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Romuald A. Janik

Publications and source records attributed to Romuald A. Janik.

At least 109 records · Page 6Linked to original sources
arXiv2000

String Fluctuations, AdS/CFT and the Soft Pomeron Intercept

We study high energy scattering amplitudes in a strongly coupled (confining) gauge theory using the AdS/CFT correspondence. The scattering described by a Wilson line/loop correlation function was shown earlier to correspond to minimal surfaces of the helicoid type, and gave amplitudes with unit intercept and linear trajectory. In this paper we find the correction to the intercept from quadratic fluctuations of the string worldsheet around the helicoid. The relevant term comes from analytical continuation of a Lüscher like term. It is coupling-constant independent and proportional to the number of effective transverse flat dimensions. The shift of the intercept, under our assumptions, is $n_\perp /96$, and for $n_\perp=7,8$ gives respectively 0.0729, 0.083. Incidentally we note that this is surprisingly close to the observed value of 0.08.

hep-th↗
arXiv1999

U(1) Problem at Finite Temperature

We model the effects of a large number of zero and near-zero modes in the QCD partition function by using sparse chiral matrix models with an emphasis on the quenched topological susceptibility in the choice of the measure. At finite temperature, the zero modes are not affected by temperature but are allowed to pair into topologically neutral near-zero modes which are gapped at high temperature. In equilibrium, chiral and U(1) symmetry are simultaneously restored for total pairing, evading mean-field arguments. We analyze a number of susceptibilities versus the light quark masses. At the transition point the topological susceptibility vanishes, and the dependence on the vacuum angle $θ$ drops out. Our results are briefly contrasted with recent lattice simulations.

hep-lat↗
arXiv1999

Gauge Theory Scattering from the AdS/CFT correspondence

We use the AdS/CFT correspondence to study near forward scattering of colourless objects in gauge theory in the high energy limit. We find an unexpected from the gauge theory perspective `gravity-like' s^1 behaviour of the amplitudes coming from bulk graviton exchange. The details of the calculations are presented in hep-th/9907177.

hep-th↗
arXiv1999

Chiral Disorder in Two-Color QCD with Abelian External Fluxes

We investigate the effects of several Abelian external fluxes $ϕ$, on the Euclidean Dirac spectrum of light quarks in QCD with two colors. Our results provide for a novel way of assessing the pion weak decay constant directly from spectral fluctuations, and discriminating a flux-rich from a flux-poor vacuum, using QCD lattice simulations.

hep-lat↗
arXiv1999

Green's Functions in Non-hermitian Random Matrix Models

We review some recent techniques for dealing with non-hermitian random matrix models based on generalized Green's functions. We introduce the diagrammatic methods in the hermitian case and generalize them to the non-hermitian case. The results are illustrated in terms of the eigenvalue distribution, eigenvector statistics and addition laws.

cond-mat.dis-nn↗
arXiv1999

The perturbative odderon intercept

We present our recent results on the odderon intercept in perturbative QCD, obtained through the solution of the Baxter equation and investigation of the spectrum of the relevant constant of motion.

hep-ph↗
arXiv1999

$θ$ Vacuum in a Random Matrix Model

Inspired by recent lattice calculations, we model certain aspects of the $θ$-vacuum using a matrix model with gaussian weights. The vacuum energy exhibits a cusp at $θ<π$ that is sensitive to both the accuracy of the numerical analysis and the maximum density of winding modes present in a finite volume.

hep-ph↗
arXiv1999

Chiral Disorder and Diffusion in The QCD Vacuum

In this talk, which popularizes some of our recent work, we provide novel insights into the bulk properties of light chiral quarks in a fixed Euclidean volume (e.g. lattice QCD). We show that the spontaneous breakdown of chiral symmetry results into diffusing quarks with a vacuum diffusion constant $D=2F_π^2/|<\bar{q}q>|$ $\approx 0.22$ fm, in striking analogy to diffusing electrons in disordered metals in one-, two- and three-dimensions.

hep-ph↗
arXiv1999

$θ$ Vacuum: A Matrix Model

We model the effects of a large number of zero modes for $N_f$ species of quarks at finite vacuum angle $θ$, using a matrix model with gaussian weights constrained by the topological susceptibility and compressibility. The quenched free energy exhibits a cusp at $θ<π$ that is sensitive to the accuracy of the numerical analysis and the maximum density of winding modes. Our results bear much in common with recent lattice simulations by Schierholtz and others. The unquenched free energy exhibits similar sensitivities, but for small quark masses or a large density of zero modes the results are in agreement with those derived using chiral effective Lagrangians.

hep-ph↗
arXiv1998

Chiral Random Matrix Models in QCD

We review some motivation behind the introduction of chiral random matrix models in QCD, with particular emphasis on the importance of the Gell-Mann-Oakes (GOR) relation for these arguments. We show why the microscopic limit is universal in power counting, and present arguments for why the macroscopic limit is generic for a class of problems that defy power counting, examples being the strong CP and U(1) problems. Some new results are discussed in light of recent lattice simulations.

hep-ph↗
arXiv1998

Chiral Disorder and QCD Phase Transitions

If QCD is to undergo a second order phase transition, the light quark return probability is universal for large times at the critical point. We show that this behavior is distinct from the one expected at the mobility edge of a metal-insulator transition or a percolation transition in d$\leq 4$. Our results are accessible to current lattice QCD simulations.

hep-ph↗
arXiv1998

Two-Color QCD and Aharonov-Bohm Fluxes

We investigate the effects of several Abelian Aharonov-Bohm fluxes $ϕ$ on the Euclidean Dirac spectrum of light quarks in QCD with two colors. A quantitative change in the quark return probability is caused by the fluxes, resulting into a change of the spectral correlations. These changes are controlled by a universal function of $σ_L ϕ^2$ where $σ_L$ is the pertinent Ohmic conductance. The quark return probability is sensitive to Abelian flux-disorder but not to $Z_2$ flux-disorder in the ergodic and diffusive regime, and may be used as a probe for the nature of the confining fields in the QCD vacuum.

hep-ph↗
arXiv1998

Chiral Disorder and Diffusion of Light Quarks in the QCD Vacuum

We give a pedagogical introduction to the concept that light quarks diffuse in the QCD vacuum following the spontaneous breaking of chiral symmetry. By analogy with disordered electrons in metals, we show that the diffusion constant for light quarks in QCD is $D=2F_π^2/|\la\bar{q}q\to|$ which is about 0.22 fm. We comment on the correspondence between the diffusive phase and the chiral phase as described by chiral perturbation theory, as well as the cross-over to the ergodic phase as described by random matrix theory. The cross-over is identified with the Thouless energy $E_c=D/\sqrt{V_4}$ which is the inverse diffusion time in an Euclidean four-volume $V_4$.

hep-ph↗
arXiv1998

Chiral Disorder and QCD at Finite Chemical Potential

We investigate the effects of a finite chemical potential $μ$ in QCD viewed as a disordered medium. In the quenched approximation, $A_4=iμ$ induces a complex electric Aharonov-Bohm effect that causes the diagonal contribution to the quark return probability to vanish at $μ=m_π/2$ (half the pion mass). In two-color QCD, the weak-localization contribution to the quark return probability remains unaffected causing a mutation in the spectral statistics. In full QCD, the complex electric flux is screened and the light quarks are shown to diffuse asymmetrically with a substantial decrease in the conductivity along the `spatial' directions. Mean-field arguments suggest that a d=1 percolation transition may take place in the range $1.5ρ_0<ρ<3ρ_0$, where $ρ_0$ is nuclear matter density.

hep-ph↗
arXiv1998

Random Matrices and Chiral Symmetry in QCD

In this talk we review some recent results from random matrix models as applied to some non-perturbative issues in QCD. All of the issues we will discuss touched upon the important phenomenon related to the spontaneous breaking of chiral symmetry. The afore mentioned insights are: 1. Spontaneous breakdown of chiral symmetry and disorder. 2. Universal microscopic properties of the eigenvalues of the Dirac operator in the vacuum. 3. Universal microscopic properties of the eigenvalues of the Dirac operator in matter. 4. Structural changes of the Dirac spectrum - finite temperature. 5. Structural changes of the Dirac spectrum - finite baryonic density - ``phony vacua'' 6. Structural changes of the Dirac spectrum - finite baryonic density - ``true vacua'' . 7. Phase diagram. 8. Critical parameters. 9. Critical exponents. 10. $U(1)_A$ problem. 11. Screening of the pseudoscalar susceptibility. 12. Strong CP violation (finite $θ$).

hep-ph↗
arXiv1998

New Results on the Odderon in QCD

We present our recent results on the odderon intercept in perturbative QCD, obtained through the solution of the Baxter equation and investigation of the spectrum of the relevant constant of motion.

hep-th↗
arXiv1997

Various Shades of Blue's Functions

We discuss random matrix models in terms of elementary operations on Blue's functions (functional inverse of Green's functions). We show that such operations embody the essence of a number of physical phenomena whether at/or away from the critical points. We illustrate these assertions by borrowing on a number of recent results in effective QCD in vacuum and matter. We provide simple physical arguments in favor of the universality of the continuum QCD spectral oscillations, whether at zero virtuality, in the bulk of the spectrum or at the chiral critical points. We also discuss effective quantum systems of disorder with strong or weak dissipation (Hatano-Nelson localization).

hep-th↗