D0-Branes As Light-Front Confined Quarks

We argue that different aspects of Light-Front QCD at confined phase can be recovered by the Matrix Quantum Mechanics of D0-branes. The concerning Matrix Quantum Mechanics is obtained from dimensional reduction of pure Yang-Mills theory to 0+1 dimension. The aspects of QCD dynamics which are studied in correspondence with D0-branes are: 1) phenomenological inter-quark potentials, 2) whiteness of hadrons and 3) scattering amplitudes. In addition, some other issues such as the large-N behavior, the gravity--gauge theory relation and also a possible justification for involving ``non-commutative coordinates'' in a study of QCD bound-states are discussed.Comment: 26 pages, LaTeX file, 3 .eps figures; v2: language is improved; v3: subsection 4.2 is changed- accepted for publication in EPJ.

First-Order Phase Transition by XY Model of Particle Dynamics

A gas-liquid type of phase transition is found based on the particle dynamics on radius-$R$ circle in which the coordinate appears as the angle-variable of 1D XY-model. Due to the specific appearance of compact-space radius (volume) in the present interpretation of XY-model, the ground-state develops a minimum at some critical radius, leading to the multi-valued Gibbs energy similar to systems with first-order phase transition.Comment: v1: LaTeX, 7 pages, 3 figs; v2: 9 pages, 5 figs, detailed comparison with magnetic system interpretation of XY-model is presented. Accepted for EP

Lost in Normalization

The consequences of the gauge-coupling dependent normalization-factor of $1/g^{\alpha}$ in the transfer-matrix of 2d U(1) lattice gauge theory are explored. It is seen by the $\alpha=1$ choice that the lowest energy develops a minimum at coupling $g_*=1.125$, leading to a \textit{multi-valued} Gibbs energy similar to the systems with the first-order phase transition. It is argued how the $1/g$ normalization may be regarded as a lost normalization in the commonly used change of variable to the dimensionless angle-variables. Based on the continuum limit at the next-leading order and the Ostrogradsky formulation of higher-order time-derivatives theories, it is argued that the spectrum at continuum is compatible only with the $\alpha=1$ choice.Comment: v1: LaTeX, 9 pages, 1 fig. v2: the power in E_0 is corrected based on proper normalization; abstract and title are modified. v3: presentation and title are changed (old title: On Significance of Transfer-Matrix Normalization in Lattice Gauge Theories), to appear in EP