The Deuteron Spin Structure Functions in the Bethe-Salpeter Approach and the Extraction of the Neutron Structure Function g1n(x)g_1^n(x)

The nuclear effects in the spin-dependent structure functions $g_1^D$ and $b_2^D$ are calculated in the relativistic approach based on the Bethe-Salpeter equation with a realistic meson-exchange potential. The results of calculations are compared with the non-relativistic calculations. The problem of extraction of the neutron spin structure function, $g_1^n$, from the deuteron data is discussed.Comment: (Talk given at the SPIN'94 International Symposium, September 15-22, 1994, Bloomington, Indiana), 6 pages, 5 figures, Preprint Alberta Thy 29-9

U(N) Gauge Theory and Lattice Strings

The U(N) gauge theory on a D-dimensional lattice is reformulated as a theory of lattice strings (a statistical model of random surfaces). The Boltzmann weights of the surfaces can have both signs and are tuned so that the longitudinal modes of the string are elliminated. The U(\infty) gauge theory is described by noninteracting planar surfaces and the 1/N corrections are produced by surfaces with higher topology as well as by contact interactions due to microscopic tubes, trousers, handles, etc. We pay special attention to the case D=2 where the sum over surfaces can be performed explicitly, and demonstrate that it reproduces the known exact results for the free energy and Wilson loops in the continuum limit. In D=4 dimensions, our lattice string model reproduces the strong coupling phase of the gauge theory. The weak coupling phase is described by a more complicated string whose world surface may have windows. A possible integration measure in the space of continuous surfaces is suggested.Comment: 37 pages, 11 figures not included ; An extended version explaining in addition the construction of the lattice string ansatz in D >2 dimensions. (Note that the title has been changed.

2D String Theory as Normal Matrix Model

We show that the $c=1$ bosonic string theory at finite temperature has two matrix-model realizations related by a kind of duality transformation. The first realization is the standard one given by the compactified matrix quantum mechanics in the inverted oscillator potential. The second realization, which we derive here, is given by the normal matrix model. Both matrix models exhibit the Toda integrable structure and are associated with two dual cycles (a compact and a non-compact one) of a complex curve with the topology of a sphere with two punctures. The equivalence of the two matrix models holds for an arbitrary tachyon perturbation and in all orders in the string coupling constant.Comment: lanlmac, 21 page

Time-dependent backgrounds of 2D string theory

We study possible backgrounds of 2D string theory using its equivalence with a system of fermions in upside-down harmonic potential. Each background corresponds to a certain profile of the Fermi sea, which can be considered as a deformation of the hyperbolic profile characterizing the linear dilaton background. Such a perturbation is generated by a set of commuting flows, which form a Toda Lattice integrable structure. The flows are associated with all possible left and right moving tachyon states, which in the compactified theory have discrete spectrum. The simplest nontrivial background describes the Sine-Liouville string theory. Our methods can be also applied to the study of 2D droplets of electrons in a strong magnetic field.Comment: 28 pages, 2 figures, lanlma

Complex Curve of the Two Matrix Model and its Tau-function

We study the hermitean and normal two matrix models in planar approximation for an arbitrary number of eigenvalue supports. Its planar graph interpretation is given. The study reveals a general structure of the underlying analytic complex curve, different from the hyperelliptic curve of the one matrix model. The matrix model quantities are expressed through the periods of meromorphic generating differential on this curve and the partition function of the multiple support solution, as a function of filling numbers and coefficients of the matrix potential, is shown to be the quasiclassical tau-function. The relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed. A general class of solvable multimatrix models with tree-like interactions is considered.Comment: 36 pages, 10 figures, TeX; final version appeared in special issue of J.Phys. A on Random Matrix Theor