On the infrared limit of Horava's gravity with the global Hamiltonian constraint

We show that Horava's theory of gravitation with the global Hamiltonian constraint does not reproduce General Relativity in the infrared domain. There is one extra propagating degree of freedom, besides those two associated with the massless graviton, which does not decouple.Comment: 7 pages, typos corrected, to be published in PR

Nonperturbative physics at short distances

There is accumulating evidence in lattice QCD that attempts to locate confining fields in vacuum configurations bring results explicitly depending on tha lattice spacing (that is, ultraviolet cut off). Generically, one deals with low-dimensional vacuum defects which occupy a vanishing fraction of the total four-dimensional space. We review briefly existing data on the vacuum defects and their significance for confinement and other nonperturbative phenomena. We introduce the notion of `quantum numbers' of the defects and draw an analogy, rather formal one, to developments which took place about 50 years ago and were triggered by creation of the Sakata model.Comment: 15 pages, contributed to International Symposium on the Jubilee of the Sakata Model (pnLambda50), Nagoya, Japan, Nov. 200

From confining fields on the lattice to higher dimensions in the continuum

We discuss relation between lattice phenomenology of confining fields in the vacuum state of Yang-Mills theories (mostly SU(2) case) and continuum theories. In the continuum, understanding of the confinement is most straightforward in the dual formulation which involves higher dimensions. We try to bridge these two approaches to the confinement, let it be on a rudimentary level. We review lattice data on low-dimensional defects, that is monopoles, center vortices, topological defects. There is certain resemblance to dual strings, domain walls, introduced in large-N Yang-Mills theories.Comment: 21 pages; based on three lectures given at the Conference ``Infrared QCD in Rio'', Rio de Janeiro, Brazil, 5-0 June 200

Self-accelerating solutions in massive gravity on an isotropic reference metric

Within the framework of the recently proposed ghost-free massive gravity, a cosmological constant-type self-accelerating solution has been obtained for Minkowski and de Sitter reference metrics. We ease the assumption on the reference metric and find the self-accelerating solution for the reference metric respecting only isotropy, thus considerably extending the range of known solutions.Comment: 4 pages; matches the published version in Phys. Rev.

Renormalons as a Bridge between Perturbative and Nonperturbative Physics

In two lectures, we overview the renormalon and renormalon-related techniques and their phenomenological applications. We begin with a single renormalon chain which is a well defined and systematic way to specify the character of corrections in inverse powers of the total energy to observables directly in Minkowski space. Renormalons demonstrate also presence of nonperturbative contributions. We proceed then to multirenormalon chains and argue that they are in fact not suppressed compared to a single chain. On one hand, this phenomenon might be a mechanism for enhancement of power corrections. On the other hand, the derivation of relations between power corrections to various observables becomes a formidable task and asks for introduction of models. In the concluding, third part we consider dynamical models for nonperturbative effects, both in infrared and ultraviolet regions, inspired by renormalons.Comment: 31 pages, LaTeX file. Talk presented at YKIS97, Kyoto, December, 199

Dual string from lattice Yang-Mills theory

We review properties of lower-dimension vacuum defects observed in lattice simulations of SU(2) Yang-Mills theories. One- and two-dimensional defects are associated with ultraviolet divergent action. The action is the same divergent as in perturbation theory but the fluctuations extend over submanifolds of the whole 4d space. The action is self tuned to a divergent entropy and the 2d defects can be thought of as dual strings populated with particles. The newly emerging 3d defects are closely related to the confinement mechanism. Namely, there is a kind of holography so that information on the confinement is encoded in a 3d submanifold. We introduce an SU(2) invariant classification scheme which allows for a unified description of d=1,2,3 defects. The scheme fits known data and predicts that the 3d defects are related to chiral symmetry breaking. Relation to stochastic vacuum model is briefly discussed as well.Comment: 11 pages,based on the talks presented at the conferences ``Quark Confinement and the Hadron Spectrum VI'' (Village Tanka, September 2004) and ``QCD and String Theory'' (Santa Barbara, November 2004

"Branes" in lattice SU(2) gluodynamics

We review lattice evidence for existence of thin vortices in the vacuum state of SU(2) gluodynamics. On the average, the non-Abelian action density per unit area is ultraviolet divergent as a^{-2} where a is the lattice spacing. At small scales, the surface looks very crumpled so that the corresponding entropy factor appears also ultraviolet divergent. The total area, however, scales in physical units. The surface is populated by monopoles which represent a tachyonic mode. The smallest value of $a$ tested is about (3 GeV)^{-1}.Comment: Talk given at 2002 International Workshop on Strong Coupling Gauge Theories and Effective Theories (SCGT 02) Nagoya Japan 10-13 Dec 200