On inflation in the heterotic superstring model

The possibility is considered of achieving inflation in the field-theory limit of the E₈ X E₈ superstring model, which is an N = 1 supergravity theory possessing a “no-scale” SU(n, 1)/SU(n) × U(1) structure. It is shown that neither type I inflation (due to higher-derivative terms O(R²)), nor inflation due to a SUSY-breaking gaugino-condensation potential, is possible, essentially because of the absence of free dimensionless parameters. Kaluza-Klein type inflation is ruled out because the internal space is Ricci flat. The occurence of type II inflation (due to some gauge singlet “inflation” field φ) depends upon the form of the superpotential F and of the Kähler potential G, but this also seems not to be possible, unless the >SU(n, 1) symmetry can be broken in a particular way. Hence, some new type of compactification scheme may be called for, or a different type of inflation.     

Equivalence of two-loop superstring amplitudes in the pure spinor and Ramond-Neveu-Schwarz formalisms

The pure spinor formalism for the superstring has recently been used to compute massless four-point two-loop amplitudes in a manifestly super-Poincaré covariant manner. In this Letter, we show that when all four external states are Neveu-Schwarz states, the two-loop amplitude coincides with the Ramond-Neveu-Schwarz result.     

Landau-Lifshitz fluctuations in heterotic superstring evaporation

By means of the Landau-Lifshitz theory for nonequilibrium thermodynamical fluctuations we calculate the correlations in the rate of dissipative fluxes of a gas of heterotic superstrings. We briefly comment on the cosmological consequences.     

Dilaton vertices of the closed superstring and the heterotic string

BRST - and conformally invariant dilaton vertices of the closed superstring and the heterotic string are constructed, whose counter terms are consistent with the dilaton terms introduced in the non-linear sigma model approach of string theory.     

Supersymmetric pure spinor theory

A theory based solely on a 2×(N=2)-component Weyl spinor field χ(x) of subcanonical dimension $\text{1}\text{2}$ allows the local construction (without derivatives) of effective fermi and bose fields with spins up to N=2. It is demonstrated that the lagrangian $\text{～:}\text{det}\text{xx}{}^1\text{: (x)}$ studied earlier is invariant under a global N=2 supersymmetry transformation and can be cast into a form $\text{～(}\text{det DD}{}^1\text{):ππ}{}^1\text{:}$ involving the scalar chiral superfield $\text{π=}\text{exp}\text{[θ}{}_{\mathrm{x}}\text{(x + iθσθ}{}^1\text{)]}$ the components of which are finite part products of the basic field. The theory can be generalized to an N-supersymmetric theory in a 2N-dimensional space-time yielding the Thirring model as special case for N=1.     

Perturbative prepotential and monodromies in N = 2 heterotic superstring

We discuss the prepotential describing the effective field theory of N = 2 heterotic superstring models. At the one loop-level the prepotential develops logarithmic singularities due to the appearance of charged massless states at particular surfaces in the moduli space of vector multiplets. These singularities modify the classical duality symmetry group which now becomes a representation of the fundamental group of the moduli space minus the singular surfaces. For the simplest two-moduli case, this fundamental group turns out to be a certain braid group and we determine the resulting full duality transformations of the prepotential, which are exact in perturbation theory.     

Exact monodromy group of N = 2 heterotic superstring

We describe an N = 2 heterotic superstring model of rank 3 which is dual to the type II string compactified on a Calabi-Yau manifold with Betti numbers b_1,1 = 2 and b_1,2 = 86. We show that the exact duality symmetry found from the type II realization contains the perturbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid SU(2) super-Yang-Mills theory. Moreover, it contains a non-perturbative monodromy which is stringy in origin and corresponds roughly to an exchange of the string coupling with the compactification radius.     

Tensor analysis on conformal supergeometry and the ghost action of the superstring

The orthogonal decomposition technique is extended to the physical and ghost tensor superfields on the two-dimensional conformal supergeometry. This method makes the meaning of the superfield functional integral clearer. The form of the ghost action of the superstring in the superspace formulation is discussed on this basis.     

A spinor equation of the pure electromagnetic field

In the early history of spinors it became evident that a single undotted covariant elementary spinor can represent a plane wave of light. Further study of that relation shows that plane electromagnetic waves satisfy the Weyl equation, in a way that indicates the correct spin angular momentum. On the subatomic scale the Weyl equation discloses more detail than the vector equations. The spinor and vector equations are equivalent when applied to plane waves, and more generally (in the absence of sources) on the large scale when the spinors are incoherent.     

A pure spinor model with composite gluons

A pure spinor model with a non-polynomial interaction with global SU(n) symmetry is quantized in the path integral formalism. The model is found to be asymptotically free.     

Complete N-point superstring disk amplitude I. Pure spinor computation

In this paper the pure spinor formalism is used to obtain a compact expression for the superstring N  -point disk amplitude. The color-ordered string amplitude is given by a sum over (N−3)!$(N-3)!$ super-Yang–Mills subamplitudes multiplied by multiple Gaussian hypergeometric functions. In order to obtain this result, the cohomology structure of the pure spinor superspace is exploited to generalize the Berends–Giele method of computing super-Yang–Mills amplitudes. The method was briefly presented in Mafra et al. (2011) [1], and this paper elaborates on the details and contains higher-rank examples of building blocks and associated cohomology objects. But the main achievement of this work is to identify these field-theory structures in the pure spinor computation of the superstring amplitude. In particular, the associated set of basis worldsheet integrals is constructively obtained here and thoroughly investigated together with the structure and properties of the amplitude in Mafra et al. (2011) [2], arXiv:1106.2646 [hep-th].     

On the spinor representation

A systematic study of the spinor representation by means of the fermionic physical space is accomplished and implemented. The spinor representation space is shown to be constrained by the Fierz–Pauli–Kofink identities among the spinor bilinear covariants. A robust geometric and topological structure can be manifested from the spinor space, wherein the first and second homotopy groups play prominent roles on the underlying physical properties, associated to fermionic fields. The mapping that changes spinor fields classes is then exemplified, in an Einstein–Dirac system that provides the spacetime generated by a fermion.     

Scattering of massive open strings in pure spinor

In Park (2008) [4], it was proposed that the D-brane geometry could be produced by open string quantum effects. In an effort to verify the proposal, we consider scattering amplitudes involving massive open superstrings. The main goal of this paper is to set the ground for two-loop “renormalization” of an oriented open superstring on a D-brane and to strengthen our skill in the pure spinor formulation of a superstring, an effective tool for multi-loop string diagrams. We start by reviewing scattering amplitudes of massless states in the 2D component method of the NSR formulation. A few examples of massive string scattering are worked out. The NSR results are then reproduced in the pure spinor formulation. We compute the amplitudes using the unintegrated form of the massive vertex operator constructed by Berkovits and Chandia (2002) [15]. We point out that it may be possible to discover new Riemann type identities involving Jacobi ?-functions by comparing a NSR computation and the corresponding pure spinor computation.     

A spinor equation of the pure electromagnetic field. II

Spinor equations, previously found valid and interesting in dealing with plane waves of light, are applied to spherical waves. It is found that the spinors pertaining to light do not form outgoing spherical waves, as the vectors do, but they can form standing spherical waves, which the vectors usually cannot. The spinors disclose details (hidden variables) which are hidden from the accepted theories of the subatomic scale.