Rational Theories of 2D Gravity from the Two-Matrix Model

The correspondence claimed by M. Douglas, between the multicritical regimes of the two-matrix model and 2D gravity coupled to (p,q) rational matter field, is worked out explicitly. We found the minimal (p,q) multicritical potentials U(X) and V(Y) which are polynomials of degree p and q, correspondingly. The loop averages W(X) and \tilde W(Y) are shown to satisfy the Heisenberg relations {W,X} =1 and {\tilde W,Y}=1 and essentially coincide with the canonical momenta P and Q. The operators X and Y create the two kinds of boundaries in the (p,q) model related by the duality (p,q) - (q,p). Finally, we present a closed expression for the two two-loop correlators and interpret its scaling limit.Comment: 24 pages, preprint CERN-TH.6834/9

Generalized two-dimensional Yang-Mills theory is a matrix string theory

We consider two-dimensional Yang-Mills theories on arbitrary Riemann surfaces. We introduce a generalized Yang-Mills action, which coincides with the ordinary one on flat surfaces but differs from it in its coupling to two-dimensional gravity. The quantization of this theory in the unitary gauge can be consistently performed taking into account all the topological sectors arising from the gauge-fixing procedure. The resulting theory is naturally interpreted as a Matrix String Theory, that is as a theory of covering maps from a two-dimensional world-sheet to the target Riemann surface.Comment: LaTeX, 10 pages, uses espcrc2.sty. Presented by A. D'adda at the Third Meeting on Constrained Dynamics and Quantum Gravity, Villasimius (Sardinia, Italy) September 13-17, 1999; to appear in the proceeding

Bound state of dimers on a spherical surface

The study of particle motion on spherical surfaces is relevant to adsorption on buckyballs and other solid particles. This paper reports results for the binding energy of such dimers, consisting of two light particles (He atoms or hydrogen molecules) constrained to move on a spherical surface. The binding energy reaches a particularly large value when the radius of the sphere is about 3/4 of the particles' diameter.Comment: 6 pages, 3 figures, submitted to JLTP, conference proceedings QFS 200

Bulk correlation functions in 2D quantum gravity

We compute bulk 3- and 4-point tachyon correlators in the 2d Liouville gravity with non-rational matter central charge c<1, following and comparing two approaches. The continuous CFT approach exploits the action on the tachyons of the ground ring generators deformed by Liouville and matter ``screening charges''. A by-product general formula for the matter 3-point OPE structure constants is derived. We also consider a ``diagonal'' CFT of 2D quantum gravity, in which the degenerate fields are restricted to the diagonal of the semi-infinite Kac table. The discrete formulation of the theory is a generalization of the ADE string theories, in which the target space is the semi-infinite chain of points.Comment: 14 pages, 2 figure

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.

Matrix strings from generalized Yang-Mills theory on arbitrary Riemann surfaces

We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically non-trivial loops. These sectors, that must be discarded in the usual quantization due to divergences occurring when two eigenvalues coincide, can be consistently kept if one modifies the action by introducing a coupling of the field strength to the space-time curvature. This leads to a generalized Yang-Mills theory whose action reduces to the usual one in the limit of zero curvature. After integrating over the non-diagonal components of the gauge fields, the theory becomes a free string theory (sum over unbranched coverings) with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to a lattice theory with a gauge group which is the semi-direct product of S_N and U(1)^N. By using well known results on the statistics of coverings, the partition function on arbitrary Riemann surfaces and the kernel functions on surfaces with boundaries are calculated. Extensions to include branch points and non-abelian groups on the world-sheet are briefly commented upon.Comment: Latex2e, 29 pages, 2 .eps figure

Power Intensification of Swelling Process

DergiPark: 245958trakyafbdMakale, boru şekilli bir parçanın şişirilmesinde ilave eksenel basınç uygulayarak güç yoğunlaştırmanın etkilerini araştırmak üzere yürütülen çalışmaların sonuçlarını özetlemektedir. Eksenel basıncın arttırılması, ?? gerilme indeksini ve gerilme halinin rijitliğini azaltarak şekil değiştirme bölgesindeki malzemenin düzgün akışını sağlamaktadır. Bu yöntemle düşük karbonlu çelik parçalar için, şişirme indeksinde % 15 civarında bir düşüş ve şekillendirilebilirlikte % 76 ile % 78 arasında bir artış elde edilmektedir.The paper deals with the outcomes of investigations carried out to determine the impact of power intensification of a deformation process by means of applying additional axial pressure over the fronts of round billets. By increasing axial pressure, the value of ?? index and the “rigidity” of the stressed state pattern drops down that promote redistribution of metal within the area of deformation. This resulted in 15% decrease of the index of swelling and 76 to 78% increase of the permissible level of swelling during deformation of low carbon steel specimen