Could Spin-Charge Separation be the Source of Confinement?

Yang-Mills gauge field with gauge group SU(2) decomposes into a single charge neutral complex vector, and two spinless charged scalar fields. At high energies these constituents are tightly confined into each other by a compact U(1) interaction, and the Yang-Mills Lagrangian describes the dynamics of asymptotically free massless gauge vectors. But in a low energy and finite density environment the interaction between the constituents can become weak, and a spin-charge separation may occur. We suggest that the separation between the spin and charge with the ensuing condensation of the charged scalars takes place when the Yang-Mills theory enters confinement. The confining phase becomes then surprisingly similar to the superconducting phase of a high-$T_c$ superconductor.Comment: Talk presented at QCD@Work 2005 (Conversano

Are Glueballs Knotted Closed Strings?

Glueballs have a natural interpretation as closed strings in Yang-Mills theory. Their stability requires that the string carries a nontrivial twist, or then it is knotted. Since a twist can be either left-handed or right-handed, this implies that the glueball spectrum must be degenerate. This degeneracy becomes consistent with experimental observations, when we identify the $\eta_L(1410)$ component of the $\eta(1440)$ pseudoscalar as a $0^{-+}$ glueball, degenerate in mass with the widely accepted $0^{++}$ glueball $f_0(1500)$. In addition of qualitative similarities, we find that these two states also share quantitative similarity in terms of equal production ratios, which we view as further evidence that their structures must be very similar. We explain how our string picture of glueballs can be obtained from Yang-Mills theory, by employing a decomposed gauge field. We also consider various experimental consequences of our proposal, including the interactions between glueballs and quarks and the possibility to employ glueballs as probes for extra dimensions: The coupling of strong interactions to higher dimensions seems to imply that absolute color confinement becomes lost.Comment: Talk given at International Symposium on Color Confinement and Hadrons in Quantum Chromodynamics - Confinement 2003, Wako, Japan, 21-24 Jul 200

Topological Sigma-model, Hamiltonian Dynamics and Loop Space Lefschetz Number

We use path integral methods and topological quantum field theory techniques to investigate a generic classical Hamiltonian system. In particular, we show that Floer's instanton equation is related to a functional Euler character in the quantum cohomology defined by the topological nonlinear $\sigma$--model. This relation is an infinite dimensional analog of the relation between Poincar\'e--Hopf and Gauss--Bonnet--Chern formul\ae$~$ in classical Morse theory, and can also be viewed as a loop space generalization of the Lefschetz fixed point theorem. By applying localization techniques to path integrals we then show that for a K\"ahler manifold our functional Euler character coincides with the Euler character determined by the finite dimensional de Rham cohomology of the phase space. Our results are consistent with the Arnold conjecture which estimates periodic solutions to classical Hamilton's equations in terms of de Rham cohomology of the phase space.Comment: 10 pages, LaTEX. New title and some modifications in the text. Version to appear in Phys. Lett.

Elliptic flow from event-by-event hydrodynamics

We present an event-by-event hydrodynamical framework which takes into account the initial density fluctuations arising from a Monte Carlo Glauber model. The elliptic flow is calculated with the event plane method and a one-to-one comparison with the measured event plane $v_2$ is made. Both the centrality- and $p_T$-dependence of the $v_2$ are remarkably well reproduced. We also find that the participant plane is a quite good approximation for the event plane.Comment: 4 pages, 3 figures. Talk given at Quark Matter 2011, 22-28 May 2011, Annecy, Franc

On Exact Evaluation of Path Integrals

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