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.

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.Comment: 21 pages, LaTex file, no figure

Integrable flows in c=1 string theory

In these notes we review the method to construct integrable deformations of the compactified c=1 bosonic string theory by primary fields (momentum or winding modes), developed recently in collaboration with S. Alexandrov and V. Kazakov. The method is based on the formulation of the string theory as a matrix model. The flows generated by either momentum or winding modes (but not both) are integrable and satisfy the Toda lattice hierarchy.Comment: sect.1 extended and typos correcte

Integrability in SFT and new representation of KP tau-function

We are investigating the properties of vacuum and boundary states in the CFT of free bosons under the conformal transformation. We show that transformed vacuum (boundary state) is given in terms of tau-functions of dispersionless KP (Toda) hierarchies. Applications of this approach to string field theory is considered. We recognize in Neumann coefficients the matrix of second derivatives of tau-function of dispersionless KP and identify surface states with the conformally transformed vacuum of free field theory.Comment: 25 pp, LaTeX, reference added in the Section 3.