An introduction to covariant superstring field theories

A pedagogical account is given of the recent developments in covariant (super)string field theories. After reviewing the construction of the free open bosonic string field theory, the super-symmetric case is treated and the space-time supersymmetry transformations are explained. The present status and some future problems are also summarized.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.On leave of absence fromNational Laboratory for High Energy Physics (KEK), Tsukuba, Ibaraki, Japan.I would like to thank A. Neveu, H. Nicolai and P. West for many discussions, and the CERN Theoretical Physics Division for hospitality and generous support.     

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.     

On the Berkovits covariant quantization of GS superstring

We study the covariant quantization of the Green–Schwarz (GS) superstrings proposed recently by Berkovits. In particular, we reformulate the Berkovits approach in a way that clarifies its relation with the GS approach and allows to derive in a straightforward way its extension to curved spacetime background. We explain the procedure working explicitly in the case of the heterotic string.     

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.     

Consistency of open superstring theories

The infinities and the anomalies in the G≠SO(32) open superstring arise from the same limit of the one-loop Riemann surfaces. The dilaton tadpole infinity is removable by an appropriate choice of background, as in the work of Fischler and Susskind. However, we find that the anomalies arise from the tadpole of an unphysical field, and cannot be removed by any choice of background. Thus, the spacetime anomalies are due to a world-sheet superconformal anomaly of topological origin. We also give a general discussion of the relation between anomalies and surface terms in moduli space, and point out several new applications.     

Supermanifold cohomology and the Wess-Zumino term of the covariant superstring action

The cohomology theory of supermanifolds is developed. Its basic properties are established and simple examples given. The Wess-Zumino term in the Green-Schwarz covariant superstring action is interpreted as a nontrivial class in the supersymmetric cohomology of flat superspace. A quotient supermanifold with nontrivial topology reflecting this class is constructed. It is shown that there is no topological quantization condition for the coefficient of the Wess-Zumino term. The superstring differs from conventional sigma models in this respect because its action is Grassmann-valued and its group manifold (superspace) is noncompact.Enrico Fermi Fellow. Research supported by the NSF (PHY 83-01221) and DOE (DE-AC02-82-ER-40073)     

BRST cohomology in superstring theories

Following the work of Freeman and Olive, it is shown that the operators counting the number of non-transverse modes of the superstrings in the Neveu-Schwarz-Ramond formalism are expressed as the anticommutators of the BRST charges Q with other operators. Also the cohomology of Q and the transverse state projection operators are discussed in terms of Q.     

Harmless axions in superstring theories

We explore the possibility of obtaining an axion in superstring theories whose decay constant lies in a phenomenologically acceptable range. We find in agreement with Choi and Kim that this is not possible in SO(32) theories. However, we find that it appears to be possible in the E₈ × E′₈ heterotic string theory.     

Symmetry structures of superstring field theories

A new extended formulation of free supersymmetric string field theories is presented. The hidden symmetries are exhibited and their quantization is given. The rigid space-time supersymmetry of the free theory is discussed.     

Low energy aspects of superstring theories

The effective theory obtained as low energy limit of theE ₈×E ₈ superstring is analyzed from the phenomenological point of view. The supersymmetry breaking manifests itself in the low energy sector only after the radiative corrections involving the goldstino field have been taken into account. A universal mass for the scalar fields, generally smaller thanm _3/2, is generated. An intermediate scale can be obtained through the radiative breaking of part of the gauge group. As a consequence, the additional particles present in the spectrum get a heavy mass, and effective interactions are induced, which make possible the breaking of the electroweak group and the radiative generation of gaugino masses.     

On the covariant formulation of quantum mechanics

We give picture-covariant formulations of the equations of motion for observables and states such that the Hamiltonian operator is transformed asH-0304;=U(t)HU (t) under a time-dependent unitary transformationU(t). Next, we consider the explicit and implicit covariance of Heisenberg's equations of motion for observables with respect to general transformations of coordinate operators. Most of our representation is spread out over a number of textbooks and articles, where the subject has been considered with greater or lesser clarity from different points of view.     

On supersymmetry breaking in superstring theories

We show that non-zero gaugino condensates of several non-abelian gauge groups G₁⊗…⊗G_k∃E₈ in low-energy d=4 superstring E₈⊗E₆ gauge theory can lead to the exponentially small (compared to the Planck scale) supersymmetry breaking scale. The Hosotani mechanism can provide the E₈→G₁⊗…⊗G_k breaking.     

Massless chiral families in superstring theories

The contribution of the U(1) and simple group factors S_k of the background gauge group ifS=Π_kS_k to the number of massless fermion generations in superstrings theories is examined. Unlike the semisimple case when only SU(n) factors contribute to the generation number, if the abelian factors are present, all groups contained in S contribute to it.