A path-dependent supersymmetric field theory of electric and magnetic charges

We present a supersymmetric field theory of electric and magnetic charges with a genuine string. As a consequence of the conventional and representation preserving constraints, the superstring variable has only a bosonic (space-time) part ξ^μ. We discuss the string-independence of the theory.     

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.     

Aspects of Pohlmeyer reduction for superstrings in AdS 5 × S 5

We review some recent work on Pohlmeyer reduced theory associated to superstring theory in AdS ₅ × S ⁵. We discuss the S-matrix of the reduced theory and also the computation of the 2-loop correction to the partition function in a non-trivial background.     

Spontaneous compactification of O(32) superstrings

We exhibit a solution of the field equations of ten-dimensional O(32) superstring theory for which space-time is the product of a three-dimensional anti de Sitter space with S¹ × S³ × S³.     

Superstring effects on D=4, N=1 supergravity

We give a lagrangian and supersymmetry transformation rules for the four-dimensional N=1 supergravity sector of superstring theories with their O(α′) corrections, obtained by the dimensional reduction á la Witten of the effective action of the ten-dimensional heterotic superstring. We also give general forms of O(α′ ″) corrections to supersymmetry transformation rules which arise through an axial vector superfield. Since our system is based on the ten-dimensional superstring without any auxiliary fields, our four-dimensional N=1 supergravity is free of auxiliary fields. Our point-field theory lagrangian is supposed to describe the mass-less fields in the untwisted sector of the ten-dimensional heterotic superstring propagating on orbifolds.     

Oscillating solutions in higher-dimensional cosmology

Behaviour characteristics of the mixmaster model of the early universe can be reproduced in ten dimensions by the low-energy superstring theory. The three-index tensor field H can produce, in the variation of the sizes of three-dimensional spaces, the characteristic jumping between Kasner solutions near a singularity. Behaviour which would otherwise by chaotic is moderated by the dilaton field of the ten-dimensional theory.     

Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing

This review is devoted to the classical integrability of the AdS ₅ × S⁵ superstring theory. It starts with a reminder of the corresponding action as a coset model. The symmetries of this action are then reviewed. The classical integrability is then considered from the lagrangian and hamiltonian points of view. The second part of this review deals with the gauge fixing of this theory. Finally, some aspects of the pure spinor formulation are also briefly reviewed.     

Field theory of interacting open superstrings in fermionic ghost representation

The field theory of interacting open superstring in the fermionic ghost representation based on anticommuting and commuting ghosts, corresponding respectively to world sheet bosonic x_μ and fermionic ψ_μ coordinates, is presented. We have to revise once more the field theory of the free Ramond (R) string and starting from a general algebraic point of view we obtain that the number of degrees of freedom in the R and NS (Neveu-Schwarz) sectors are equal, permitting us to construct a supersymmetric operator. We propose to solve a specific equation guaranteeing superinvariance in order to find the R-R-NS and NS-R-R vertices in the term of the NS-NS-NS vertex.     

Five-brane effective action in M-theory

On the world-volume of an M-theory five-brane propagates a two-form with self-dual field strength. As this field is non-Lagrangian, there is no obvious framework for determining its partition function. An analogous problem exists in Type IIB superstring theory for the self-dual five-form. The resolution of these problems and definition of the partition function is explained. A more complete analysis of perturbative anomaly cancellation for M-theory five-branes is also presented, uncovering some surprising details.     

Plane waves in effective field theories of superstrings

Exact plane wave solutions of d = 10, N = 1 Einstein-Yang-Mills supergravity theory are presented and their possible modifications in superstring effective theories are examined. It is found that the solutions are not affected by any of the known heterotic string corrections. It is argued that plane waves satisfy the effective field equations of the heterotic string theory in all powers of the string tension parameter α′, possibly after including a totally antisymmetric torsion field and reinterpreting the constants. Similar remarks also apply for type I superstrings. Further properties of the solutions are discussed.     

Three-loop β-functions for the superstring and heterotic string

The β-function for the (1,1) superstring is calculated explicitly up to three loops, using two different choices of the fermion quantum field. In both cases the bosonic contribution is exactly cancelled by the fermionic contribution. The calculation is repeated for the heterotic string and the non-vanishing β-function is shown to be compatible with an O(α′²) effective action in which there are no terms cubic in the Riemann tensor- or gauge-field strength. A renormalization group equation for the gauge field is constructed and its β-function is shown to vanish at the two-loop level.     

String Non(anti)commutativity for Neveu-Schwarz Boundary Conditions

The appearance of non(anti)commutativity in superstring theory, satisfying the Neveu-Schwarz boundary conditions is discussed in this paper. Both an open free superstring and also one moving in a background antisymmetric tensor field are analyzed to illustrate the point that string non(anti)commutativity is a consequence of the nontrivial boundary conditions. The method used here is quite different from several other approaches where boundary conditions were treated as constraints. An interesting observation of this study is that, one requires that the bosonic sector satisfies Dirichlet boundary conditions at one end and Neumann at the other in the case of the bosonic variables X ^μ being antiperiodic. The non(anti)commutative structures derived in this paper also leads to the closure of the super constraint algebra which is essential for the internal consistency of our analysis.     

Higher derivative modifications ofD=10 superspace Yang-Mills theories

We extend the superspace treatment of higher derivative supersymmetric Yang-Mills theories, emphasizing the role played by manifestD=10 Lorentz covariance and supersymmetry invariance. As an example, the superspace formulation of the effective action is considered for the massless fields in the open superstring, as well as in theSO(32) andE ₈×E₈ superstring theories. We show that there exists a unique modification of thef-tensor supercurrent which can provide the embedding of theO(α'³) string corrections in the slope parameter expansion for the Yang-Mills sector inD=10 superspace. The new correction term is relevant for the understanding of nonperturbative effects.     

Compactification and inflation in the superstring theory from the condensation of gravitino pairs

We discuss the possibility that inflation can occur in the E₈×E₈′ heterotic superstring theory, if there is a pair condensation of the gravitino field ψ_A and also of the Majorana-Weyl spinor λ, as suggested by the Helayël-Neto and Smith. In the absence of a condensation of the anti-symmetric tensor field H_MNP, then the associated potential V(θ,φ) is bounded from below and independent of the dilaton field φ. It can be made to vanish at the minimum, where the compactification scale θ is fixed. Alternatively, a small cosmological constant may remain (ultimately to be cancelled by radiative corrections at the lower energy scale of the gaugino condensation), which could in principle lead to inflation.     

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.     

On second-quantized open superstring theory

The SO(32) theory, in the limit where it is an open superstring theory, is completely specified in the light-cone gauge as a second-quantized string theory in terms of a “matrix string” model. The theory is defined by the neighborhood of a 1 + 1-dimensional fixed point theory, characterized by an Abelian gauge theory with type IB Green-Schwarz form. Non-orientability and SO(32) gauge symmetry arise naturally, and the theory effectively constructs an orientifold projection of the (weakly coupled) matrix type IIB theory (also discussed herein). The fixed point theory is a conformal field theory with boundary, defining the free string theory. Interactions involving the interior of open and closed strings are governed by a twist operator in the bulk, while string endpoints are created and destroyed by a boundary twist operator.     

Relation between anomaly in type-I superstring and anomaly in its effective theory

We explicitly calculate the hexagon and heptagon (covariant) gauge anomaly including the precise numerical coefficients in type-I open superstring. The calculation is performed by using the Pauli-Villars regularization on the basis of the stringy Ward identity, which is an assumption weaker than the cancelled propagator argument. We show that the anomalies in the effective theory are realized as the zero slope limit (α^′→0) of the string anomalies in a very non-trivial way in the present calculational scheme. This non-trivial realization in higher point (n≧8) anomalies is also discussed.     

1616 supergravity coupled to matter: The low energy limit of the superstring

We analyze irreducible, N = 1 supergravity theories with 16 fermionic degrees of freedom. The lagrangians for pure $\text{16}\text{16}$ supergravity, and for $\text{16}\text{16}$ supergravity coupled to arbitrary chiral superfields are constructed. These theories are shown to have natural SU(1,1) non-compact symmetry. The low energy field theory limit of the superstring is conjectured to be of this type.