Chung-I Tan

Strings at high energy densities and complex temperature

We discuss quantum and classical statistical mechanics of springs at high energy densities using a complex temperature formalism. The high energy behavior of the microcanonical distribution is governed by the singularities of the canonical partition function in the complex β-plane. We identify the nature and locations of the singularities in addition to the Hagedorn singularity for strings in both compact and noncompact spaces and deduce thermodynamic properties from the resulting microcanonical distribution.

Symmetry breaking in the double-well hermitian matrix models

We study symmetry breaking in Z2 symmetric large N matrix models. In the planar approximation for both the symmetric double-well φ4 model and the symmetric Penner model, we find there is an infinite family of broken symmetry solutions characterized by different sets of recursion coefficients Rn and Sn that all lead to identical free energies and eigenvalue densities. These solutions can be parameterized by an arbitrary angle θ(x), for each value of x = n/N<1. In the duoble scaling limit, this class reduces to a smaller family of solutions with distinct free energies already at the torus level. For the double-well φ4 theory the double scaling string equations are parameterized by a conserved angular momentum parameter in the range 0 ⩽ l < ∞ and a single arbitrary U(1) phase angle.

Forward scattering at collider energies and eikonal unitarization of the odderon

Abstract The continuing increase of hadron total cross sections up to the highest energies currently available can most naturally be understood through an eikonal mechanism, leading to the saturation of the Froissart bound. This picture can be motivated in a nonperturbative treatment of QCD, e.g., in the large- N limit. It is then natural to ask whether this same mechanism would lead to the maximal allowed behavior for the difference of the particle-particle and antiparticle-particle cross section, i.e., the “maximal odderon”. We shall show in this paper that, using eikonals which are dynamically meaningful for high-energy hadron-hadron scattering at collider energies, this behavior is not possible.

Phase structure of large-N lattice QCD with mixed fundamental-adjoint action☆

Abstract The diagram for the N = ∞ lattice QCD with a mixed fundamental-adjoint plaquette action is discussed. The general expectations are substantiated by treating first QCD 2 analytically and then case of the higher dimensions by a variational meanfield analysis.

High energy amplitude as an admixture of ‘soft’ and ‘hard’ Pomerons

Abstract In this paper an attempt is made to find an interface of the perturbative BFKL Pomeron with the non-perturbative Pomeron originating from non-perturbative QCD phenomena such as QCD instantons and/or scale anomaly. The main idea is that the non-perturbative Pomeron involves a large scale ( M 0 ≈2 GeV), which is larger than the scale from which perturbative QCD is applicable. One key result is that even for processes involving a large hard scale (such as DIS) the low x behavior is determined by an effective Pomeron with an intercept having an essential non-perturbative QCD contribution.

New structure in the energy spectrum of reggeon quantum mechanics with quartic couplings

Abstract We find general that the energy spectrum of the reggeon hamiltonian with cubic plus quartic interactions at D =0 is more complicated than previously assumed. We observe the phenomenon of “ground state oscillation”, which suggests, for D ≠ 0, the existence of multiple phases. We find that for certain values of the parameters of the theory complex energy eigenvalues occur. We also find complicated level crossings among higher eigenvalues as the quartic coupling strength is increased.

Can pions be the dominant linkage in multiperipheral cluster models

Abstract The consequence of pion-pole dominance in multiperipheral cluster models is investigated. It is shown that the observed size of hadronic total cross sections and the observed average multiplicities are incompatible with the premise that the dominant high energy production is the repeated-pion-exchange in a multiperipheral cluster chain. We discuss implications of our findings and comment on various alternatives for the search of a realistic multiperipheral cluster model.

Reduced large-N lattice gauge theory without spontaneous symmetry breaking

Abstract A reduced finite lattice theory with a U(1) symmetry is constructed whoch solved the large- N limit of the standard Wilson lattice gauge theory, without spontaneous symmetry breaking. In a consistent-field treatment, it is comparable to the quenched version of the Eguchi-Kawai model. A simple conjecture for an alternate model is also proposed.

Test of Pomeron-f identity hypothesis

Abstract We test the Pomeron-f identity hypothesis with total cross sections and vector meson production data. The model of Chew-Rosenzweig and other less restrictive models are shown to fail. Our analysis suggests, however, that this hypothesis may be tenable if baryonium mixing and/or overlapping clusters in the cylinder topology are taken into account.

Universality violation and large N interpolations

Abstract The restoration of universality based on a large N motivated asymptotically free scaling formula is re-examined. A mixed SU (N) − SU (N) Z 2 system which serves as a counter-example to teh reduction scheme of Grossman and Samuel is studied. However, a certain general universal pattern for the constant string tension lines is observed.