U-duality and D-brane Combinatorics

We investigate D-brane instanton contributions to R^4 couplings in any toroidal compactification of type II theories. Starting from the 11D supergravity one-loop four-graviton amplitude computed by Green, Gutperle and Vanhove, we derive the non-perturbative O(e^{-1/\lambda}) corrections to R^4 couplings by a sequence of T-dualities, and interpret them as precise configurations of bound states of D-branes wrapping cycles of the compactification torus. Dp-branes explicitely appear as fluxes on D(p+2)-branes, and as gauge instantons on D(p+4)-branes. Specific rules for weighting these contributions are obtained, which should carry over to more general situations. Furthermore, it is shown that U-duality in D<=6 relates these D-brane configurations to O(e^{-1/\lambda^2}) instantons for which a geometric interpretation is still lacking.Comment: 17 pages, LaTeX2e, intro. shortened and minor typos corrected, final versio

4D gravity on a brane from bulk higher-curvature terms

We study a gravity model where a tensionful codimension-one three-brane is embedded on a bulk with infinite transverse length. We find that 4D gravity is induced on the brane already at the classical level if we include higher-curvature (Gauss-Bonnet) terms in the bulk. Consistency conditions appear to require a negative brane tension as well as a negative coupling for the higher-curvature terms.Comment: 10 pages, no figures; a minor change in wording (to appear in MPLA

Heterotic/Type II Triality and Instantons on K3K_3

A detailed understanding of instanton effects for half-BPS couplings is pursued in theories with 16 supersymmetries. In particular, we investigate the duality between heterotic string on $T^4$ and type IIA on $K_3$ at the $T^4/Z_2$ orbifold point, as well as their higher and lower dimensional versions. We present a remarkably clean quantitative test of the duality at the level of $F^4$ couplings, by completely matching a purely one-loop heterotic amplitude to a purely tree-level type II result. The triality of SO(4,4) and several other miracles are shown to be crucial for the duality to hold. Exact non-perturbative new results for type I', F on $K_3$, M on $K_3$, and IIB on $K_3$ are found, and the general form of D-instanton contributions in type IIA or B on $T^4/Z_2$ is obtained. We also analyze the NS5-brane contributions in type II on $K_3\times T^2$, and predict the value $\mu (N)=\sum_{d|N} (1/d^3)$ for the bulk contribution to the index of the NS5-brane world-volume theory on $K_3 \times T^2$.Comment: 52 pages, uses JHEP.cls; v2: minor corrections and 2 refs added. Final version for JHE

The Lie h-Invariant Conformal Field Theories and the Lie h-Invariant Graphs

We use the Virasoro master equation to study the space of Lie h-invariant conformal field theories, which includes the standard rational conformal field theories as a small subspace. In a detailed example, we apply the general theory to characterize and study the Lie h-invariant graphs, which classify the Lie h-invariant conformal field theories of the diagonal ansatz on SO(n). The Lie characterization of these graphs is another aspect of the recently observed Lie group-theoretic structure of graph theory.Comment: 38p

Higher order corrections to the Newtonian potential in the Randall-Sundrum model

The general formalism for calculating the Newtonian potential in fine-tuned or critical Randall-Sundrum braneworlds is outlined. It is based on using the full tensor structure of the graviton propagator. This approach avoids the brane-bending effect arising from calculating the potential for a point source. For a single brane, this gives a clear understanding of the disputed overall factor 4/3 entering the correction. The result can be written on a compact form which is evaluated to high accuracy for both short and large distances.Comment: 12 pages, LaTeX2e with RevTeX4, 3 postscript figures; Minor corrections, references update

Eisenstein Series in String Theory

We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. The Eisenstein series are constructed using G(Z)-invariant mass formulae and are manifestly invariant modular functions on the symmetric space K\G(R) of non-compact type, with K the maximal compact subgroup of G(R). In particular, we show how Eisenstein series of the T-duality group SO(d,d,Z) can be used to represent one- and g-loop amplitudes in compactified string theory. We also obtain their non-perturbative extensions in terms of the Eisenstein series of the U-duality group E_{d+1(d+1)}(Z).Comment: 11 pages, Latex, submitted to Proceedings of Strings '99, published versio

R^2 Corrections and Non-perturbative Dualities of N=4 String ground states

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 a.R\wedge 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 \Gamma(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.Comment: Latex2e, 51 pages, 1 figur

Correlators of N=1 Superconformal Currents

We give an explicit expression for the M-point correlator of the superconformal current in two dimensional N=1 superconformal field theories.Comment: 8 pages. Some typos fixed. Unfortunately, these typos exist in the published version in J Phys

Unoriented D-brane Instantons vs Heterotic worldsheet Instantons

We discuss Fermi interactions of four hyperini generated by ``stringy'' instantons in a Type I / Heterotic dual pair on T^4/Z_2.Comment: Minor corrections and clarifications. Added reference

Closed Bosonic String Partition Function in Time Independent Exact PP-Wave Background

The modular invariance of the one-loop partition function of the closed bosonic string in four dimensions in the presence of certain homogeneous exact pp-wave backgrounds is studied. In the absence of an axion field the partition function is found to be modular invariant. In the presence of an axion field modular invariace is broken. This can be attributed to the light-cone gauge which breaks the symmetry in the $\sigma$-, $t$-directions. Recovery of this broken modular invariance suggests the introduction of twists in the world-sheet directions. However, one needs to go beyond the light-cone gauge to introduce such twists.Comment: 17 pages, added reference