Some New/Old Approaches to QCD

This is a talk delivered at the Meeting on Integrable Quantum Field Theories, Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent attempts to revive two old ideas regarding an analytic approach to QCD-the development of a string representation of the theory and the large N limit of QCD.Comment: 20 page

Quark-Gluon Plasma - New Frontiers

As implied by organizers, this talk is not a conference summary but rather an outline of progress/challenges/``frontiers'' of the theory. Some fundamental questions addressed are: Why is sQGP such a good liquid? Do we understand (de)confinement and what do we know about ``magnetic'' objects creating it? Can we understand the AdS/CFT predictions, from the gauge theory side? Can they be tested experimentally? Can AdS/CFT duality help us understand rapid equilibration/entropy production? Can we work out a complete dynamical ``gravity dual'' to heavy ion collisions?Comment: final talk at Quark Matter 2008, Jaipur, India, Feb.200

An amphitropic cAMP-binding protein in yeast mitochondria

ABSTRACT: We describe the first example of a mitochondrial protein with a covalently attached phos-phatidylinositol moiety acting as a membrane anchor. The protein can be metabolically labeled with both stearic acid and inositol. The stearic acid label is removed by phospholipase D whereupon the protein with the retained inositol label is released from the membrane. This protein is a cAMP receptor of the yeast Saccharomyces cereuisiae and tightly associated with the inner mitochondrial membrane. However, it is converted into a soluble form during incubation of isolated mitochondria with Ca2+ and phospholipid (or lipid derivatives). This transition requires the action of a proteinaceous, N-ethylmaleimide-sensitive component of the intermembrane space and is accompanied by a decrease in the lipophilicity of the cAMP receptor. We propose that the component of the intermembrane space triggers the amphitropic behavior of the mitochondrial lipid-modified CAMP-binding protein through a phospholipase activity. Only in recent years specific fatty acids have been recog-nized to play important roles in the association of proteins with membranes. Both noncovalent and covalent interactions be-tween fatty acids and proteins have been reported. Among the latter are GTP-binding proteins (Molenaar et al., 1988)

Exponentiation of Multiparticle Amplitudes in Scalar Theories

It is argued that the amplitudes of the production of $n$ soft scalar particles by one or a few energetic ones in theories like $\lambda\phi^4$ has the exponential form, $A_n\propto\sqrt{n!}\exp[{1\over\lambda}F(\lambda n,\epsilon)]$, in the regime $\lambda\to 0$, $\lambda n={fixed}$, $\epsilon={fixed}$, where $\epsilon$ is the typical kinetic energy of outgoing particles. Existing results support this conjecture. Several new analytical and numerical results in favor of the exponential behavior of multiparticle amplitudes are presented.Comment: Revtex 3.0, 45 pages, 11 figures (some requires bezier.sty, two postscript figures appended after \end{document}), INR-866/9

High Temperature Limit of the Confining Phase

The deconfining transition in non-Abelian gauge theory is known to occur by a condensation of Wilson lines. By expanding around an appropriate Wilson line background, it is possible at large $N$ to analytically continue the confining phase to arbitrarily high temperatures, reaching a weak coupling confinement regime. This is used to study the high temperature partition function of an $SU(N)$ electric flux tube. It is found that the partition function corresponds to that of a string theory with a number of world-sheet fields that diverges at short distance.Comment: 13 page

d dimensional SO(d)-Higgs Models with Instanton and Sphaleron: d=2,3

The Abelian Higgs model and the Georgi-Glashow model in 2 and 3 Euclidean dimensions respectively, support both finite size instantons and sphalerons. The instantons are the familiar Nielsen-Oleson vortices and the 't Hooft-Polyakov monopole solutions respectively. We have constructed the sphaleron solutions and calculated the Chern-Simons charges N_cs for sphalerons of both models and have constructed two types of noncontractible loops between topologically distinct vacuua. In the 3 dimensional model, the sphaleron and the vacuua have zero magnetic and electric flux while the configurations on the loops have non vanishing magnetic flux.Comment: 24 pages, 3 figures, LaTe

Phenomenological Equations of State for the Quark-Gluon Plasma

Two phenomenological models describing an SU(N) quark-gluon plasma are presented. The first is obtained from high temperature expansions of the free energy of a massive gluon, while the second is derived by demanding color neutrality over a certain length scale. Each model has a single free parameter, exhibits behavior similar to lattice simulations over the range T_d - 5T_d, and has the correct blackbody behavior for large temperatures. The N = 2 deconfinement transition is second order in both models, while N = 3,4, and 5 are first order. Both models appear to have a smooth large-N limit. For N >= 4, it is shown that the trace of the Polyakov loop is insufficient to characterize the phase structure; the free energy is best described using the eigenvalues of the Polyakov loop. In both models, the confined phase is characterized by a mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop expectation value zero. In the deconfined phase, the rotation of the eigenvalues in the complex plane towards 1 is responsible for the approach to the blackbody limit over the range T_d - 5T_d. The addition of massless quarks in SU(3) breaks Z(3) symmetry weakly and eliminates the deconfining phase transition. In contrast, a first-order phase transition persists with sufficiently heavy quarks.Comment: 22 pages, RevTeX, 9 eps file

Weak coupling large-N transitions at finite baryon density

We study thermodynamics of free SU(N) gauge theory with a large number of colours and flavours on a three-sphere, in the presence of a baryon number chemical potential. Reducing the system to a holomorphic large-N matrix integral, paying specific attention to theories with scalar flavours (squarks), we identify novel third-order deconfining phase transitions as a function of the chemical potential. These transitions in the complex large-N saddle point configurations are interpreted as "melting" of baryons into (s)quarks. They are triggered by the exponentially large (~ exp(N)) degeneracy of light baryon-like states, which include ordinary baryons, adjoint-baryons and baryons made from different spherical harmonics of flavour fields on the three-sphere. The phase diagram of theories with scalar flavours terminates at a phase boundary where baryon number diverges, representing the onset of Bose condensation of squarks.Comment: 38 pages, 7 figure

Semiquantal dynamics of fluctuations: Ostensible quantum chaos

The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be derived via the Ehrenfest theorem and recast as an extended classical gradient system with the fluctuation variables coupled to the average variables. An extended potential is constructed for a one-dimensional system. The semiquantal behavior is shown to be chaotic even though the system has regular classical behavior and the quantum behavior had been assumed regular.Comment: 9 pages, TeX, 2 figures (not attached; hard copies available immediately on request). To appear in Physical Review Letter