Note on Nonlinear Schr\"odinger Equation, KdV Equation and 2D Topological Yang-Mills-Higgs Theory

In this paper we discuss the relation between the (1+1)D nonlinear Schr\"odinger equation and the KdV equation. By applying the boson/vortex duality, we can map the classical nonlinear Schr\"odinger equation into the classical KdV equation in the small coupling limit, which corresponds to the UV regime of the theory. At quantum level, the two theories satisfy the Bethe Ansatz equations of the spin-$\frac{1}{2}$ XXX chain and the XXZ chain in the continuum limit respectively. Combining these relations with the dualities discussed previously in the literature, we propose a duality web in the UV regime among the nonlinear Schr\"odinger equation, the KdV equation and the 2D $\mathcal{N}=(2,2)^*$ topological Yang-Mills-Higgs theory.Comment: 20 pages, 1 figure; V2: typos correcte

Gravity Dual of Two-Dimensional N=(2,2)∗\mathcal{N} = (2,2)^* Supersymmetric Yang-Mills Theory and Integrable Models

The 2D $\mathcal{N}=(2,2)^*$ supersymmetric Yang-Mills theory can be obtained from the 2D $\mathcal{N}=(4,4)$ theory with a twisted mass deformation. In this paper we construct the gravity dual theory of the 2D $\mathcal{N}=(2,2)^*$ supersymmetric $U(N)$ Yang-Mills theory at the large $N$ and large 't Hooft coupling limit using the 5D gauged supergravity. In the UV regime, this construction also provides the gravity dual of the 2D $\mathcal{N}=(2,2)^*$ $U(N)$ topological Yang-Mills-Higgs theory. We propose a triality in the UV regime among integrable model, gauge theory and gravity, and we make some checks of this relation at classical level.Comment: 49 pages, 3 figures; V2: typos corrected, more discussions adde

Jet Tomography of Quark Gluon Plasma

Recent experimental measurements of high $p_T$ hadron spectra and jet correlation at RHIC are analyzed within a parton model which incoporates initial jet production and final propagation in heavy-ion collisions. The suppresion of single hadron spectra, back-to-back correlation, their centrality dependence and azimuthal anisotropy point to a dense matter with an initial parton density about 30 times of that in a cold heavy nucleus.Comment: 7 pages in RevTex, 4 figures. Invited talk at Confinement 2003-International Symposium on ``Color Confinement and Hadrons in Quantum Chromodynamics", RIKEN, Japan, July 21-24, 2003 and XXIV Brazilian Meeting of Particle and Field Physics, Caxambu, Brazil, Oct. 1-3, 200

Modified Fragmentation Function and Jet Quenching at RHIC

Medium modification of jet fragmentation functions and parton energy loss in cold and hot matter are reviewed. The predicted nuclear modification of the jet fragmentation function agrees well with the recent HERMES data with a resultant energy loss dE/dx approximately 0.5 GeV/fm. From the the recent PHENIX data of high p_T pi_0 spectra in central Au+Au collisions at sqrt(s)=130 GeV, one extracts an energy loss for a 10 GeV parton that is equivalent to dE/dx=7.3 GeV/fm in a static medium with the same gluon density as in the initial stage of the collision at tau_0=0.2 fm/c. Constraints on jet quenching by the central rapidity density of charged hadrons is also discussed.Comment: Invited talk at International Symposium on Statistical QCD, Bielefeld, Germany, 26-30 Aug 2001; 11 pages with 6 postscript figure

Hard Probes in High-energy Heavy-ion Collisions

Hard QCD processes in ultrarelativistic heavy-ion collisions become increasingly relevant and they can be used as probes of the dense matter formed during the violent scatterings. We will discuss how one can use these hard probes to study the properties of the dense matter and the associated phenomenologies. In particular, we study the effect of jet quenching due to medium-induced energy loss on inclusive particle $p_T$ distributions and investigate how one can improve the measurement of parton energy loss in direct photon eventsComment: Talk given at the International School on Physics of the Quark Gluon Plasma, Hiroshima, June 3-6, 1997 and the 5th International Workshop on Relativistic Aspects of Nuclear Physics, Rio de Janeiro, August 27-29. 17 pages with 9 ps figure