Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string

In this paper we derive the tree-level S-matrix of the effective theory of Goldstone bosons known as the non-linear sigma model (NLSM) from string theory. This novel connection relies on a recent realization of tree-level open-superstring S-matrix predictions as a double copy of super-Yang-Mills theory with Z-theory --- the collection of putative scalar effective field theories encoding all the alpha'-dependence of the open superstring. Here we identify the color-ordered amplitudes of the NLSM as the low-energy limit of abelian Z-theory. This realization also provides natural higher-derivative corrections to the NLSM amplitudes arising from higher powers of alpha' in the abelian Z-theory amplitudes, and through double copy also to Born-Infeld and Volkov-Akulov theories. The Kleiss-Kuijf and Bern-Carrasco-Johansson relations obeyed by Z-theory amplitudes thereby apply to all alpha'-corrections of the NLSM. As such we naturally obtain a cubic-graph parameterization for the abelian Z-theory predictions whose kinematic numerators obey the duality between color and kinematics to all orders in alpha'.Comment: 37 pages; v2: references, explanations and arguments for factorization added; published versio

Superpotential de-sequestering in string models

Non-perturbative superpotential cross-couplings between visible sector matter and K\"ahler moduli can lead to significant flavour-changing neutral currents in compactifications of type IIB string theory. Here, we compute corrections to Yukawa couplings in orbifold models with chiral matter localised on D3-branes and non-perturbative effects on distant D7-branes. By evaluating a threshold correction to the D7-brane gauge coupling, we determine conditions under which the non-perturbative corrections to the Yukawa couplings appear. The flavour structure of the induced Yukawa coupling generically fails to be aligned with the tree-flavour structure. We check our results by also evaluating a correlation function of two D7-brane gauginos and a D3-brane Yukawa coupling. Finally, by calculating a string amplitude between n hidden scalars and visible matter we show how non-vanishing vacuum expectation values of distant D7-brane scalars, if present, may correct visible Yukawa couplings with a flavour structure that differs from the tree-level flavour structure.Comment: 37 pages + appendices, 8 figure

Explicit BCJ Numerators from Pure Spinors

We derive local kinematic numerators for gauge theory tree amplitudes which manifestly satisfy Jacobi identities analogous to color factors. They naturally emerge from the low energy limit of superstring amplitudes computed with the pure spinor formalism. The manifestation of the color--kinematics duality is a consequence of the superstring computation involving no more than (n-2)! kinematic factors for the full color dressed n-point amplitude. The bosonic part of these results describe gluon scattering independent on the number of supersymmetries and captures any N^kMHV helicity configuration after dimensional reduction to D=4 dimensions.Comment: 32 pages, harvma

On the cubic interactions of massive and partially-massless higher spins in (A)dS

Cubic interactions of massive and partially-massless totally-symmetric higher-spin fields in any constant-curvature background of dimension greater than three are investigated. Making use of the ambient-space formalism, the consistency condition for the traceless and transverse parts of the parity-invariant interactions is recast into a system of partial differential equations. The latter can be explicitly solved for given s_1-s_2-s_3 couplings and the 2-2-2 and 3-3-2 examples are provided in detail for general choices of the masses. On the other hand, the general solutions for the interactions involving massive and massless fields are expressed in a compact form as generating functions of all the consistent couplings. The St\"uckelberg formulation of the cubic interactions as well as their massless limits are also analyzed.Comment: 42 pages, 2 tables, LaTex. Comments on two-derivative couplings involving partially-massless spin-2 fields added, typos corrected, references added. v2: final version to appear in JHEP. v3: formulae (3.4) and (3.9) correcte

Three particle superstring amplitudes with massive legs

On-shell superspaces and associated spinor helicity techniques give an efficient formulation of the Ward identities of on-shell supersymmetry for scattering amplitudes and supply tools to construct their solutions. Based on these techniques in this paper the general solutions of the Ward identities are presented for three particle scattering amplitudes with one, two or three massive legs for simple supersymmetry in ten and eight dimensions. It is shown in examples how these solutions may be used to obtain concrete amplitudes for the closed (IIB) and open superstring in a flat background. Explicit results include all three point amplitudes with one massive leg whose functional form is shown to be dictated completely by super-Poincare symmetry. The resulting surprisingly simple series only involves massive superfields labelled by completely symmetric little group representations. The extension to more general explicit three and higher point amplitudes in string theory is initiated. In appendices the field content of the fundamental massive superfields of the open and closed superstring are listed in terms of the Dynkin labels of a variety of groups which may be of independent interest.Comment: 45 pages. v2: typos corrected, references adde

Reactive direction control for a mobile robot: A locust-like control of escape direction emerges when a bilateral pair of model locust visual neurons are integrated

Locusts possess a bilateral pair of uniquely identifiable visual neurons that respond vigorously to the image of an approaching object. These neurons are called the lobula giant movement detectors (LGMDs). The locust LGMDs have been extensively studied and this has lead to the development of an LGMD model for use as an artificial collision detector in robotic applications. To date, robots have been equipped with only a single, central artificial LGMD sensor, and this triggers a non-directional stop or rotation when a potentially colliding object is detected. Clearly, for a robot to behave autonomously, it must react differently to stimuli approaching from different directions. In this study, we implement a bilateral pair of LGMD models in Khepera robots equipped with normal and panoramic cameras. We integrate the responses of these LGMD models using methodologies inspired by research on escape direction control in cockroaches. Using ‘randomised winner-take-all’ or ‘steering wheel’ algorithms for LGMD model integration, the khepera robots could escape an approaching threat in real time and with a similar distribution of escape directions as real locusts. We also found that by optimising these algorithms, we could use them to integrate the left and right DCMD responses of real jumping locusts offline and reproduce the actual escape directions that the locusts took in a particular trial. Our results significantly advance the development of an artificial collision detection and evasion system based on the locust LGMD by allowing it reactive control over robot behaviour. The success of this approach may also indicate some important areas to be pursued in future biological research

The Structure of n-Point One-Loop Open Superstring Amplitudes

In this article we present the worldsheet integrand for one-loop amplitudes in maximally supersymmetric superstring theory involving any number n of massless open string states. The polarization dependence is organized into the same BRST invariant kinematic combinations which also govern the leading string correction to tree level amplitudes. The dimensions of the bases for both the kinematics and the associated worldsheet integrals is found to be the unsigned Stirling number S_3^{n-1} of first kind. We explain why the same combinatorial structures govern on the one hand finite one-loop amplitudes of equal helicity states in pure Yang Mills theory and on the other hand the color tensors at quadratic alpha prime order of the color dressed tree amplitude.Comment: 75 pp, 8 figs, harvmac TeX, v2: published versio

Segregation distortion of wild-type alleles at the Machado-Joseph disease locus: a study in normal families from the Azores islands (Portugal)

Machado-Joseph disease (MJD) is caused by an expansion of a triplet repeat with a CAG motif at the ATXN3 gene. The putative segregation ratio distortion (SRD) of alleles can play an important role in the non-Mendelian behaviour of triplet repeat loci. To study the stability and infer the segregation patterns of wild-type MJD alleles, the size of the (CAG)(n) tract was analysed in 102 normal sibships, representing 428 meioses. No mutational events were detected during the transmission of alleles. Segregation analysis showed that the smaller alleles were preferentially transmitted (56.9%). Considering maternal meioses alone, such preference was still detected (55.7%) but without statistical significance. A positive correlation was observed for the difference in length between the two alleles constituting the transmitters' genotype (D) and the frequency of transmission of the smaller alleles. The results suggest that small D values are not enough to modify the probability of allele transmission. When transmissions involving genotypes with D <or= 2 were excluded, SRD in favour of the smaller allele became significant for both maternal and paternal transmissions. Therefore, the genotypic composition of the transmitters in a sample to be analysed should influence the ability to detect SRD, acting as a confounding factor.This work was supported by ‘‘Projecto Regional Integrado— DMJ (PRI-DMJ)’’ (funded by Regional Government of the Azores), ‘‘Construyendo una Bio-Región Europea—Biopolis’’ (05/MAC/2.3/ C14, funded by PIC Interreg III B, Azores—Madeira—Canarias) and MANSEEBMO (MI.2.1/004/2005, funded by ‘‘Direcção Regional da Ciência e Tecnologia’’). CB (SFRH/BD/21875/2005) is a recipient of a Ph.D. grant, and RM (SFRH/BPD/32473/2006) and CS (SFRH/BPD/ 20944/2004) are postdoctoral fellows from ‘‘Fundação para a Ciência e a Tecnologia’’ (FCT)