Interacting field theory of open superstrings

A proposal for a gauge invariant nonlinear classical field theory of open superstrings is explored. The gauge fixing that gives rise to the standard structure in the Ramond sector is described, answering questions that have been raised in recent literature. The model is shown to possess space-time supersymmetry as well as gauge invariance. The proof of space-time supersymmetry uses the covariant form of the fermion emission vertex and the associated picture changing operation, in accord with suggestions by several authors. Also discussed are the canonical formulation of the theory, and some issues connected with the extension of the work to closed strings.     

N-Superstring vertex and the vertex operator for the emission of the superstring

The BRST invariant, supersymmetric N-string vertex which applies to both, the Neveu-Schwarz and Ramond sector of the superstring is formulated using the vertex operator for the emission of a superstring. It is shown that the N-superstring vertex thus obtained is cyclic symmetric when GSO projected on-shell states and operators for the external strings are applied. The constraint equations of this vertex and their singularity structure are examined and we show that this vertex also has the required property of a transition operator. We also give a proof of its BRST invariance and supersymmetry.     

Higgs boson production at CLIC in SUSY models with hierarchy of the vacuum expectation values

Many theoretical schemes predict the existence of unconventional quarks and leptons not fitting the standard pattern of fermion families. We consider two possible kinds of non-standard fermions, mirror fermions and exceptional fermions. Mirror fermions arise in a variety of models ranging from family unification to extended supersymmetry and Kaluza-Klein theories; exceptional fermions come along with the groupE ₆ which is believed to be the low energy gauge symmetry of the superstring theory. We discuss some physical properties of these non-standard particles relevant for the LEP     

Neutrino mass and new light gauge boson in superstring models

The proposal that the neutrino owes the smallness of its mass to the spontaneous breaking of R parity in superstring models with an additional gauge boson coupled to the right-handed neutrino is analysed. The right-handed neutrino can not in general decouple from the low-energy theory in models with supersymmetry at the TeV scale and which possess the light Higgs doublets necessary for generating fermion masses. Experimental limits on neutrino mass then imply an upper limit on the new gauge boson mass m_Zr ⪅ 220 GeV.     

(2, 0) supersymmetry and space-time supersymmetry in the heterotic string theory

Criteria for unbroken N=1 space-time supersymmetry in the heterotic string theory in the presence of background fields are discussed. We make use of the construction of the fermion vertex operator in the Neveu-Schwarz-Ramond model. (2, 0) world-sheet supersymmetry is shown to be one of the necessary conditions for space-time supersymmetry in most cases. Constraints on the various background fields implied by (2, 0) world-sheet supersymmetry are derived, taking into account the effect of σ-model loop corrections. Special care is taken to study the effect of local Lorents and gauge anomaly on these constraints. Our analysis determines the constraints unambigously up to field redefinitions.     

Anomalies,ambiguities and superstrings

It is shown that anomalies only change trivially if a covariant term is added to the gauge connection. As a result, for the superstring, the anomalies can be cancelled if the anti-symmetric tensor field strength H is modified by the Chern-Simons form of any spin-connection, possibly with torsion. The low-energy effective field theory is, then, not uniquely determined by requiring anomaly cancellation and supersymmetry. Implications for string compactifications are considered.     

Contact interactions in superstring theory

Contact interactions are shown to be required in superstring theory in order to ensure either world-sheet supersymmetry in a covariant formalism or spacetime supersymmetry in the light-cone gauge. These interactions only contribute for specific ranges of the momenta of the emitted particles. Their rôle is to ensure analyticity of S-matrix elements in much the same way as with contact terms in ordinary field theories with point particles. For tree diagrams the usual functional calculations, performed at sufficiently spacelike momentum transfer, give correct results. For other values of the momenta the correct answer is obtained either by analytic continuation or by adding the contribution of the contact interactions. In certain loop calculations the effect of the contact interactions must be taken into account. In the light-cone gauge formalism the contact terms ensure positivity of the hamiltonian.     

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.     

Derivation and uniqueness of vacuum solutions of conformally covariant coupled nonlinear field equations

We derive the solutions of conformally covariant coupled Dirac and scalar fields including a nonlinear fermion self-coupling term for which the conformally covariant (not the canonical, nor the symmetric) energy-momentum tensor θ_μν vanishes. This “vacuum” state is degenerate.     

Modified formulation for a green-schwarz superstring having irreducible links of the first kind

A space which receives covariant action is proposed for aD=10, N=1 superstring in a suitably extended configuration space having the following properties: a) a theory can be constructed dynamically equivalent to the Green-Schwarz superstring, and b) the fermion links may be separated into types in an explicitly covariant fashion, where the links of the first kind are irreducible. Tomsk Polytechnical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 3–6. June, 1997.     

Gauge Invariance of a Critical Number of Flavours in QED3

The fermion propagator in an arbitrary covariant gauge can be obtained from the Landau gauge result via a Landau–Khalatnikov–Fradkin transformation. This transformation can be written in a practically useful form in both configuration and momentum space. It is therefore possible to anticipate effects of a gauge transformation on the propagator’s analytic properties. These facts enable one to establish that if a critical number of flavours for chiral symmetry restoration and deconfinement exists in noncompact QED3, then its value is independent of the gauge parameter. This is explicated using simple forms for the fermion–photon vertex and the photon vacuum polarisation. The illustration highlights pitfalls that must be avoided in order to arrive at valid conclusions. Landau gauge is seen to be the covariant gauge in which the propagator avoids modification by a non-dynamical gauge-dependent exponential factor, whose presence can obscure truly observable features of the theory.     

Decoupling in supersymmetric theories

We examine the decoupling of massive states in supergravity theories. Using superspace functional techniques to “integrate out” the massive modes we derive the effective low-energy lagrangian. The technique is extended to the case of large supersymmetry breaking and we show how the effective lagrangian correctly accounts for vacuum expectation values of massive fields. We discuss the structure of effective theories following from the superstring in which the effects of Kaluza-Klein modes and states massive after intermediate scale breaking are included. It is shown in the case of large intermediate scale breaking the theory should possess discrete symmetries to protect light states from large supersymmetry breaking and we list the conditions for viable models.     

Cancellation of leading divergences in multiloop closed superstring amplitudes

We discuss the general problem of divergences and the particularly important “tadpole” configuration for multiloop amplitudes in the closed superstring - or heterotic string - covariant theory, with any number of external legs. We show that, due to a factor coming from the supermoduli, the tachyon divergence in the tadpole is cancelled in each spin structure contribution separately.     

Perturbation theory in terms of superfields and its application to gauge theories

We formulate a perturbation theory in terms of superfields for Lagrangian field theories which are expressable by chiral or general scalar superfields. Especially we consider the generalized QED model of Wess and Zumino where an additional local gauge symmetry is present. Our calculations are manifestly covariant with respect to supersymmetry and local gauge transformations.     

Superfield formulation of relativistic superparticle

We present a superfield action for the massless relativistic superparticle. As we use a new gauge in our construction, it is clear in our formulation how the reparametrization and the local supersymmetry descend from a united origin which we call “superreparametrization”. In our gauge, the action is manifestly invariant under these transformations.     

Proton decay in locally supersymmetric GUT

Proton decay is studied in the supergravity model with “the hidden sector” as the source of supersymmetry breaking. Each dimension-five operator is found to accompany ΔB ≠ 0 four-scalar interactions. The Higgs fermion exchange for loop diagrams at low energies can be as important as the gauge fermion exchange, if the associated Yukawa coupling is significant as suggested by the radiatively induced SU(2) × U(1) breaking mechanism. The experimental bound for p → K⁰μ⁺ gives the lower bound of the order of 10¹⁶ GeV for the mass of the baryon-number violating Higgs particle.     

Commutator of gauge generators in non-abelian chiral theory

Commutators among non-abelian fermion currents are calculated using the BJL limit. The relation between the covariant seagull and the gauge dependence of the fermion current is derived for a canonical non-abelian theory using the path integral formulation. We observe that in a non-abelian theory with coupling to chiral fermions this relation is violated and this produces a non-trivial commutator of gauge group generators.     

Gauge Covariant Fermion Propagator in the Presence of Arbitrary External Gauge Field and Its Schwinger--Dyson Equation

Gauge covariance for Green＇s functions of a gauge theory through a fermion propagator in the presence of arbitrary external gauge field is proven and a formalism of gauge and Lorentz covariant Schwinger-Dyson equation for the fermion propagator with external gauge field is built up within ladder approximation.     

Supersymmetry transformation of quantum fields

If supersymmetry is realized non-linearly as is the case when auxiliary fields are eliminated and/or one works in the Wess–Zumino gauge it is usually incorporated in terms of BRS transformations and Slavnov–Taylor identities. On the vertex functional susy transformations act even non-locally. Furthermore, the gauge fixing term breaks supersymmetry. In the present paper we clarify in which sense supersymmetry is still a symmetry of the system and how it is realized on the level of quantum fields. We treat the Wess–Zumino model as an example for chiral models, SQED and massless SYM as prototypes of gauge theories.     

Non-compact symmetries and scalar masses in superstring-inspired models

We show that one-loop corrections in the presence of broken supersymmetry do not generate gauge non-singlet scalar masses in no-scale supergravity models that possess a partial invariance under a non-compact Heisenberg group of global transformations. This invariance is a remnant of an invariance of ten-dimensional supergravity that survives in some compactification of ten-dimensional supergravity that survives in some compactification schemes. We discuss the conditions under which compactification of a ten-dimensional superstring theory yields a Heisenberg symmetry.