A. D'Adda

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.

Confinement and chiral symmetry breaking in CPn−1 models with quarks

We study the low-energy physics of quarks in two dimensions, which are minimally coupled to CPn−1 fields. Within the 1n expansion, heavy quarks are confined, the U(1)A chiral symmetry is spontaneously broken and a light isoscalar pseudoscalar boson is avoided via the axial anomaly.

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.

Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions

Abstract We propose a lattice action for two-dimensional super-Yang–Mills theory with a twisted N = 2 supersymmetry. The extended supersymmetry is fully and exactly realized on the lattice. The method employed is quite general and its extension to the N = 4 supersymmetry in four dimensions is briefly presented. The lattice has a new type of “fermionic” links, where odd Grassmann variables, supercharges and fermionic connections sit. The Leibniz rule is preserved on the lattice, although in a modified “shifted” form that takes into account the link nature of both derivatives and supercharges. Superfields are semi-local objects and superfield expansion is naturally embedded in the lattice structure. The Dirac–Kahler twist generates the extended twisted supersymmetry, turning the multiplicity of species doublers into the multiplicity due to the extended supersymmetry. In this way the balance between bosonic and fermionic degrees of freedom is preserved.

Twisted superspace on a lattice

Abstract We propose a new formulation which realizes exact twisted supersymmetry for all the supercharges on a lattice by twisted superspace formalism. We show explicit examples of N = 2 twisted supersymmetry invariant BF and Wess–Zumino models in two dimensions. We introduce mild lattice non-commutativity to preserve Leibniz rule on the lattice. The formulation is based on the twisted superspace formalism for N = D = 2 supersymmetry which was proposed recently. From the consistency condition of the non-commutativity of superspace, we find an unexpected three-dimensional lattice structure which may reduce into two-dimensional lattice where the superspace describes semilocally scattered fermions and bosons within a double size square lattice.

Regge calculus as a local theory of the Poincaré group

Abstract We reformulate Regge calculus in terms of dynamical variables belonging to the Poincare group. Our formulation uses the dual lattice, is naturally related in the continuum limit to the Einstein action written in terms of differential forms, and retains and possibility of choosing between the first order and the second order formalism.

Unified dual model for interacting open and closed strings

We construct the vertices which describe the emission of closed string particles (pomerons) out of open string states (reggeons). Using those vertices we can construct a ghost-free unified dual model for the amplitude of an arbitrary number of reggeons and pomerons which contains both the conventional Veneziano model and the Shapiro- Virasoro model. The factorization properties of this model are studied in detail. In particular, we extract the reggeon-pomeron direct coupling from the channels where both reggeons and pomerons can be exchanged.

Space Dimensions From Supersymmetry for the

Abstract Following a view diametrically opposite to recent attempts to obtain the supersymmetric string by compactifying the bosonic string in a high number of dimensions, we reinterpret the N=2, d=2 spinning string as an N=1, d=4 model, without using compactification.

N=2

We calculate the partition functions of QCD in two dimensions on a cylinder and on a torus, in the gauge ∂0A0 = 0, by integrating explicitly over the non-zero modes of the Fourier expansion in the periodic time variable. The result is a one-dimensional Kazakov-Migdal matrix model with eigenvalues on a circle rather than on a line. We prove that our result coincides with the standard expansion in representations of the gauge group. This involves a non-trivial modular transformation from an expansion in exponentials of g2 to one in exponentials of 1/g2. Finally, we argue that the states of the U(N) or SU(N) partition function can be interpreted as a gas of N free fermions, and we give explicitly the grand canonical partition function of such ensemble in terms of infinite products.