2 − 1 in relation to U(N ) versus SU(N ) is even higher order (see e.g. [30]). …”