I try to recreate the scientific atmosphere during Wilson's visits to Moscow in '60-s and '70-s

This is a review of topics which haunted me for the last 40 years, starting with spontaneous symmetry breaking and ending with gauge/string/space-time correspondence. While the first part of this article is mostly historical, the second contains some comments, opinions and conjectures which are new. This work is prepared for the volume Fifty Years of the Yang- Mills Theory

We consider the one-dimensional Burgers equation randomly stirred at large scales by a Gaussian short-time correlated force. Using the method of dissipative anomalies, we obtain velocity and velocity-difference probability density functions and confirm the results with high-resolution numerical simulations.

Single phase nanostructured Al-Cu-Fe quascrystalline powders, with various grain sizes, were synthesized by low intensity mechanical milling of spray deposited icosahedral quasicrystals. Structural evolution as a function of temperature was studied in-situ using high energy synchrotron X-ray diffraction. Coefficient of thermal expansion was calculated using the change in d-spacing. The diffraction results revealed a change in the lattice parameter, grain size and quasi-lattice strain with increasing temperature. During heating, onset of appreciable grain growth in different nanostructured quascrystalline powders was observed at a certain critical temperature, which was closely related with the milling time. Quasicrystalline powders milled for 1 and 80 h exhibited appreciable grain coarsening at 923 and 573 K, respectively. For all the samples, the activation energy for grain growth (Egg) was ~30–35 kJ/mol. In addition, the β Al(Cu,Fe) phase with B2-type structure evolved during heating of powder samples milled for 10 h. Onset temperature for β phase formation showed an inverse relationship with the milling time.

We explore gauge fields - strings duality by means of the loop equations and the zigzag symmetry. The results are striking and incomplete. Striking - because we find that the string ansatz proposed in [A.M. Polyakov, hep-th/9711002] satisfies gauge theory Schwinger-Dyson equations precisely at the critical dimension D=4. Incomplete - since we get these results only in the WKB approximation and only for a special class of contours. The ways to go beyond these limitations and in particular the OPE for operators defined on the loop are also discussed.

We propose a hypothesis that all gauge theories are equivalent to a certain non-standard string theory. Different gauge groups are accounted for by weights ascribed to the world sheets of different topologies. The hypothesis is checked in the case of the compact abelian theories, where we show how condensing monopole-instanton fields are reproduced by the summation over surfaces. In the non-abelian case we prove that the loop equations are satisfied modulo contact terms. The structure of these terms unfortunately remains undetermined.

Physics and Mathematics of Strings, pp. 1-15 (1990) No AccessGAUGE TRANSFORMATIONS AND DIFFEOMORPHISMSA. M. PolyakovA. M. PolyakovCenter for Theoretical Physics Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology Cambridge, Massachusetts 02139, U.S.A.https://doi.org/10.1142/9789814434461_0001Cited by:2 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The following sections are included: INTRODUCTION DIFFEOMORPHISMS OUT OF GAUGE TRANSFORMATIONS CONSEQUENCES FOR WZNW ACTIONS THE CASE OF SL(3) ACKNOWLEDGEMENTS REFERENCES This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) tinder contract #DE-AC02-76ER03069. FiguresReferencesRelatedDetailsCited By 2Unitarity bounds in AdS3 higher spin gravityAlejandra Castro, Eliot Hijano and Arnaud Lepage-Jutier1 June 2012 | Journal of High Energy Physics, Vol. 2012, No. 6On W-gravity in two dimensionsA. Gerasimov, A. Levin and A. Marshakov1 Aug 1991 | Nuclear Physics B, Vol. 360, No. 2-3 Physics and Mathematics of StringsMetrics History PDF download

We discuss sources of neutral fermions in paramagnetic insulators which apparently play a major role in high-Tc superconductivity

We analyze three-dimensional gauge theory with Chern-Simons action, which arises in the context of high Tc superconductivity. We show that the main effect in this theory is the change of spin and statistics of charged particles. Also, the amplitudes of particle propagation acquire phases dependent on the topology of the knot formed by their trajectories. In the end, we discuss possible generalizations of this theory, and their relations to strings.

We show that in (2+1) -dimensional abelian gauge theory with the Chern-Simons term in the action, charged particles reverse their statistics.

Strings are important objects for physics, although it has not been proved yet. It is a common hope, that they are fundamental elements of grand unification. Much less common is the hope that they describe color-electric fluxes and help to solve gluodynamics and also that they are relevant for the solution of the three-dimensional Ising model. In my talk I shall describe various topics, important for all three problems. I believe that in order to reach understanding it is useful to keep them in mind simultaneously. Unfortunately, my presentation will be fragmentary, because my understanding of the subject is far from complete.

We present an exact solution for the two-dimensional chiral fields with multivalued action, and consider the relation of this theory to the CP-asymmetric Thirring model, free fermions, surrent algebras and Heisenberg antiferromagnets. Also, the parity violating lagrangian for the n-fields based on the Hopf topological invariant is briefly discussed.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. PERTURBATIVE QUANTUM CHROMODYNAMICS A. Polyakov

The formalism of the previous paper is extended to the case of supersymmetric strings. The effective theory which sums up fermionic surfaces is described by the supersymmetric Liouville equation. At D = 10 effective decoupling of the Liouville dilaton takes place and our theory coincides with the old ones. At D = 3 our theory is equilavent to the three-dimensional Ising model, which is thus reduced to the two-dimensional supersymmetric Liouville theory.

We develop a formalism for computing sums over random surfaces which arise in all problems containing gauge invariance (like QCD, three-dimensional Ising model etc.). These sums are reduced to the exactly solvable quantum theory of the two-dimensional Liouville lagrangian. At D = 26 the string dynamics is that of harmonic oscillators as was predicted earlier by dual theorists, otherwise it is described by the nonlinear integrable theory.

In this paper we take the view that gauge fields can be considered as chiral fields on a loop space, both in classical and in quantum theories. As a result, gauge interactions are interpreted as propagation of the infinitely thin rings formed by the lines of color-electric flux. Equations of motion governing this propagation are derived. In the three-dimensional case some higher conserved currents in the loop space are obtained, indicating that hidden symmetry is present in the theory. In the four-dimensional case the question of hidden symmetry remains unclear. Ward identities in the loop space are obtained and their mathematical structure is investigated. Possible extensions and applications of these results are discussed.