13 research outputs found

### Structure Constants in the $N=1$ Super-Liouville Field Theory

The symmetry algebra of $N=1$ Super-Liouville field theory in two dimensions
is the infinite dimensional $N=1$ superconformal algebra, which allows one to
prove, that correlation functions, containing degenerated fields obey some
partial linear differential equations. In the special case of four point
function, including a primary field degenerated at the first level, this
differential equations can be solved via hypergeometric functions. Taking into
account mutual locality properties of fields and investigating s- and t-
channel singularities we obtain some functional relations for three- point
correlation functions. Solving this functional equations we obtain three-point
functions in both Neveu-Schwarz and Ramond sectors.Comment: LaTeX file, 17 pages, no figure

### Topological current algebras in two dimensions

Two-dimensional topological field theories possessing a non-abelian current
symmetry are constructed. The topological conformal algebra of these models is
analysed. It differs from the one obtained by twisting the $N=2$ superconformal
models and contains generators of dimensions $1$, $2$ and $3$ that close a
linear algebra. Our construction can be carried out with one and two bosonic
currents and the resulting theories can be interpreted as topological sigma
models for group manifoldsComment: 16 page

### Second Quantization of the Wilson Loop

Treating the QCD Wilson loop as amplitude for the propagation of the first
quantized particle we develop the second quantization of the same propagation.
The operator of the particle position $\hat{\cal X}_{\mu}$ (the endpoint of the
"open string") is introduced as a limit of the large $N$ Hermitean matrix. We
then derive the set of equations for the expectation values of the vertex
operators \VEV{ V(k_1)\dots V(k_n)} . The remarkable property of these
equations is that they can be expanded at small momenta (less than the QCD mass
scale), and solved for expansion coefficients. This provides the relations for
multiple commutators of position operator, which can be used to construct this
operator. We employ the noncommutative probability theory and find the
expansion of the operator $\hat{\cal X}_\mu$ in terms of products of creation
operators $a_\mu^{\dagger}$. In general, there are some free parameters left
in this expansion. In two dimensions we fix parameters uniquely from the
symplectic invariance. The Fock space of our theory is much smaller than that
of perturbative QCD, where the creation and annihilation operators were
labelled by continuous momenta. In our case this is a space generated by $d =
4$ creation operators. The corresponding states are given by all sentences made
of the four letter words. We discuss the implication of this construction for
the mass spectra of mesons and glueballs.Comment: 41 pages, latex, 3 figures and 3 Mathematica files uuencode

### Three-dimensional description of the $\Phi_{1,3}$ deformation of minimal models

We discuss the $2+1$ dimensional description of the $\Phi_{1,3}$ deformation
of the minimal model $M_p$ leading to a transition $M_p \rightarrow M_{p-1}$.
The deformation can be considered as an addition of the charged matter to the
Chern-Simons theory describing a minimal model. The $N=1$ superconformal case
is also considered.Comment: 12 pages, plain Late

### Multicritical Phases of the O(n) Model on a Random Lattice

We exhibit the multicritical phase structure of the loop gas model on a
random surface. The dense phase is reconsidered, with special attention paid to
the topological points $g=1/p$. This phase is complementary to the dilute and
higher multicritical phases in the sense that dense models contain the same
spectrum of bulk operators (found in the continuum by Lian and Zuckerman) but a
different set of boundary operators. This difference illuminates the well-known
$(p,q)$ asymmetry of the matrix chain models. Higher multicritical phases are
constructed, generalizing both Kazakov's multicritical models as well as the
known dilute phase models. They are quite likely related to multicritical
polymer theories recently considered independently by Saleur and Zamolodchikov.
Our results may be of help in defining such models on {\it flat} honeycomb
lattices; an unsolved problem in polymer theory. The phase boundaries
correspond again to ``topological'' points with $g=p/1$ integer, which we study
in some detail. Two qualitatively different types of critical points are
discovered for each such $g$. For the special point $g=2$ we demonstrate that
the dilute phase $O(-2)$ model does {\it not} correspond to the Parisi-Sourlas
model, a result likely to hold as well for the flat case. Instead it is proven
that the first {\it multicritical} $O(-2)$ point possesses the Parisi-Sourlas
supersymmetry.}Comment: 28 pages, 4 figures (not included

### Topologically Nontrivial Sectors of the Maxwell Field Theory on Algebraic Curves

In this paper the Maxwell field theory is considered on the $Z_n$ symmetric
algebraic curves. As a first result, a large family of nondegenerate metrics is
derived for general curves. This allows to treat many differential equations
arising in quantum mechanics and field theory on Riemann surfaces as
differential equations on the complex sphere. The examples of the scalar fields
and of an electron immersed in a constant magnetic field will be briefly
investigated. Finally, the case of the Maxwell equations on curves with $Z_n$
group of automorphisms is studied in details. These curves are particularly
important because they cover the entire moduli space spanned by the Riemann
surfaces of genus $g\le 2$. The solutions of these equations corresponding to
nontrivial values of the first Chern class are explicitly constructed.Comment: 24 pages, latex file + 3 ps figure

### Enumerative geometry of Calabi-Yau 4-folds

Gromov-Witten theory is used to define an enumerative geometry of curves in
Calabi-Yau 4-folds. The main technique is to find exact solutions to moving
multiple cover integrals. The resulting invariants are analogous to the BPS
counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold
invariants to be integers and expect a sheaf theoretic explanation.
Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including
the sextic Calabi-Yau in CP5, are also studied. A complete solution of the
Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic
anomaly equation.Comment: 44 page

### Strings with Discrete Target Space

We investigate the field theory of strings having as a target space an
arbitrary discrete one-dimensional manifold. The existence of the continuum
limit is guaranteed if the target space is a Dynkin diagram of a simply laced
Lie algebra or its affine extension. In this case the theory can be mapped onto
the theory of strings embedded in the infinite discrete line $\Z$ which is the
target space of the SOS model. On the regular lattice this mapping is known as
Coulomb gas picture. ... Once the classical background is known, the amplitudes
involving propagation of strings can be evaluated by perturbative expansion
around the saddle point of the functional integral. For example, the partition
function of the noninteracting closed string (toroidal world sheet) is the
contribution of the gaussian fluctuations of the string field. The vertices in
the corresponding Feynman diagram technique are constructed as the loop
amplitudes in a random matrix model with suitably chosen potential.Comment: 65 pages (Sept. 91

### Entropy in Tribology: in the Search for Applications

The paper discusses the concept of entropy as applied to friction and wear. Friction and wear are classical examples of irreversible dissipative processes, and it is widely recognized that entropy generation is their important quantitative measure. On the other hand, the use of thermodynamic methods in tribology remains controversial and questions about the practical usefulness of these methods are often asked. A significant part of entropic tribological research was conducted in Russia since the 1970s. Surprisingly, many of these studies are not available in English and still not well known in the West. The paper reviews various views on the role of entropy and self-organization in tribology and it discusses modern approaches to wear and friction, which use the thermodynamic entropic method as well as the application of the mathematical concept of entropy to the dynamic friction effects (e.g., the running-in transient process, stick-slip motion, etc.) and a possible connection between the thermodynamic and information approach. The paper also discusses non-equilibrium thermodynamic approach to friction, wear, and self-healing. In general, the objective of this paper is to answer the frequently asked question “is there any practical application of the thermodynamics in the study of friction and wear?” and to show that the thermodynamic methods have potential for both fundamental study of friction and wear and for the development of new (e.g., self-lubricating) materials