207 research outputs found
String fine tuning
We develop further a new geometrical model of a discretized string, proposed
in [1] and establish its basic physical properties. The model can be considered
as the natural extention of the usual Feynman amplitude of the random walks to
random surfaces. Both amplitudes coinside in the case, when the surface
degenarates into a single particle world line. We extend the model to open
surfaces as well. The boundary contribution is proportional to the full length
of the boundary and the coefficient of proportionality can be treated as a
hopping parameter of the quarks. In the limit, when this parameter tends to
infinity, the theory is essentialy simlplified. We prove that the contribution
of a given triangulation to the partition function is finite and have found the
explicit form for the upper bound. The question of the convergence of the full
partition function remains open. In this model the string tension may vanish at
the critical point, if the last one exists, and possess a nontrivial scaling
limit. The model contains hidden fermionic variables and can be considered as
an independent model of hadrons.Comment: 14 pages, pTeX fil
Interaction Hierarchy. Gonihedric String and Quantum Gravity
We have found that the Regge gravity \cite{regge,sorkin}, can be represented
as a of less complicated theory of random surfaces with
as an action. This extends to Regge gravity our previous
result \cite{savvidy}, which allows to represent the gonihedric string
\cite{savvidy1} as a superposition of less complicated theory of random paths
with action. We propose also an alternative linear action
for the four and high dimensional quantum gravity. From these
representations it follows that the corresponding partition functions are equal
to the product of Feynman path integrals evaluated on time slices with
curvature and length action for the gonihedric string and with Euler character
and gonihedric action for the Regge gravity. In both cases the interaction is
proportional to the overlapping sizes of the paths or surfaces on the
neighboring time slices. On the lattice we constructed spin system with local
interaction, which have the same partition function as the quantum gravity. The
scaling limit is discussed.Comment: 11 pages,Late
Stability of the Rotating Ellipsoidal D0-brane System
In this note we prove the complete stability of the classical fluctuation
modes of the rotating ellipsoidal membrane. The analysis is carried out in the
full SU(N) setting, with the conclusion that the fluctuation matrix has only
positive eigenvalues. This proves that the solution will remain close to the
original one for all time, under arbitrary infinitesimal perturbations of the
gauge fields.Comment: 10 pages, LaTe
Gonihedric String Equation
We discuss the basic properties of the gonihedric string and the problem of
its formulation in continuum. We propose a generalization of the Dirac equation
and of the corresponding gamma matrices in order to describe the gonihedric
string. The wave function and the Dirac matrices are infinite-dimensional. The
spectrum of the theory consists of particles and antiparticles of increasing
half-integer spin lying on quasilinear trajectories of different slope.
Explicit formulas for the mass spectrum allow to compute the string tension and
thus demonstrate the string character of the theory.Comment: 40 pages, Latex, 9 figure
Phase structure of four-dimensional gonihedric spin system
We perform Monte Carlo simulations of a gauge invariant spin system which
describes random surfaces with gonihedric action in four dimensions. The
Hamiltonian is a mixture of one-plaquette and additional two- and
three-plaquette interaction terms with specially adjusted coupling constants.
For the system with the large self-intersection coupling constant we
observe the second-order phase transition at temperature . The string tension is generated by quantum fluctuations as it was
expected theoretically. This result suggests the existence of a noncritical
string in four dimensions. For smaller values of the system undergoes the
first order phase transition and for close to zero exhibits a smooth
crossover.Comment: 14 pages, Latex, 10 figure
Tensionless Strings. Vertex Operator for Fixed Helicity States
The tensionless string theory with perimeter action has pure massless
spectrum of higher-spin gauge fields. The multiplicity of these massless states
grows linearly. It is therefore much less compared with the standard string
theory and is larger compared with the field theory models of the Yang-Mills
type. It is important to define nontrivial interaction between infinite amount
of massless particles of the perimeter string theory. The appropriate vertex
operators were defined recently and I study the lowest order vertex operators
and the corresponding scattering amplitudes in tree approximation. I emphasize
the special importance of the vertex operator for fixed helicity states.Comment: 12 pages, Latex fil
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