Nonperturbative QCD Coupling and its β\beta function from Light-Front Holography

The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a nonperturbative effective coupling $\alpha_s^{AdS}(Q^2)$. It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale $\sim 1$ GeV. The resulting $\beta$ function appears to capture the essential characteristics of the full $\beta$ function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on $\alpha_s^{AdS}(Q^2)$.Comment: 32 pages, 7 figures. Final version published in Phys. Rev.

High Energy Photon-Photon Collisions at a Linear Collider

High intensity back-scattered laser beams will allow the efficient conversion of a substantial fraction of the incident lepton energy into high energy photons, thus significantly extending the physics capabilities of an electron-electron or electron-positron linear collider. The annihilation of two photons produces C=+ final states in virtually all angular momentum states. The annihilation of polarized photons into the Higgs boson determines its fundamental two-photon coupling as well as determining its parity. Other novel two-photon processes include the two-photon production of charged lepton pairs, vector boson pairs, as well as supersymmetric squark and slepton pairs and Higgstrahlung. The one-loop box diagram leads to the production of pairs of neutral particles. High energy photon-photon collisions can also provide a remarkably background-free laboratory for studying possibly anomalous $W W$ collisions and annihilation. In the case of QCD, each photon can materialize as a quark anti-quark pair which interact via multiple gluon exchange. The diffractive channels in photon-photon collisions allow a novel look at the QCD pomeron and odderon. Odderon exchange can be identified by looking at the heavy quark asymmetry. In the case of electron-photon collisions, one can measure the photon structure functions and its various components. Exclusive hadron production processes in photon-photon collisions test QCD at the amplitude level and measure the hadron distribution amplitudes which control exclusive semi-leptonic and two-body hadronic B-decays.Comment: Invited talk, presented at the 5th International Workshop On Electron-Electron Interactions At TeV Energies, Santa Cruz, California, 12-14 December 200

Generalized sum rules of the nucleon in the constituent quark model

We study the generalized sum rules and polarizabilities of the nucleon in the framework of the hypercentral constituent quark model. We include in the calculation all the well known $3^*$ and $4^*$ resonances and consider all the generalized sum rules for which there are data available. To test the model dependence of the calculation, we compare our results to the results obtained in the harmonic oscillator CQM. We furthermore confront our results to the model-independent sum rules values and to the predictions of the phenomenological MAID model. The CQM calculations provide a good description of most of the presented generalized sum rules in the intermediate $Q^2$ region (above $\sim0.2$ GeV$^2$) while they encounter difficulties in describing these observables at low $Q^2$, where the effects of the pion cloud, not included in the present calculation, are expected to be important.Comment: 26 pages, 10 figure

Quantization and holomorphic anomaly

We study wave functions of B-model on a Calabi-Yau threefold in various polarizations.Comment: 15 page

Electromagnetic couplings of elementary vector particles

On the basis of the three fundamental principles of (i) Poincar\'{e} symmetry of space time, (ii) electromagnetic gauge symmetry, and (iii) unitarity, we construct an universal Lagrangian for the electromagnetic interactions of elementary vector particles, i.e., massive spin-1 particles transforming in the /1/2,1/2) representation space of the Homogeneous Lorentz Group (HLG). We make the point that the first two symmetries alone do not fix the electromagnetic couplings uniquely but solely prescribe a general Lagrangian depending on two free parameters, here denoted by \xi and g. The first one defines the electric-dipole and the magnetic-quadrupole moments of the vector particle, while the second determines its magnetic-dipole and electric-quadrupole moments. In order to fix the parameters one needs an additional physical input suited for the implementation of the third principle. As such, one chooses Compton scattering off a vector target and requires the cross section to respect the unitarity bounds in the high energy limit. In result, we obtain the universal g=2, and \xi=0 values which completely characterize the electromagnetic couplings of the considered elementary vector field at tree level. The nature of this vector particle, Abelian versus non-Abelian, does not affect this structure. Merely, a partition of the g=2 value into non-Abelian, g_{na}, and Abelian, g_{a}=2-g_{na}, contributions occurs for non-Abelian fields with the size of g_{na} being determined by the specific non-Abelian group appearing in the theory of interest, be it the Standard Model or any other theory.Comment: 10 pages, 2 figures, contributed to the XI Mexican Workshop on Particles and Fields. Accepted in Phys. Rev.

Quark-Hadron Duality and Parity Violating Asymmetry of Electroweak Reactions in the Delta Region

A dynamical model of electroweak pion production reactions in the Delta(1232) region has been extended to include the neutral current contributions for examining the local Quark-Hadron Duality in neutrino-induced reactions and for investigating how the axial N-Delta form factor can be determined by the parity violating asymmetry of N(\vec{e},e') reactions. We first show that the recent data of (e,e') structure functions F_1 and F_2, which exhibit the Quark-Hadron Duality, are in good agreement with our predictions. For possible future experimental tests, we then predict that the structure functions F_1, F_2, and F_3 for (\nu,e) and (\nu,\nu') processes also show the similar Quark-Hadron Duality. The spin dependent structure functions g_1 and g_2 of (e,e') have also been calculated from our model. It is found that the local Quark-Hadron Duality is not seen in the calculated g_1 and g_2, while our results for g_1 and some polarization observables associated with the exclusive p(\vec{e},e' pi) and \vec{p}(\vec{e},e' pi) reactions are in reasonably good agreement with the recent data. In the investigation of parity violating asymmetry A of N(\vec{e},e') reactions, it is found that the non-resonant contribution is small at the Delta peak and a measurement of A can be used to distinguish two previously determined axial N-Delta transition form factors. The predicted asymmetry A are also compared with the Parton Model predictions for future experimental investigations of Quark-Hadron Duality.Comment: 28 pages, 19 figures v2; figures and references adde

String theory and classical integrable systems

We discuss different formulations and approaches to string theory and $2d$ quantum gravity. The generic idea to get a unique description of {\it many} different string vacua altogether is demonstrated on the examples in $2d$ conformal, topological and matrix formulations. The last one naturally brings us to the appearance of classical integrable systems in string theory. Physical meaning of the appearing structures is discussed and some attempts to find directions of possible generalizations to ``higher-dimensional" models are made. We also speculate on the possible appearence of quantum integrable structures in string theory.Comment: lecture given at III Baltic Rim student seminar, Helsinki, September 1993} 33pp, late

Quantitative uniqueness for elliptic equations with singular lower order terms

We use a Carleman type inequality of Koch and Tataru to obtain quantitative estimates of unique continuation for solutions of second order elliptic equations with singular lower order terms. First we prove a three sphere inequality and then describe two methods of propagation of smallness from sets of positive measure.Comment: 23 pages, v2 small changes are done and some mistakes are correcte

M-Theory of Matrix Models

Small M-theories unify various models of a given family in the same way as the M-theory unifies a variety of superstring models. We consider this idea in application to the family of eigenvalue matrix models: their M-theory unifies various branches of Hermitean matrix model (including Dijkgraaf-Vafa partition functions) with Kontsevich tau-function. Moreover, the corresponding duality relations look like direct analogues of instanton and meron decompositions, familiar from Yang-Mills theory.Comment: 12 pages, contribution to the Proceedings of the Workshop "Classical and Quantum Integrable Systems", Protvino, Russia, January, 200