R. Pettorino

Supersymmetric Strings and Color Confinement

The (infinite-dimensional) supersymmetry algebra in 1 + 1 space-time dimension is extended in order to incorporate, in a non-trivial way, an internal symmetry. It turns out that this requirement implies that the internal symmetry is realized as a local gauge symmetry. Moreover, it is possible to construct string-like models with this underlying symmetry, where colour confinement is exactly realized as a consequence of the gauge constraints.

Dual String with U(1) Color Symmetry

Abstract The string model with a U(1) colour symmetry is analyzed in detail. It is shown that the critical dimension of this model is D = 2. There are no tachyons in the U(1) string. Moreover the massless ground state is the only physical particle of the spectrum. All other states are decoupled because of the gauge conditions. The n -point amplitudes of the U(1) string are derived and shown to be equivalent to the tree diagrams of a conventional non-polynomial field theory in two dimensions, namely the non-linear σ model where the pion particle is identified with the massless ground state of the string with an isotopic Chan-Paton symmetry.

Dual String Models with Nonabelian Color and Flavor Symmetries

Abstract Dual string models with non-Abelian colour and flavour symmetries are investigated. For the exceptional case of SU(2) as a gauge colour symmetry a conventional string formulation is given and it is shown that the particles of the spectrum, which are colour singlets, are classified according to representations of a flavour group SU(2). The model turns out to contain ghosts independently of the value of the space-time dimension. This is also the case for models based on an O( N ) underlying colour symmetry.

Large N, chiral approach to pseudoscalar masses, mixings and decays

Abstract Recent results on the combined chiral and large N limit of QCD are used for an improved treatment of the pseudoscalar nonet mass matrix and of η, η′ decays. We point out that a few next-to-leading terms in 1 N and m Λ are necessary and sufficient for a reasonable overall agreement with existing data.

Planckian Energy Scattering and Surface Terms in the Gravitational Action

Abstract We propose a new approach to four-dimensional planckian-energy scattering in which the phase of the S-matrix - to leading order in ℏ and to all orders in R/b = Gs/J - is written in terms of the surface term of the gravitational action and of a boundary term for the colliding quanta. The proposal is checked at leading order in R/b and also against some already known examples of scattering in strong external gravitational fields.

Lattice CPN−1 models and their large-N behaviour

Abstract Two different lattice actions reproducing the CPN−1 model in the continuum are discussed and, in the two cases, strong and weak coupling expansions relative to different physical quantities are obtained. Large-N behaviour is analyzed by evaluating the limiting value of the two partition functions. In neither case does a smooth transition seem possible between strong and weak coupling regions for the limiting model.

Covariant multitadpole operator and bosonization in fermionic strings

Abstract Using the bosonization technique we construct the tadpole operator for a scalar field with anomaly Q on a general Riemann surface. Specifying to the case Q = 2 we derive the multitadpole operator for the fermionic string and show that it has the expected singularity cancellations.

AN ATTEMPT AT REALISTIC SUPERCOMPOSITENESS

Composite models of quarks, leptons and Higgs bosons based on softly broken supercolour are both predictive and capable of giving some of the desired mass hierarchies. In the SQCD examples we have explored, however, massive neutrinos (mν ∼ mef) and light spin-12 leptoquarks (m1q ⪅ 1 GeV) can only be avoided at the price of introducing further elementary particles (spectators).

Mass gap and universality for euclidean O(N) and CPN−1 models

Abstract From a suitably defined correlation function we evaluate the strong coupling expansion for the mass gap of an euclidean version of the O( N ) models in 2D. Good agreement is found for N = 0, 1 and 2 with the known values of the critical temperature and for N ⩾ 3 with the continuum mass gap as evaluated in an hamiltonian approach. Another test of universality based on the use of an asymmetric lattice also yields good results. An analogous discussion for the CP N −1 models is performed.

BRST invariant tadpole operator in the bosonic string

Abstract Using a BRST invariant three-reggeon vertex we construct an explicit expression for the BRST invariant planar tadpole operator for the bosonic string. Joined to an ( N +1)-reggeon vertex it yields the correct expression for the one-loop N -tachyon amplitude.