On the Nonperturbative Consistency of d=2d=2 String Theory

An infinite number of distinct $d=1$ matrix models reproduce the perturbation theory of $d=2$ string theory. Due to constraints of causality, however, we argue that none of the existing constructions gives a consistent nonperturbative definition of the $d=2$ string.Comment: 10 pages, 2 figures, LaTeX (author's name added

Non-renormalization for the Liouville wave function

Using an exact functional method, within the framework of the gradient expansion for the Liouville effective action, we show that the kinetic term for the Liouville field is not renormalized.Comment: 13 pages Latex, no figure

Automorphisms of the affine SU(3) fusion rules

We classify the automorphisms of the (chiral) level-k affine SU(3) fusion rules, for any value of k, by looking for all permutations that commute with the modular matrices S and T. This can be done by using the arithmetic of the cyclotomic extensions where the problem is naturally posed. When k is divisible by 3, the automorphism group (Z_2) is generated by the charge conjugation C. If k is not divisible by 3, the automorphism group (Z_2 x Z_2) is generated by C and the Altsch\"uler--Lacki--Zaugg automorphism. Although the combinatorial analysis can become more involved, the techniques used here for SU(3) can be applied to other algebras.Comment: 21 pages, plain TeX, DIAS-STP-92-4

On the Yang-Lee and Langer singularities in the O(n) loop model

We use the method of `coupling to 2d QG' to study the analytic properties of the universal specific free energy of the O(n) loop model in complex magnetic field. We compute the specific free energy on a dynamical lattice using the correspondence with a matrix model. The free energy has a pair of Yang-Lee edges on the high-temperature sheet and a Langer type branch cut on the low-temperature sheet. Our result confirms a conjecture by A. and Al. Zamolodchikov about the decay rate of the metastable vacuum in presence of Liouville gravity and gives strong evidence about the existence of a weakly metastable state and a Langer branch cut in the O(n) loop model on a flat lattice. Our results are compatible with the Fonseca-Zamolodchikov conjecture that the Yang-Lee edge appears as the nearest singularity under the Langer cut.Comment: 38 pages, 16 figure

Classical Solutions in Two-Dimensional String Theory and Gravitational Collapse

A general solution to the $D=2$ 1-loop beta functions equations including tachyonic back reaction on the metric is presented. Dynamical black hole (classical) solutions representing gravitational collapse of tachyons are constructed. A discussion on the correspondence with the matrix-model approach is given.Comment: 7 pages, UTTG-31-9

Can a Lattice String Have a Vanishing Cosmological Constant?

We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must satisfy.Comment: 14 page

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

Simulating hot Abelian gauge dynamics

The time evolution of soft modes in a quantum gauge field theory is to first approximation classical, but the equations of motion are non-local. We show how they can be written in a local and Hamiltonian way in an Abelian theory, and that this formulation is particularly suitable for numerical simulations. This makes it possible to simulate numerically non-equilibrium processes such as the phase transition in the Abelian Higgs model and and to study, for instance, bubble nucleation and defect formation. Such simulations would also help to understand phase transitions in more complicated gauge theories. Moreover, we show that the existing analytical results for the time-evolution in a pure-gauge theory correspond to a special class of initial conditions and that different initial conditions can lead to qualitatively different behavior. We compare the results of the simulations to analytical calculations and find an excellent agreement.Comment: 18 pages, 5 figures, REVTe

Spinons and parafermions in fermion cosets

We introduce a set of gauge invariant fermion fields in fermionic coset models and show that they play a very central role in the description of several Conformal Field Theories (CFT's). In particular we discuss the explicit realization of primaries and their OPE in unitary minimal models, parafermion fields in $Z_k$ CFT's and that of spinon fields in $SU(N)_k, k=1$ Wess-Zumino-Witten models (WZW) theories. The higher level case ($k>1$) will be briefly discussed. Possible applications to QHE systems and spin-ladder systems are addressed.Comment: 6 pages, Latex file. Invited talk at International Seminar dedicated to the memory of D.V.Volkov, Kharkov, January 5-7, 199

A simple way to generate high order vacuum graphs

We describe an efficient practical procedure for enumerating and regrouping vacuum Feynman graphs of a given order in perturbation theory. The method is based on a combination of Schwinger-Dyson equations and the two-particle-irreducible ("skeleton") expansion. The regrouping leads to skeletons containing only free propagators, together with "ring diagrams" containing all the self-energy insertions. As a consequence, relatively few diagrams need to be drawn and integrations carried out at any single stage of the computation and, in low dimensions, overlapping ultraviolet/infrared subdivergences can be cleanly isolated. As an illustration we enumerate the graphs contributing to the 4-loop free energy in QCD, explicitly in a continuum and more compactly in a lattice regularization.Comment: 19 pages. Reference added. To appear in Phys.Rev.