String fine tuning

Abstract

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.

14 pages, missing two figures added

Cited by in corpus (40)

• Geometrical String and Spin Systems
• Self-Avoiding Gonihedric Srting and Spin Systems
• Interaction Hierarchy
• Plaquette Ising models, degeneracy and scaling
• Phase Transition in Lattice Surface Systems with Gonihedric Action
• Non-Standard Finite-Size Scaling at First-Order Phase Transitions
• Evidence for a first order transition in a plaquette 3d Ising-like action
• Low temperature expansion of the gonihedric Ising model
• Dual Statistical Systems and Geometrical String
• Gonihedric 3D Ising Actions
• Slow dynamics in the 3--D gonihedric model
• The Phase Diagram of the Gonihedric 3d Ising Model via CVM
• Tensionless strings, correspondence with SO(D,D) sigma model
• String tension in gonihedric 3D Ising models
• The chaotic emergence of thermalization in highly excited string decays
• Gonihedric (and Fuki-Nuke) Order
• Covariant perturbations in the gonihedric string model
• Phase structure of four-dimensional gonihedric spin system
• Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual
• Scaling in Steiner Random Surfaces
• Exact solutions to plaquette Ising models with free and periodic boundaries
• Four-dimensional gonihedric gauge spin system
• Alternative actions for quantum gravity and the intrinsic rigidity of the spacetime
• Three-dimensional gonihedric spin system
• Weyl Invariant Gonihedric Strings
• Loop transfer matrix and gonihedric loop diffusion
• The Dual Gonihedric 3D Ising Model
• The spectrum of a transfer matrix for loops
• The Gonihedric Paradigm Extensions of the Ising Model
• Quantum gravity with linear action. Intrinsic rigidity of spacetime
• Fixed boundary conditions analysis of the 3d Gonihedric Ising model with $\kappa =0$
• Hamiltonian dynamics of gonihedric string theory
• (Four) Dual Plaquette 3D Ising Models
• Curvature representation of the gonihedric action
• Superstring with Extrinsic Curvature Action
• On gonihedric loops and quantum gravity
• Vacuum structure of gauge theory on lattice with two parallel plaquette action
• Three-dimensional Gonihedric Potts model
• The QCD string and the generalised wave equation
• Tensionless Strings. Vertex Operator for Fixed Helicity States