Operators on Pure Spinor Spaces

Abstract

Abstract. Pure spinors are relevant to the formulation of supersymmetric theories, and provide the only known way to maintain manifest maximal supersymmetry. The (non-linear) pure spinor constraint makes it nontrivial to find well defined operators on pure spinor wave functions. We discuss how such operators are defined. One application concerns covariant gauge fixing in maximally supersymmetric Yang-Mills (and string theory). Another issue is the construction of a manifestly supersymmetric action for 11-dimensional supergravity in terms of a scalar superfield. We describe some work in progress.Keywords: extended supersymmetry, superfields, pure spinors PACS: 11.10Ef, 11.30Pb There is a close relation between supermultiplets and pure spinors. The algebra of covariant fermionic derivatives in flat superspace is generically of the formIf a bosonic spinor λ α is pure, i.e., if the vector part (λ γ a λ ) of the spinor bilinear vanishes, the operator Q = λ α D α becomes nilpotent, and may be used as a BRST operator. This is, schematically, the starting point for pure spinor superfields. (The details of course depend on the actual space-time and the amount of supersymmetry. The pure spinor constraint may need to be further specified. Eq. (1) may also contain more terms, due to super-torsion and curvature.) The cohomology of Q will consist of supermultiplets, which in case of maximal supersymmetry are on-shell. The idea of manifesting maximal supersymmetry off-shell by using pure spinor superfields Ψ(x, θ , λ ) is to find an action whose equations of motion is QΨ = 0. The fact that pure spinors had a rôle to play in maximally supersymmetric models was recognised early by Nilsson [1] and Howe [2,3]. Pure spinor superfields were developed with the purpose of covariant quantisation of superstrings by Berkovits [4,5,6,7] and the cohomological structure was independently discovered in supersymmetric field theory and supergravity, originally in the context of higher-derivative deformations [8,9,10,11,12,13,14,15]. The present lecture only deals with pure spinors for maximally supersymmetric field theory.The canonical example of pure spinors is in D = 10.

Ganil-Spiral2: A New Era

“…Gamma-rays emitted following the 58 Ni ( 36 Ar, 2n) 92 Pd fusion-evaporation reaction were identified using a combination of state-of-the-art high-resolution -rays, charged-particle and neutron detector systems (EXOGAM,DIAMANT,NEDA). The results reveal evidence for a spin-aligned, isoscalar neutron-proton coupling scheme, different from the previous prediction (see Ref [8] and figure. 2).…”

“…A modern variation of the Rutherford experiment to probe the tunnelling of exotic nuclear matter from the measurement of the residues formed in the bombardment of 197 Au by extremely neutron-rich 8 He nuclei was carried out. Using a novel off-beam technique the most precise and accurate measurements of fusion and neutron transfer involving reaccelerated unstable beams are reported.…”

“…Using a novel off-beam technique the most precise and accurate measurements of fusion and neutron transfer involving reaccelerated unstable beams are reported. The results show unusual behaviour of the tunnelling of 8 He compared to that for lighter helium isotopes, highlighting the role of the intrinsic structure of composite many-body quantum systems and pairing correlations [2].…”

“…After ionization in an ion source, the particles are injected into the CIME cyclotron to be accelerated to energies of 1.7 to 25 MeV per nucleon. Since its start-up, various ions have been produced and accelerated in the SPIRAL facility, ranging from exotic nuclei as light as 8 He to heavier nuclei like 76 At GANIL, the rather unique capabilities, using both "In flight" and "ISOL" techniques, to produce a large variety of light and medium "exotic" species have boosted the scientific program.…”

Superalgebras, constraints and partition functions

“…It may be called a singleton representation, since it only consists of a "leading trajectory" of Spin (10) representations with highest weights (0000k) at each U(1) charge 4 + k. The lowering operator µ α can be identified with the gauge invariant (in the sense that it respects the ideal) derivative with respect to a pure spinor constructed in ref. [40].…”