Weyl invariant gonihedric strings

Savvidy, George; Manvelyan, Ruben

doi:10.1016/s0370-2693(02)01557-5

Cited by 10 publications

(6 citation statements)

References 43 publications

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“…We start with the kinematic description of the gonihedric string, [1,2,3,4,5,7,13] Σ, described by the action functional 1…”

Section: The Gonihedric String Modelmentioning

confidence: 99%

Hamiltonian dynamics of gonihedric string theory

Molgado,

Rojas

2020

Preprint

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We develop in a consistent manner the Ostrogradski-Hamilton framework for gonihedric string theory. The local action describing this model, being invariant under reparametrizations, depends on the modulus of the mean extrinsic curvature of the worldsheet swept out by the string, and thus we are confronted with a genuine secondorder in derivatives field theory. In our geometric approach, we consider the embedding functions as the field variables and, even though the highly non-linear dependence of the action on these variables, we are able to complete the classical analysis of the emerging constraints for which, after implementing a Dirac bracket, we are able to identify both the gauge transformations and the proper physical degrees of freedom of the model. The Ostrogradski-Hamilton framework is thus considerable robust as one may recover in a straightforward and consistent manner some existing results reported in the literature. Further, in consequence of our geometrical treatment, we are able to unambiguously recover as a by-product the Hamiltonian approach for a particular relativistic point-particle limit associated with the gonihedric string action, that is, a model linearly depending on the first Frenet-Serret curvature.

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“…We start with the kinematic description of the gonihedric string, [1,2,3,4,5,7,13] Σ, described by the action functional 1…”

Section: The Gonihedric String Modelmentioning

confidence: 99%

Hamiltonian dynamics of gonihedric string theory

Molgado,

Rojas

2020

Preprint

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“…The convergence of the partition function was proven rigorously in [13,14,15] . Because the action is proportional to the "perimeter" of the surface, and not to its area, the classical string tension is equal to zero and the model can equally well be called a model of tensionless strings [8,9,10,11].…”

Section: Extension Of Feynman Path Integralmentioning

confidence: 99%

“…At low temperature the Wegner-Wilson loop correlation functions have perimeter behavior. At high temperature the fluctuations of the surface induce the area behavior signaling that there is a confinement -deconfinement (or area -perimeter) phase transition [5,6,8]. In this model a nonzero string tension is entirely generated by quantum (thermodynamical)…”

Section: Extension Of Feynman Path Integralmentioning

confidence: 99%

The gonihedric paradigm extension of the Ising model

Savvidy

2015

Mod. Phys. Lett. B

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We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the partition function are analysed. The model can also be formulated as a spin system with identical partition function.The spin system represents a generalisation of the Ising model with ferromagnetic, antiferromagnetic and quartic interactions. Higher symmetry of the model allows to construct dual spin systems in three and four dimensions. In three dimensions the transfer matrix describes the propagation of closed loops and we found its exact spectrum. It is a unique exact solution of the tree-dimensional statistical spin system. In three and four dimensions the system exhibits the second order phase transitions. The gonihedric spin systems have exponentially degenerated vacuum states separated by the potential barriers and can be used as a storage of binary information.

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“…This paper, motivated mainly from some recent reviews [9,10], is devoted specifically to obtain a manifestly covariant expression to describe the classically perturbations in a relativistic surface described by the gonihedric string model. Unlike some perturbative analyzes [4,5,11] for this model, our emphasis is on the worldsheet geometry by taking advantage of the inherent geometric structures defined on the worldsheet. The perturbation analysis we develop is about classical solutions with the advantage of bringing to the foreground how the covariance under rotations of the normals to the worldsheet enters into the game.…”

Section: Introductionmentioning

confidence: 99%

“…The action functional is defined in a way that, when the worldsdsheet swept out by a closed string, degenerates into a worldline such an action must be reduced to an action of a point-like relativistic particle [1][2][3]. This field theory, at classical level, predicts the existence of tensionless strings possessing a massless spectrum of higher integer spin gauge fields [4][5][6] whereas, at quantum level, fluctuations generate a nonzero string tension [1][2][3]. Moreover, when the theory is formulated on an Euclidean lattice it has a close relationship with a spin system which generalizes the Ising model with ferromagnetic, antiferromagnetic and quartic interactions [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Covariant perturbations in the gonihedric string model

Rojas

2017

Int. J. Mod. Phys. A

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We provide a covariant framework to study classically the stability of small perturbations on the so-called gonihedric string model by making precise use of variational techniques. The local action depends of the square root of the quadratic mean extrinsic curvature of the worldsheet swept out by the string, and is reparametrization invariant. A general expression for the worldsheet perturbations, guided by Jacobi equations without any early gauge fixing, is obtained. This is manifested through a set of highly coupled nonlinear differential partial equations where the perturbations are described by scalar fields, Φ i , living in the worldsheet. This model contains, as a special limit, to the linear model in the mean extrinsic curvature. In such a case the Jacobi equations specialize to a single wave-like equation for Φ.

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Weyl invariant gonihedric strings

Cited by 10 publications

References 43 publications

Hamiltonian dynamics of gonihedric string theory

Hamiltonian dynamics of gonihedric string theory

The gonihedric paradigm extension of the Ising model

Covariant perturbations in the gonihedric string model

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