Higher derivative type II string effective actions, automorphic forms and E11

By dimensionally reducing the ten-dimensional higher derivative type IIA string theory effective action we place constraints on the automorphic forms that appear in the effective action in lower dimensions. We propose a number of properties of such automorphic forms and consider the prospects that E11 can play a role in the formulation of the higher derivative string theory effective action.Comment: 34 page

Constraints on Automorphic Forms of Higher Derivative Terms from Compactification

By dimensionally reducing the higher derivative corrections of ten-dimensional IIB theory on a torus we deduce constraints on the E_{n+1} automorphic forms that occur in d=10-n dimensions. In particular we argue that these automorphic forms involve the representation of E_{n+1} with fundamental weight \lambda^{n+1}, which is also the representation to which the string charges in d dimensions belong. We also consider a similar calculation for the reduction of higher derivative terms in eleven-dimensional M-theory.Comment: Minor corrections, to appear in JHE

Holographic non-perturbative corrections to gauge couplings

We give a direct microscopic derivation of the F-theory background that corresponds to four D7 branes of type I' theory by taking into account the D-instanton contributions to the emission of the axio-dilaton field in the directions transverse to the D7's. The couplings of the axio-dilaton to the D-instanton moduli modify its classical source terms which are shown to be proportional to the elements of the D7 brane chiral ring. Solving the bulk field equations with the non-perturbatively corrected sources yields the full F-theory background. This solution represents the gravitational dual of the four-dimensional theory living on a probe D3 brane of type I', namely of the N=2, Sp(1) SYM theory with Nf=4. Our results provide an explicit microscopic derivation of the non-perturbative gravitational dual of this theory. They also explain the recent observation that the exact coupling for this theory can be entirely reconstructed from its perturbative part plus the knowledge of the chiral ring on the D7 branes supporting its flavor degrees of freedom.Comment: Latex, 39 pages, 6 figure

Microscopic unitary description of tidal excitations in high-energy string-brane collisions

The eikonal operator was originally introduced to describe the effect of tidal excitations on higher-genus elastic string amplitudes at high energy. In this paper we provide a precise interpretation for this operator through the explicit tree-level calculation of generic inelastic transitions between closed strings as they scatter off a stack of parallel Dp-branes. We perform this analysis both in the light-cone gauge, using the Green-Schwarz vertex, and in the covariant formalism, using the Reggeon vertex operator. We also present a detailed discussion of the high energy behaviour of the covariant string amplitudes, showing how to take into account the energy factors that enhance the contribution of the longitudinally polarized massive states in a simple way.Comment: 58 page

D-brane anomaly inflow revisited

Axial and gravitational anomaly of field theories, when embedded in string theory, must be accompanied by canceling inflow. We give a self-contained overview for various world-volume theories, and clarify the role of smeared magnetic sources in I-brane/D-brane cases. The proper anomaly descent of the source, as demanded by regularity of RR field strengths H's, turns out to be an essential ingredient. We show how this allows correct inflow to be generated for all such theories, including self-dual cases, and also that the mechanism is now insensitive to the choice between the two related but inequivalent forms of D-brane Chern-Simons couplings. In particular, SO(6)_R axial anomaly of d=4 maximal SYM is canceled by the inflow onto D3-branes via the standard minimal coupling to C_4. We also propose how, for the anomaly cancelation, the four types of Orientifold planes should be coupled to the spacetime curvatures, of which conflicting claims existed previously.Comment: 41 pages, references updated; version to appear in JHE

R^4 counterterm and E7(7) symmetry in maximal supergravity

The coefficient of a potential R^4 counterterm in N=8 supergravity has been shown previously to vanish in an explicit three-loop calculation. The R^4 term respects N=8 supersymmetry; hence this result poses the question of whether another symmetry could be responsible for the cancellation of the three-loop divergence. In this article we investigate possible restrictions from the coset symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as well as a double-soft scalar limit relation derived recently by Arkani-Hamed et al. We implement these relations for the matrix elements of the R^4 term that occurs in the low-energy expansion of closed-string tree-level amplitudes. We find that the matrix elements of R^4 that we investigated all obey the double-soft scalar limit relation, including certain non-maximally-helicity-violating six-point amplitudes. However, the single-soft limit does not vanish for this latter set of amplitudes, which suggests that the E7(7) symmetry is broken by the R^4 term.Comment: 33 pages, typos corrected, published versio

Quantum theory of massless (p,0)-forms

We describe the quantum theory of massless (p,0)-forms that satisfy a suitable holomorphic generalization of the free Maxwell equations on Kaehler spaces. These equations arise by first-quantizing a spinning particle with a U(1)-extended local supersymmetry on the worldline. Dirac quantization of the spinning particle produces a physical Hilbert space made up of (p,0)-forms that satisfy holomorphic Maxwell equations coupled to the background Kaehler geometry, containing in particular a charge that measures the amount of coupling to the U(1) part of the U(d) holonomy group of the d-dimensional Kaehler space. The relevant differential operators appearing in these equations are a twisted exterior holomorphic derivative and its hermitian conjugate (twisted Dolbeault operators with charge q). The particle model is used to obtain a worldline representation of the one-loop effective action of the (p,0)-forms. This representation allows to compute the first few heat kernel coefficients contained in the local expansion of the effective action and to derive duality relations between (p,0) and (d-p-2,0)-forms that include a topological mismatch appearing at one-loop.Comment: 32 pages, 3 figure

6D Effective Action of Heterotic Compactification on K3 with nontrivial Gauge Bundles

We compute the six-dimensional effective action of the heterotic string compactified on K3 for the standard embedding and for a class of backgrounds with line bundles and appropriate Yang-Mills fluxes. We compute the couplings of the charged scalars and the bundle moduli as functions of the geometrical K3 moduli from a Kaluza-Klein analysis. We derive the D-term potential and show that in the flux backgrounds U(1) vector multiplets become massive by a Stuckelberg mechanism.Comment: 41 pages, typos corrected, references adde

On-shell Recursion in String Theory

We prove that all open string theory disc amplitudes in a flat background obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a possible reality condition on a kinematic invariant. Arguments that the same holds for tree level closed string amplitudes are given as well. Non-adjacent BCFW-shifts are related to adjacent shifts through monodromy relations for which we provide a novel CFT based derivation. All possible recursion relations are related by old-fashioned string duality. The field theory limit of the analysis for amplitudes involving gluons is explicitly shown to be smooth for both the bosonic string as well as the superstring. In addition to a proof a less rigorous but more powerful argument based on the underlying CFT is presented which suggests that the technique may extend to a much more general setting in string theory. This is illustrated by a discussion of the open string in a constant B-field background and the closed string on the level of the sphere.Comment: 36 + 9 pages text, one figure, v3: added discussion on relation to old-fashioned factorization, typos corrected, published versio