5,634 research outputs found
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 , (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
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