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

Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring

We construct a zero-curvature Lax connection in a sub-sector of the superstring theory on AdS(4) x CP(3) which is not described by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet fermions associated to eight broken supersymmetries of the type IIA background are physical fields. As such, the prescription for the construction of the Lax connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4) does not do the job. So, to construct the Lax connection we have used an alternative method which nevertheless relies on the isometry of the target superspace and kappa-symmetry of the Green-Schwarz superstring.Comment: 1+26 pages; v2: minor typos corrected, acknowledgements adde

Kaluza-Klein gauge and minimal integrable extension of OSp(4|6)/(SO(1,3) x U(3)) sigma-model

Basing upon experience from performing double-dimensional reduction of the D=11 supermembrane on AdS_4 x S^7 background to Type IIA superstring on AdS_4 x CP^3 we introduce Kaluza-Klein (partial) kappa-symmetry gauge as a vanishing condition of the contribution to the D=11 supervielbein components tangent to D=10 space-time proportional to the differential of the coordinate parametrizing compact 11-th space-time dimension, that is identified with the supermembrane world-volume compact dimension. For AdS_4 x S^7 supermembrane Kaluza-Klein gauge removes half Grassmann coordinates associated with 8 space-time supersymmetries, broken by the AdS_4 x CP^3 superbackground, by imposing D=3 (anti-)Majorana condition on them. The consideration relies on the realization of osp(4|8) isometry superalgebra of the AdS_4 x S^7 superbackground as D=3 N=8 superconformal algebra. Requiring further vanishing of the D=10 dilaton leaves in the sector of broken supersymmetries just two Grassmann coordinates organized into D=3 (anti-)Majorana spinor that defines minimal SL(2,R)-covariant extension of the OSp(4|6)/(SO(1,3)x U(3)) sigma-model. Among 4 possibilities of such a minimal extension we consider in detail one, that corresponds to picking out D=3 Majorana coordinate related to broken Poincare supersymmetry, and show that the AdS_4 x CP^3 superstring equations of motion in this partial kappa-symmetry gauge are integrable. Also the relation between the OSp(4|6)/(SO(1,3) x U(3)) sigma-model and the AdS_4 x CP^3 superstring is revisited.Comment: LaTeX, 22 pages; v2: minor improvements in the text, typos corrected, references adde

Mixed correlation function and spectral curve for the 2-matrix model

We compute the mixed correlation function in a way which involves only the orthogonal polynomials with degrees close to $n$, (in some sense like the Christoffel Darboux theorem for non-mixed correlation functions). We also derive new representations for the differential systems satisfied by the biorthogonal polynomials, and we find new formulae for the spectral curve. In particular we prove the conjecture of M. Bertola, claiming that the spectral curve is the same curve which appears in the loop equations.Comment: latex, 1 figure, 55 page

Derivation of determinantal structures for random matrix ensembles in a new way

There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a new approach to calculate averages over ratios of characteristic polynomials. At first sight paradoxically, one can coin our approach "supersymmetry without supersymmetry" because we use structures from supersymmetry without actually mapping onto superspaces. We address two kinds of integrals which cover a wide range of applications for random matrix ensembles. For probability densities factorizing in the eigenvalues we find determinantal structures in a unifying way. As a new application we derive an expression for the k-point correlation function of an arbitrary rotation invariant probability density over the Hermitian matrices in the presence of an external field.Comment: 36 pages; 2 table

Canonical description of D=10 superstring formulated in supertwistor space

Canonical description of the D=10 superstring action involving supertwistor variables generalizing Penrose-Ferber supertwistors is developed. Primary and secondary constraints are identified and arranged into the first- and second-class sets. Dirac brackets are introduced and the deformation of the Poisson bracket algebra of the first-class constraints is studied. The role of the deformation parameter is played by alpha'.Comment: 20 pages, LateX. V2: comments and references added. Version accepted to J.Phys.

D=3 N=6 superconformal symmetry of AdS_4 x CP^3 superstring

Invariance of the AdS_4 x CP^3 superstring under D=3 N=6 superconformal symmetry is discussed in the sector described by the OSp(4|6)/(SO(1,3) x U(3)) supercoset sigma-model action presented in the conformal basis for the osp(4|6)/(so(1,3) x u(3)) Cartan forms. Transformation rules under D=3 N=6 superconformal symmetry for the (10|24)-dimensional 'reduced' AdS_4 x CP^3 superspace coordinates are obtained and used to derive corresponding world-sheet currents.Comment: LaTeX, 23 pages; v2: presentation refined, typos corrected, references adde