Integrable Quantum Field Theories with Unstable Particles

A new family of S-matrix theories with resonance poles is constructed and conjectured to correspond to the Homogeneous sine-Gordon theories associated with simply laced compact Lie groups, where some of the resonance poles can be traced to the presence of unstable particles in the spectrum. These theories are unitary in the usual S S^\dagger =1 sense, they are not parity invariant, and they exhibit continuous coupling constants that determine both the mass spectrum of stable particles and the masses and the position of the resonance poles.Comment: One reference added, 12 pages, LaTeX fil

Social Evolution: New Horizons

Cooperation is a widespread natural phenomenon yet current evolutionary thinking is dominated by the paradigm of selfish competition. Recent advanced in many fronts of Biology and Non-linear Physics are helping to bring cooperation to its proper place. In this contribution, the most important controversies and open research avenues in the field of social evolution are reviewed. It is argued that a novel theory of social evolution must integrate the concepts of the science of Complex Systems with those of the Darwinian tradition. Current gene-centric approaches should be reviewed and com- plemented with evidence from multilevel phenomena (group selection), the constrains given by the non-linear nature of biological dynamical systems and the emergent nature of dissipative phenomena.Comment: 16 pages 5 figures, chapter in forthcoming open access book "Frontiers in Ecology, Evolution and Complexity" CopIt-arXives 2014, Mexic

Tau-Functions and Generalized Integrable Hierarchies

The tau-function formalism for a class of generalized ``zero-curvature'' integrable hierarchies of partial differential equations, is constructed. The class includes the Drinfel'd-Sokolov hierarchies. A direct relation between the variables of the zero-curvature formalism and the tau-functions is established. The formalism also clarifies the connection between the zero-curvature hierarchies and the Hirota-type hierarchies of Kac and Wakimoto.Comment: 23 page

A Systematic Study of Power Corrections from World Deep Inelastic Scattering Measurements

By performing an analysis in moment space using high statistics DIS world data, we extract the values of both the QCD parameter $\Lambda^{(4)}_{\bar{MS}}$ up to NLO and of the power corrections to the proton structure function, $F_2$. At variance with previous analyses, the use of moments allows us to extend the kinematical range to larger values of $x$, where we find that power corrections are quantitatively more important. Our results are consistent with the $n$ dependence predicted by IR renormalon calculations. We discuss preliminary results on nuclear targets with the intent of illustrating a possible strategy to disentangle power corrections ascribed to IR renormalons from the ones generated dynamically e.g. from rescattering in the final state. The latter appear to be modified in nuclear targets.Comment: 4 pages, 2 figures, LateX with espcrc2 and epsfi

Universality and Non-Perturbative Definitions of 2D Quantum Gravity from Matrix Models

The universality of the non-perturbative definition of Hermitian one-matrix models following the quantum, stochastic, or $d=1$-like stabilization is discussed in comparison with other procedures. We also present another alternative definition, which illustrates the need of new physical input for $d=0$ matrix models to make contact with 2D quantum gravity at the non-perturbative level.Comment: 20 page

Non-local conservation laws and flow equations for supersymmetric integrable hierarchies

An infinite series of Grassmann-odd and Grassmann-even flow equations is defined for a class of supersymmetric integrable hierarchies associated with loop superalgebras. All these flows commute with the mutually commuting bosonic ones originally considered to define these hierarchies and, hence, provide extra fermionic and bosonic symmetries that include the built-in N=1 supersymmetry transformation. The corresponding non-local conserved quantities are also constructed. As an example, the particular case of the principal supersymmetric hierarchies associated with the affine superalgebras with a fermionic simple root system is discussed in detail.Comment: 36 pages, LaTeX fil

Pohlmeyer reduction revisited

A systematic group theoretical formulation of the Pohlmeyer reduction is presented. It provides a map between the equations of motion of sigma models with target-space a symmetric space M=F/G and a class of integrable multi-component generalizations of the sine-Gordon equation. When M is of definite signature their solutions describe classical bosonic string configurations on the curved space-time R_t\times M. In contrast, if M is of indefinite signature the solutions to those equations can describe bosonic string configurations on R_t\times M, M\times S^1_\vartheta or simply M. The conditions required to enable the Lagrangian formulation of the resulting equations in terms of gauged WZW actions with a potential term are clarified, and it is shown that the corresponding Lagrangian action is not unique in general. The Pohlmeyer reductions of sigma models on CP^n and AdS_n are discussed as particular examples of symmetric spaces of definite and indefinite signature, respectively.Comment: 45 pages, LaTeX, more references added, accepted for publication in JHE