Ten-dimensional Superspace Research Articles

Multiloop superstring amplitudes from non-minimal pure spinor formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of $\theta$'s.

Super-Poincaré covariant two-loop superstring amplitudes

The super-Poincare covariant formalism for the superstring is used to compute massless four-point two-loop amplitudes in ten-dimensional superspace. The computations are much simpler than in the RNS formalism and include both external bosons and fermions.

Massive IIA supergravities

We perform a systematic search for all possible massive deformations of IIA supergravity in ten dimensions. We show that there exist exactly two possibilities: Romans supergravity and Howe-Lambert-West supergravity. Along the way we give the full details of the ten-dimensional superspace formulation of the latter. The scalar superfield at canonical mass dimension zero (whose lowest component is the dilaton), present in both Romans and massless IIA supergravities, is not introduced from the outset but its existence follows from a certain integrability condition implied by the Bianchi identities. This fact leads to the possibility for a certain topological modification of massless IIA, reflecting an analogous situation in eleven dimensions.

Non-commutative superspace from string theory

Turning on background fields in string theory sometimes has an alternative interpretation as a deformation of the target space geometry. A particularly well-known case is the NS–NS two form B, which gives rise to spacetime non-commutativity. In this Letter we point out that this phenomenon extends to ten-dimensional superspace when employing a covariant quantization of the superstring, generalizing an observation by Ooguri and Vafa in four dimensions. In particular, we will find that RR field strengths give rise to a non-zero {θ,θ} anti-commutator, just as in four dimensions, whereas the gravitino yields a non-zero value for [x,θ].

Self-dual N=(1,0) supergravity in eight dimensions with reduced holonomy Spin(7)

We construct chiral N=(1,0) self-dual supergravity in Euclidean eight dimensions with reduced holonomy Spin(7), including all the higher-order interactions in a closed form. We first establish the non-chiral N=(1,1) superspace supergravity in eight dimensions with SO(8) holonomy without self-duality, as the foundation of the formulation. In order to make the whole computation simple, and the generalized self-duality compatible with supersymmetry, we adopt a particular set of superspace constraints similar to the one originally developed in ten-dimensional superspace. The intrinsic properties of octonionic structure constants make local supersymmetry, generalized self-duality condition, and reduced holonomy Spin(7) all consistent with each other.

Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring

It has recently been shown that the ten-dimensional superstring can be quantized using the BRST operator Q=∮ λ α d α , where λ α is a pure spinor satisfying λγ m λ=0 and d α is the fermionic supersymmetric derivative. In this paper, the pure spinor version of superstring theory is formulated in a curved supergravity background and it is shown that nilpotency and holomorphicity of the pure spinor BRST operator imply the on-shell superspace constraints of the supergravity background. This is shown to lowest order in α′ for the heterotic and Type II superstrings, thus providing a compact pure spinor version of the ten-dimensional superspace constraints for N=1 Type IIA and Type IIB supergravities. Since quantization is straightforward using the pure spinor version of the superstring, it is expected that these methods can also be used to compute higher-order α′ corrections to the ten-dimensional superspace constraints.

Fierz identities in ten-dimensional superspace

All SO(1,9)-irreducible bases composed of tensors and tensor–spinors, which span the whole space up to 16th-order polynomials in θ, θj ( j=1–16) being Majorana–Weyl spinors of SO(1,9), are explicitly constructed. Any superfield φ(xm,θ) in ten-dimensional superspace can be expanded by these bases, expansion coefficients being ordinary tensor and tensor–spinor fields. Then explicit formulas are given for φ(x,θ)Φ(x,θ) (Φ being another superfield) up to sixth order in θ in terms of ordinary fields, while those for (∂/∂θ̄)φ(x,θ) and Γmθ ∂mφ(x,θ) are given up to eighth order in θ.