The Character of Pure Spinors

The character of holomorphic functions on the space of pure spinors in 10, 11 and 12 dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the superstring. We also derive in a simple way the zero momentum cohomology of the pure spinor BRST operator for the D=10 and D=11 superparticle Mathematics Subject Classifications (2000): 81T30, 83E30, 83E50     

Covariant first and second quantization of the N = 2, D = 10 Brink-Schwarz superparticle

Using a new type of harmonic superspace variables, we reduce the N = 2, D = 10 Brink-Schwarz (BS) superparticle to a system whose constraints are (i) first class, (ii) functionally independent and (iii) Lorentz covariant. We show that these features are essential for a correct covariant quantization. Q_BRST is first rank. By using it to second quantize the system, we obtain a covariant off-shell unconstrained superfield action of the linearized D = 10 type IIB supergravity. A corresponding procedure for the Green Schwarz (GS) superstring is conjectured.     

Space-time supersymmetry of the covariant superstring

We explicitly derive the ghost oscillator contribution to the gauge covariant fermion emission vertex. This vertex is used to construct the space-time supersymmetry transformation laws which are shown to be an invariance of the free gauge covariant action of the superstring. We develop methods to deal with the quadratic exponentials which appear in the fermion emission vertex, in order to study the closure of the supersymmetry algebra. As a by-product, we complete the proof of the equivalence between the “old” and “new” formulations of the superstring.     

Supermoduli spaces

The connection between different supermoduli spaces is studied. It is shown that the coincidence of the moduli space of (1/1) dimensional complex manifolds andN=2 superconformal moduli space is connected with hiddenN=2 superconformal symmetry in the superstring theory.     

Manifestly superPoincaré-covariant quantization of the Green-Schwarz superstring

The Green-Schwarz (GS) superstring is reformulated in a physically equivalent way by embedding it into a larger system containing additional fermionic string-as well as bosonic harmonic variables and possessing additional gauge invariances. The main feature of the new GS superstring system is that it contains covariant and functionally independent first-class constraints only. This allows straightforward application of the BFV-BRST formalism for a manifestly superPoincaré-covariant canonical quantization. The corresponding BRST charge turns out to be of second rank and, therefore, the BFV-BRST action contains fourth-order ghost terms.     

The heterotic string and the geometry of the supersymmetric Einstein-Yang-Mills background

It is shown that the Wess-Zumino term of a heterotic superstring in aN = 1,D = 10 supergravity background can be given in terms of the torsion of the background in both versions (IA and IB) of theN = 1,D = 10 supergravity theory. The gauge degrees of freedom of the background are included according to the ideas of Kaluza and Klein. Explicit expressions for the vielbein, connection, torsion, and curvature of a space with 506 bosonic and 16 fermionic coordinates are given.     

Super p-branes

It is shown that the extension of the spacetime supersymmetric Green-Schwarz covariant action p-dimensional extended objects (p-branes) is possible if and only if the on-shell p-dimensional Bose and Fermi degrees of freedom are equal. This is further evidence for world-tube supersymmetry in these models. All the p-branes models are related to superstring actions in d=3, 4, 6 or 10 dimensions by double dimensional reduction (which we generalise to reduction on arbitrary compact spaces), and we also show how they may be considered as topological defects of supergravity theories.     

Covariant canonical quantization of the green-schwarz superstring

Introducing a new type of D = 10 harmonic superspace with two generations of harmonic coordinates, we reduce the Green-Schwarz (GS) superstring to a system whose constraints are Lorentz covariant and functionally independent. These features allow us to impose Lorentz-covariant gauge fixing conditions for the reparametrization and the fermionic κ-invariances. The resulting Q_BRST corresponds to the finite-dimensional Lie algebra of the remaining purely harmonic constraints. The super-Poincaré symmetry acts in a manifestly Lorentz-covariant form and is apparently anomaly free.     

Superstring theory

Dual string theories, initially developed as phenomenological models of hadrons, now appear more promising as candidates for a unified theory of fundamental interactions. Type I superstring theory (SST I), is a ten-dimensional theory of interacting open and closed strings, with one supersymmetry, that is free from ghosts and tachyons. It requires that an SO(n) or Sp(2n) gauge group be used. A light-cone-gauge string action with space-time supersymmetry automatically incorporates the superstring restrictions and leads to the discovery of type II superstring theory (SST II). SST II is an interacting theory of closed strings only, with two D = 10 supersymmetries, that is also free from ghosts and tachyons. By taking six of the spatial dimensions to form a compact space, it becomes possible to reconcile the models with our four-dimensional perception of spacetime and to define low-energy limits in which SST I reduces to N = 4, D = 4 super Yang-Mills theory and SST II reduces to N = 8, D = 4 supergravity theory. The superstring theories can be described by a light-cone-gauge action principle based on fields that are functionals of string coordinates. With this formalism any physical quantity should be calculable. There is some evidence that, unlike any conventional field theory, the superstring theories provide perturbatively renormalizable (SST I) or finite (SST II) unifications of gravity with other interactions.     

Ghost triality and superstring partition functions

In three or more space-time dimensions a heterotic string can have just four kinds of space-time supersymmetry, corresponding to the exceptional algebras E₆, E₇, E₈ and F₄. We give a simple argument why this correspondence, first observed in the context of the covariant lattice construction, holds for any heterotic superstring, no matter how it is constructed. Using the fact that SO(8) triality is an inner automorphism of the exceptional algebras, we derive a set of identities for character-valued partition functions, valid for any superstring in any space-time dimension and at any genus. These identities have exactly the structure of the Riemann identities, and are identical to the Riemann identities in the case of ten-dimensional strings. Their relavance for proving vanishing of the cosmological constant and non-renormalization theorems is discussed.     

BRST cohomology of the super-Virasoro Algebras

We study the superextension of the semi-infinite cohomology theory of the Virasoro Algebra. In particular, we examine the BRST complex with coefficients in the Fock Space of the RNS superstring. We prove a theorem of vanishing cohomology, and establish the unitary equivalence between a positive definite transversal space, a physical subspace and the zeroth cohomology group. The cohomology of a subcomplex is identified as the covariant equivalent of the well-known GSO subspace. An exceptional case to the vanishing theorem is discussed.Supported by NSF Grant DMS-8703581     

On the confining potential in 4D SU(N_{\mathrm c}) gauge theory with dilaton

Using the formal analogy between the Dick superstring inspired model and the problem of the building of an Eguchi–Hanson metric in 4D N = 2 harmonic superspace (HS), we derive a general formula for the quark–quark interaction potential V(r) including the Dick confining potential. The interquark potential V(r) depends on the dilaton–gluon coupling and may be related to the parameterization of confinement by the quark and gluon vacuum condensates. It is also shown how the axion field may be incorporated in agreement with 10D type IIB superstring requirements. Others features are also discussed. Received: 23 December 1999 / Published online: 6 March 2000     

Classical superstring mechanics

We describe the classical mechanics of the superstring in both hamiltonian and lagrangian formulations, including massless external fields. The formulation is a modification of that of Green and Schwarz that allows supersymmetric Lorentz covariant quantization.     

The effective interactions of chiral families in four-dimensional superstrings

The low-energy effective interactions in four-dimensional superstrings with N = 2 and N = 1 space-time supersymmetry and massless twisted (family) sector are obtained. Our results rely on some general symmetry properties of superstring particle states and on tensor-calculus techniques for supergravity couplings. The novel feature is that the N = 2 quaternionic manifold and N = 1 Kähler space of the scalar superpartners of family multiplets are non-symmetric spaces whose structure can be obtained by “integrating out” the massive superstring modes.     

几种典型背景中Green-Schwarz超弦的κ-对称性

Metsaev和Tseytlin(MT)给出的AdS₅S⁵背景中Green-Schwarz(GS) IIB超弦的Polyakov作用量可以写成等价的Nambu-Goto形式.对于这种形式，给出了新的与靶空间的流有关的投影算子，并用其构造了使作用量不变的局域κ-变换.κ-对称性的这种新方案是由Schwarz对于GS模型提出的.由于MT模型与GS模型有所不同，文中所构造的局域κ-变换有一些新的特点，且适用于其他类似于MT模型的系统.文中分别以AdS₅S¹背景中IIB弦及Polyakov新提出的模型为例，构造了κ-对称性的靶空间形式. 关键词： Green-Schwarz超弦 κ-对称性')" href="#">κ-对称性 AdS₅S⁵')" href="#">AdS₅S⁵ AdS₅S¹')" href="#">AdS₅S¹     

Space-time supersymmetry in covariant superstring field theory

It is shown that the existence of a transition operator, which interchanges the BRS charges of the Neveu-Schwarz and the Ramond sectors, implies space-time supersymmetry in the covariant free open superstring field theory proposed previously by the present authors.     

On the Dirac eigenvalues as observables of the on-shell <Emphasis Type="Italic">N</Emphasis> = 2<Emphasis Type="Italic">D</Emphasis> = 4 Euclidean supergravity

We generalize previous works on the Dirac eigenvalues as dynamical variables of Euclidean gravity and N =1 D = 4 supergravity to on-shell N = 2 D = 4 Euclidean supergravity. The covariant phase space of the theory is defined as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.      

Mathematical formulation of Witten's superstring field theory

The physical and ghost vertex operators in covariant superstring field theory are obtained. The integral and star operations are given in oscillator form and the free and interaction lagrangians are explicitly displayed for the massless fields.