The Schwinger SU(3) construction - I: Multiplicity problem and relation to induced representations

The Schwinger oscillator operator representation of SU(3) is analysed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an $Sp(2,R)$ unitary representation commuting with the SU(3) representation, the infinity of occurrences of each SU(3) irreducible representation can be handled in complete detail. A natural `generating representation' for SU(3), containing each irreducible representation exactly once, is identified within a subspace of the Schwinger construction; and this is shown to be equivalent to an induced representation of SU(3).Comment: Latex, 25 page

The cohomology of superspace, pure spinors and invariant integrals

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to \a'^3. Some partial results on $N=2,d=10$ and $N=1,d=11$ are also given.Comment: 24 pages. Minor changes; added reference

Characteristics of long-duration inhibitory postsynaptic potentials in rat neocortical neurons in vitro

1. The characteristics of long-duration inhibitory postsynaptic potentials (l-IPSPs) which are evoked in rat frontal neocortical neurons by local electrical stimulation were investigated with intracellular recordings from anin vitro slice preparation. 2. Stimulation with suprathreshold intensities evoked l-IPSPs with typical durations of 600–900 msec at resting membrane potential. Conductance increases of 15–60% were measured at the peak amplitude of l-IPSPs (150–250 msec poststimulus). 3. The duration of the conductance increases during l-IPSPs displayed a significant voltage dependence, decreasing as the membrance potential was depolarized and increasing with hyperpolarization. 4. The reversal potential of l-IPSPs is significantly altered by reductions in the extracellular potassium concentration. Therefore it is concluded that l-IPSPs in rat neocortical neurons are generated by the activation of a potassium conductance. 5. l-IPSPs exhibit stimulation fatigue. Stimulation with a frequency of 1 Hz produces a complete fatigue of the conductance increases during l-IPSPs after approximately 20 consecutive stimuli. Recovery from this fatigue requires minutes. 6. l-IPSPs are not blocked by bicuculline but are blocked by baclofen

Kappa-symmetry for coincident D-branes

A kappa-symmetric action for coincident D-branes is presented. It is valid in the approximation that the additional fermionic variables, used to incorporate the non-abelian degrees of freedom, are treated classically. The action is written as a Bernstein-Leites integral on the supermanifold obtained from the bosonic worldvolume by adjoining the extra fermions. The integrand is a very simple extension of the usual Green-Schwarz action for a single brane; all symmetries, except for kappa, are manifest, and the proof of kappa-symmetry is very similar to the abelian case.Comment: 18 pages. References adde

Spatial incoherence of solar granulation: a global analysis using BiSON 2B data

A poor understanding of the impact of convective turbulence in the outer layers of the Sun and Sun-like stars challenges the advance towards an improved understanding of their internal structure and dynamics. Assessing and calibrating these effects is therefore of great importance. Here we study the spatial coherence of granulation noise and oscillation modes in the Sun, with the aim of exploiting any incoherence to beat-down observed granulation noise, hence improving the detection of low-frequency p-modes. Using data from the BiSON 2B instrument, we assess the coherence between different atmospheric heights and between different surface regions. We find that granulation noise from the different atmospheric heights probed is largely incoherent; frequency regions dominated by oscillations are almost fully coherent. We find a randomised phase difference for the granulation noise, and a near zero difference for the evanescent oscillations. A reduction of the incoherent granulation noise is shown by application of the cross-spectrum.Comment: 8 pages, 7 figures, MNRAS in pres

Orthosymplectically invariant functions in superspace

The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically symmetric functions can be used to solve orthosymplectically invariant Schroedinger equations in superspace, such as the (an)harmonic oscillator or the Kepler problem. Finally the obtained machinery is used to prove the Funk-Hecke theorem and Bochner's relations in superspace.Comment: J. Math. Phy

BPS Solitons in M5-Brane Worldvolume Theory with Constant Three-Form Field

We study BPS solutions for a self-dual string and a neutral string in M5-brane worldvolume theory with constant three-form field. We further generalize such solitons to superpose with a calibrated surface. We also study a traveling wave on a calibrated surface in the constant three-form field background.Comment: 12 pages, LaTeX, minor correction, added referenc

Towards a manifestly supersymmetric action for 11-dimensional supergravity

We investigate the possibility of writing a manifestly supersymmetric action for 11-dimensional supergravity. The construction involves an explicit relation between the fields in the super-vielbein and the super-3-form, and uses non-minimal pure spinors. A simple cubic interaction term for a single scalar superfield is found.Comment: 22 pp., plain tex. v2: references adde

Free Differential Algebras and Pure Spinor Action in IIB Superstring Sigma Models

In this paper we extend to the case of IIB superstring sigma models the method proposed in hep-th/10023500 to derive the pure spinor approach for type IIA sigma models. In particular, starting from the (Free) Differential Algebra and superspace parametrization of type IIB supergravity, extended to include the BRST differential and all the ghosts, we derive the BRST transformations of fields and ghosts as well as the standard pure spinor constraints for the ghosts $\lambda$ related to supersymmetry. Moreover, using the method first proposed by us, we derive the pure spinor action for type IIB superstrings in curved supergravity backgrounds (on shell), in full agreement with the action first obtained by Berkovits and Howe.Comment: 24 page

Ten-Dimensional Super-Twistors and Super-Yang-Mills

Four-dimensional super-twistors provide a compact covariant description of on-shell N=4 d=4 super-Yang-Mills. In this paper, ten-dimensional super-twistors are introduced which similarly provide a compact covariant description of on-shell d=10 super-Yang-Mills. The super-twistor variables are Z=(lambda^alpha, mu_alpha, Gamma^m) where lambda^alpha and mu_alpha are constrained bosonic d=10 spinors and Gamma^m is a constrained fermionic d=10 vector. The Penrose map relates the twistor superfield Phi(Z) with the d=10 super-Yang-Mills vertex operator lambda^alpha A_alpha(x,theta) which appears in the pure spinor formalism of the superstring, and the cubic super-Yang-Mills amplitude is proportional to the super-twistor integral \int dZ Phi_1 Phi_2 Phi_3.Comment: 14 pages harvmac, added short clarificatio