The low energy expansion of the one-loop type II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.Comment: harvmac (b), 25 pages, 3 eps figures. v2: Factors of 2 corrected. Conclusion unchange

A String Motivated Approach to the Relativistic Point Particle

Using concepts developed in string theory, Cohen, Moore, Nelson and Polchinski calculated the propagator for a relativistic point particle. Following these authors we extend the technique to include the case of closed world lines. The partition function found corresponds to the Feynmann and Schwinger proper time formalism. We also explicitly verify that the partition function is equivalent to the usual path length action partition function. As an example of a sum over closed world lines, we compute the Euler-Heisenberg effective Lagrangian in a novel way.Comment: Talk at Balfest, Salerno 200

A Curious Truncation of N=4 Yang-Mills

The coupling constant dependence of correlation functions of BPS operators in N=4 Yang-Mills can be expressed in terms of integrated correlation functions. We approximate these integrated correlators by using a truncated OPE expansion. This leads to differential equations for the coupling dependence. When applied to a particular sixteen point correlator, the coupling dependence we find agrees with the corresponding amplitude computed via the AdS/CFT correspondence. We conjecture that this truncation becomes exact in the large N and large 't Hooft coupling limit.Comment: 10 pages, LaTeX; additional comments, added reference

Decays of near BPS heterotic strings

The decay of highly excited massive string states in compactified heterotic string theories is discussed. We calculate the decay rate and spectrum of states carrying momentum and winding in the compactified direction. The longest lived states in the spectrum are near BPS states whose decay is dominated by a single decay channel of massless radiation which brings the state closer to being BPS.Comment: 28 pages, harvmac, 3 figure

Supersymmetry Constraints on Type IIB Supergravity

Supersymmetry is used to derive conditions on higher derivative terms in the effective action of type IIB supergravity. Using these conditions, we are able to prove earlier conjectures that certain modular invariant interactions of order alpha' **3 relative to the Einstein-Hilbert term are proportional to eigenfunctions of the Laplace operator on the fundamental domain of SL(2,Z). We also discuss how these arguments generalize to terms of higher order in alpha', as well as to compactifications of supergravity.Comment: 31 pages, harvmac (b); minor correction

D-instanton partition functions

Duality arguments are used to determine D-instanton contributions to certain effective interaction terms of type II supergravity theories in various dimensions. This leads to exact expressions for the partition functions of the finite N D-instanton matrix model in d=4 and 6 dimensions that generalize our previous expression for the case d=10. These results are consistent with the fact that the Witten index of the T-dual D-particle process should only be non-vanishing for d=10.Comment: 20 pages, harvmac, typos corrected, reference adde

Automorphic properties of low energy string amplitudes in various dimensions

This paper explores the moduli-dependent coefficients of higher derivative interactions that appear in the low-energy expansion of the four-graviton amplitude of maximally supersymmetric string theory compactified on a d-torus. These automorphic functions are determined for terms up to order D^6R^4 and various values of d by imposing a variety of consistency conditions. They satisfy Laplace eigenvalue equations with or without source terms, whose solutions are given in terms of Eisenstein series, or more general automorphic functions, for certain parabolic subgroups of the relevant U-duality groups. The ultraviolet divergences of the corresponding supergravity field theory limits are encoded in various logarithms, although the string theory expressions are finite. This analysis includes intriguing representations of SL(d) and SO(d,d) Eisenstein series in terms of toroidally compactified one and two-loop string and supergravity amplitudes.Comment: 80 pages. 1 figure. v2:Typos corrected, footnotes amended and small clarifications. v3: minor corrections. Version to appear in Phys Rev

D-brane interactions in type IIB plane-wave background

The cylinder diagrams that determine the static interactions between pairs of Dp-branes in the type IIB plane wave background are evaluated. The resulting expressions are elegant generalizations of the flat-space formulae that depend on the value of the Ramond-Ramond flux of the background in a non-trivial manner. The closed-string and open-string descriptions consistently transform into each other under a modular transformation only when each of the interacting D-branes separately preserves half the supersymmetries. These results are derived for configurations of euclidean signature D(p+1)-instantons but also generalize to lorentzian signature Dp-branes.Comment: 24 pages, Normalisation of boundary states correcte

I-Brane Inflow and Anomalous Couplings on D-Branes

We show that the anomalous couplings of $D$-brane gauge and gravitational fields to Ramond-Ramond tensor potentials can be deduced by a simple anomaly inflow argument applied to intersecting $D$-branes and use this to determine the eight-form gravitational coupling.Comment: 8 pages, harvmac, no figure

Duality and higher derivative terms in M theory

Dualities of M-theory are used to determine the exact dependence on the coupling constant of the D^6R^4 interaction of the IIA and IIB superstring effective action. Upon lifting to eleven dimensions this determines the coefficient of the D^6R^4 interaction in eleven-dimensional M-theory. These results are obtained by considering the four-graviton two-loop scattering amplitude in eleven-dimensional supergravity compactified on a circle and on a two-torus -- extending earlier results concerning lower-derivative interactions. The torus compactification leads to an interesting SL(2,Z)-invariant function of the complex structure of the torus (the IIB string coupling) that satisfies a Laplace equation with a source term on the fundamental domain of moduli space. The structure of this equation is in accord with general supersymmetry considerations and immediately determines tree-level and one-loop contributions to D^6R^4 in perturbative IIB string theory that agree with explicit string calculations, and two-loop and three-loop contributions that have yet to be obtained in string theory. The complete solution of the Laplace equation contains infinite series' of single D-instanton and double D-instanton contributions, in addition to the perturbative terms. General considerations of the higher loop diagrams of eleven-dimensional supergravity suggest extensions of these results to interactions of higher order in the low energy expansion.Comment: harvmac. 41 pages. 3 figures. v2 typos corrected and reference list updated. v3. Significant new subsection deriving the non-zero coefficient of the IIB string theory three-loop contributio