| In 1997,the paper,Int.J.Theor.Phys.38(1999)1113-1133,Adv.Theor.Math.Phys.2(1998)231-252,pointed out that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-de Sitter spacetimes,spheres and other compact manifolds.This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk.They observed that,in this limit of low energy and large N,one can still trust the near horizon geometry.The improved supersymmetries of the near horizon geometry are dual to the extra supersymmetry generators appear at the superconformal group(as opposed to just the super-Poincare group).The 't Hooft limit of 4-d = 4super-Yang-Mills at the conformal point is proved to contain IIB strings.So they conjectured that compactifications of M/string theory on different Antide Sitter spacetimes corresspond to various conformal field theories.This causes a new advise for a definition of M-theory which could be extended to contain five non-compact dimensions.In 1998,the paper,Adv.Theor.Math.Phys.2(1998)253-291 elaborated on above idea and put forward an accurate correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity.Specially,dimensions of operators in conformal field theory are given by masses of particles in supergravity.As quantitative proof of this correspondence,they noted that the Kaluza-Klein modes of Type IIB supergravity on (95× 5 spacetime match with the chiral operators of = 4 super Yang-Mills theory in four dimensions.With some further assumptions,one can deduce a Hamiltonian version of the correspondence and show that the = 4 theory has a large N phase transition closely related to the thermodynamics of Ad S black holes.In addition,the paper,Phys.Rev.Lett.104(2010)212001,showed that using highenergy heavy-ion collisions at the Relativistic Heavy Ion Collider(RHIC)and the Large Hadron Collider(LHC)one can study the behavior of QCD at high energy densities.Very strong color electric and color magnetic fields are produced during these collisions.In addition,very strong(electromagnetic)magnetic fields are present in non-central collisions,albeit for a extremely short time.By simulating the finite temperature magnetized background at the Relativistic Heavy Ion Collider and LHC energies,we systematically study the characteristics of the thermal width and potential of heavy quarkonia.It is found that the magnetic field has less influence on the real potential but has a significant influence on the imaginary potential,especially in the low deconfined temperature.Extracted from the effect of thermal worldsheet fluctuations about the classical configuration,the thermal width of ?(1)at the finite temperature magnetized background is investigated.It is found that at the low deconfined temperature the magnetic field can generate a significant thermal fluctuation of the thermal width of ?(1),but with the increase of temperature,the effect of magnetic field on the thermal width becomes less important,which means the effect of high temperature completely exceeds that of magnetic field and magnetic field becomes less important at high temperature.The thermal width decreases with the increasing rapidity at the finite temperature magnetized background.It is also observed that the effect of the magnetic field on the thermal width when the dipole is moving perpendicular to the magnetic field is larger than that moving parallel to the magnetic field at Tc <T<1.5Tc,which implies that the magnetic field tends to enhance thermal fluctuation when the dipole is moving perpendicular to magnetic field,but when T>2Tc,the effect of magnetic field on the thermal fluctuation is almost the same whether dipole moving perpendicular or parallel to the magnetic field. |
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