arXiv subjects

Victor Petrov

Publications and source records attributed to Victor Petrov.

42 records · Page 3Linked to original sources

arXiv2000

Nucleons as chiral solitons

In the limit of large number of colors N the nucleon consisting of N quarks is heavy, and one can treat it semiclassically, like the large-Z Thomas--Fermi atom. The role of the semiclassical field binding the quarks in the nucleon is played by the pion or chiral field; its saddle-point distribution inside the nucleon is called the chiral soliton. The old Skyrme model for this soliton is an over-simplification. One can do far better by exploiting a realistic and theoretically-motivated effective chiral lagrangian presented in this paper. As a result one gets not only the static characteristics of the nucleon in a fair accordance with the experiment (such as masses, magnetic moments and formfactors) but also much more detailed dynamic characteristics like numerous parton distributions. We review the foundations of the Chiral Quark-Soliton Model of the nucleon as well as its recent applications to parton distributions, including the recently introduced `skewed' distributions, and to the nucleon wave function on the light cone.

hep-ph↗

arXiv2000

On the Non-Abelian Stokes Theorem

We present the non-Abelian Stokes theorem for the Wilson loop in various forms and discuss its meaning. Its validity has been recently questioned by Faber, Ivanov, Troitskaya and Zach. We demonstrate that all points of their criticism are based on mistakes in mathematics. Finally, we derive a variant of our formula for the Wilson loop in lattice regularization.

hep-lat↗

arXiv2000

Non-Abelian Stokes Theorems in Yang-Mills and Gravity Theories

We recall the non-Abelian Stokes theorem for the Wilson loop in the Yang-Mills theory and discuss its meaning. Then we move to `gravitational Wilson loops', i.e. to holonomies in curved d=2,3,4 spaces and derive non-Abelian Stokes theorems for these quantities as well, which are similar to our formula in the Yang-Mills theory. In particular we derive an elegant formula for the holonomy in the case of a constant-curvature background in three dimensions and a formula for small-area loops in any number of dimensions.

hep-th↗

arXiv2000

Yang-Mills Theory in Three Dimensions as Quantum Gravity Theory

We perform the dual transformation of the Yang-Mills theory in d=3 dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but embedded into a flat 6-dimensional space (for the SU(2) gauge group). In the continuum limit the theory can be reformulated in terms of 6-component gauge-invariant scalar fields having the meaning of the external coordinates of the dual lattice sites. These 6-component fields induce a metric and a curvature of the 3-dimensional dual colour space. The Yang-Mills theory can be identically rewritten as a quantum gravity theory with the Einstein-Hilbert action but purely imaginary Newton constant, plus a homogeneous `matter' term. Interestingly, the theory can be formulated in a gauge-invariant and local form without explicit colour degrees of freedom.

hep-th↗

arXiv1999

To what distances do we know the confining potential?

We argue that asymptotically linear static potential is built in into the common procedure of extracting it from lattice Wilson loop measurements. To illustrate the point, we extract the potential by the standard lattice method in a model vacuum made of instantons. A beautiful infinitely rising linear potential is obtained in the case where the true potential is actually flattening. We argue that the flux tube formation might be also an artifact of the lattice procedure and not necessarily a measured physical effect. We conclude that at present the rising potential is known for sure up to no more than about 0.7 fm. It may explain why no screening has been clearly observed so far for adjoint sources and for fundamental sources but with dynamical fermions. Finally, we speculate on how confinement could be achieved even if the static potential in the pure glue theory is not infinitely rising.

hep-lat↗

arXiv1996

Non-Abelian Stokes Theorem and Quark-Monopole Interaction

We derive a new non-abelian Stokes theorem by rewriting the Wilson loop as a gauge-invariant area integral, at the price of integrating over an auxiliary field from the coset SU(N) / [U(1)]^{N-1} space. We then introduce the relativistic quark--monopole interaction as a Wess--Zumino-type action, and extend it to the non-abelian case. We show that condensation of monopoles and confinement can be investigated in terms of the behaviour of the monopole world lines. One can thus avoid hard problems of how to introduce monopole fields and dual Yang--Mills potentials.

hep-th↗