R2 corrections and non-perturbative dualities of N = 4 string ground states

Abstract

We compute and analyse a variety of four-derivative gravitational terms in the effective action of six-and four-dimensional type II string ground states with N = 4 supersymmetry. In six dimensions, we compute the relevant perturbative corrections for the type II string compactified on K3. In four dimensions we do analogous computations for several models with (4, 0) and (2, 2) supersymmetry. Such ground states are related by heterotic-type II duality or type II-type II U-duality. Perturbative computations in one member of a dual pair give a non-perturbative result in the other member. In particular, the exact CP-even R 2 coupling on the (2, 2) side reproduces the tree-level term plus NS 5-brane instanton contributions on the (4, 0) side. On the other hand, the exact CP-odd coupling yields the one-loop axionic interaction aR ∧ R together with a similar instanton sum. In a subset of models, the expected breaking of the SL(2, Z) S S-duality symmetry to a Γ(2) S subgroup is observed on the non-perturbative thresholds. Moreover, we present a duality chain that provides evidence for the existence of heterotic N = 4 models in which N = 8 supersymmetry appears at strong coupling.

Calculable effects

“…and disappears in D = 6. This is similar to the vanishing of the one-loop R 2 corrections in type IIB theory on K3 [13]. We conclude that there are no (∂∂ϕ 6 ) 2 interactions in D = 6…”

“…We examine the limit that corresponds to the weak coupling regime of the dual type II theory compactified on K3 × T 2 . The result reproduces the perturbative type II expression [8,13] which an exact result has been conjectured in Ref. [5].…”

N=(4,2) chiral supergravity in six dimensions and solvable Lie algebras

“…If in the decompactification limits the N = 6 supersymmetry is extented to N = 8 due to the presence of extra massless states, then B 6 = 0 must be found in both limits. In order to derive B 2n in string theory it is convenient to define the helicity generating partition function [21], [15], [16], [25], [24]:…”

“…The v,v modifications due to the 2d fermionic degrees of freedom give rise to non-zero characteristics to the fermionic θ[ [21], [15], [16], [25], [24]. The analytic expression of ξ(v) is: …”

“…Therefore, the only non-trivial helicity supertrace is 25) receiving non-vanishing contribution from the N = 6 sector with (h, g) = (0, 0). Furthermore, using the identities 4iQ θ[…”