arXiv subjects
Publications and source records attributed to D. T. Son.
It is pointed out that $K^0$ condensation in high density matter gives rise to an extremely light Goldstone boson whose mass comes entirely from weak interactions. This implies the existence of metastable non-topological domain walls with a long lifetime. We comment on the mass of the superfluid mode if baryon number is violated.
We discuss QCD with two light flavors at large baryon chemical potential mu. Color superconductivity leads to partial breaking of the color SU(3) group. We show that the infrared physics is governed by the gluodynamics of the remaining SU(2) group with an exponentially soft confinement scale Lambda_QCD' Delta*exp[-a*mu/(g*Delta)], where Delta<<mu is the superconducting gap, g is the strong coupling, and a=0.81... We estimate that at moderate baryon densities Lambda_QCD' is O(10 MeV) or smaller. The confinement radius increases exponentially with density, leading to "asymptotic deconfinement." The velocity of the SU(2) gluons is small due to the large dielectric constant of the medium.
Using the anti-de Sitter/conformal field theory correspondence, we relate the shear viscosity ηof the finite-temperature N=4 supersymmetric Yang-Mills theory in the large N, strong-coupling regime with the absorption cross section of low-energy gravitons by a near-extremal black three-brane. We show that in the limit of zero frequency this cross section coincides with the area of the horizon. From this result we find η=π/8 N^2T^3. We conjecture that for finite 't Hooft coupling (g_YM)^2N the shear viscosity is η=f((g_YM)^2N) N^2T^3, where f(x) is a monotonic function that decreases from O(x^{-2}\ln^{-1}(1/x)) at small x to π/8 when x\to\infty.
We show that in very dense quark matter there must exist metastable domain walls where the axial U(1) phase of the color-superconducting condensate changes by 2pi. The decay rate of the domain walls is exponentially suppressed and we compute it semiclassically. We give an estimate of the critical chemical potential above which our analysis is under theoretical control.
A Coulomb gas representation of dense-matter QCD is derived from a dual transformation of the low-energy effective Lagrangian. The point-like charges Q=+1,-1 of the gas are identified with the instantons and anti-instantons of such topological charges. An instanton repels another instanton with the same force as it attracts an anti-instanton, in contrast to the semiclassical interaction.
We describe how thermalization occurs in heavy ion collisions in the framework of perturbative QCD. When the saturation scale $Q_s$ is large compared to $Λ_{QCD}$, thermalization takes place during a time of order $α^{-13/5}Q_s^{-1}$ and the maximal temperature achieved is $α^{2/5}Q_s$.
QCD at finite isospin chemical potential mu_I has no fermion sign problem and can be studied on the lattice. We solve this theory analytically in two limits: at low mu_I where chiral perturbation theory is applicable, and at asymptotically high mu_I where perturbative QCD works. At low isospin density the ground state is a pion condensate, whereas at high density it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pion. This leads us to a conjecture that the transition from hadron to quark matter is smooth, which passes several tests. Our results imply a nontrivial phase diagram in the space of temperature and chemical potentials of isospin and baryon number.
We use 2-color QCD as a model to study the effects of simultaneous presence of chemical potentials for isospin charge, $μ_I$, and for baryon number, $μ_B$. We determine the phase diagrams for 2 and 4 flavor theories using the method of effective chiral Lagrangians at low densities and weak coupling perturbation theory at high densities. We determine the values of various condensates and densities as well as the spectrum of excitations as functions of $μ_I$ and $μ_B$. A similar analysis of QCD with quarks in the adjoint representation is also presented. Our results can be of relevance for lattice simulations of these theories. We predict a phase of inhomogeneous condensation (Fulde-Ferrel-Larkin-Ovchinnikov phase) in the 2 colour 2 flavor theory, while we do not expect it the 4 flavor case or in other realizations of QCD with a positive measure.
QCD at finite isospin chemical potential mu_I is studied. This theory has no fermion sign problem and can be simulated on the lattice using present-day techniques. We solve this theory analytically in two limits: low mu_I where chiral perturbation theory is applicable, and asymptotically high mu_I where perturbative QCD is at work. At low isospin density the ground state is a superfluid pion condensate. At very high density it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pions. Motivated by this observation, we put forward a conjecture that the transition from hadron to quark matter is smooth. The conjecture passes several nontrivial tests. Our results imply a nontrivial phase diagram in the space of temperature and chemical potentials of isospin and baryon number. At asymtotically large values of mu_I and small values of baryon chemical potential the ground state is in a phase similar to Fulde-Ferrell-Larkin-Ovchinnikov phase. It is characterized by a spatially modulated superfluid order parameter and may be the asymptotic limit of the inhomogeneous pion condensation phase advocated by Migdal and others.
We show how hydrodynamics of relativistic system with broken continuous symmetry can be constructed using the Poisson bracket technique. We illustrate the method on the example of relativistic superfluids.
Using the Poisson bracket method, we construct the hydrodynamics of nuclear matter in the chiral limit, which describes the dynamics of all low-energy degrees of freedom, including the fluid-dynamical and pionic ones. The hydrodynamic equations contain, beside five Euler equations of relativistic fluid dynamics, Nf^2-1 second order equations describing propagating pions and Nf^2-1 first order equations describing the advection of the baryonic vector isospin charges. We present hydrodynamic arguments showing that the pion velocity vanishes at the second order phase transition at Nf=2.
We correct a mistake in the calculation of meson masses at large baryon chemical potential made in hep-ph/9910491v2
We derive the effective Lagrangian for the low-energy massive meson excitations of the color-flavor-locking (CFL) phase of QCD with 3 flavors of light quarks. We compute the decay constants, the maximum velocities, and the masses of the mesons at large baryon chemical potential mu. The decay constants are linear in mu. The meson maximum velocities are close to that of sound. The meson masses in the CFL phase are significantly smaller than in the normal QCD vacuum and depend only on bare quark masses. The order of the meson masses is, to some extent, reversed compared to that in the QCD vacuum. In particular, the lightest particle is eta'.
Deryagin, Grigoriev, and Rubakov (DGR) have shown that in finite-density QCD at infinite Nc the Fermi surface is unstable with respect to the formation of chiral waves with wavenumber twice the Fermi momentum, while the BCS instability is suppressed. We show here that at large, but finite Nc, the DGR instability only occurs in a finite window of chemical potentials from above Lambda_QCD to mu_critical = exp(gamma ln^2 Nc + O(ln Nc ln ln Nc))Lambda_QCD, where gamma = 0.02173. Our analysis shows that, at least in the perturbative regime, the instability occurs only at extremely large Nc, Nc > 1000 Nf, where Nf is the number of flavors. We conclude that the DGR instability is not likely to occur in QCD with three colors, where the ground state is expected to be a color superconductor. We speculate on possible structure of the ground state of finite-density QCD with very large Nc.
We show that the decay of a passive scalar $θ$ advected by a random incompressible flow with zero correlation time in Batchelor limit can be mapped exactly to a certain quantum-mechanical system with a finite number of degrees of freedom. The Schroedinger equation is derived and its solution is analyzed for the case when at the beginning the scalar has Gaussian statistics with correlation function of the form $e^{-|x-y|^2}$. Any equal-time correlation function of the scalar can be expressed via the solution to the Schroedinger equation in a closed algebraic form. We find that the scalar is intermittent during its decay and the average of $|θ|^α$ (assuming zero mean value of $θ$) falls as $e^{-γ_αDt}$ at large $t$, where $D$ is a parameter of the flow, $γ_α=α(6-α)/4$ for $0<α<3$, and $γ_α=9/4$ for $α\geq 3$, independent of $α$.
We argue that in quark matter at high densities, the color magnetic field remains unscreened and leads to the phenomenon of color superconductivity. Using the renormalization group near the Fermi surface, we find that the long-range nature of the magnetic interaction changes the asymptotic behavior of the gap $Δ$ at large chemical potential $μ$ qualitatively. We find $Δ\simμg^{-5}\exp(-{3π^2\over\sqrt{2}}{1\over g})$, where $g$ is the small gauge coupling. We discuss the possibility of breaking rotational symmetry by the formation of a condensate with nonzero angular momentum, as well as interesting parallels to some condensed matter systems with long-range forces.
We show that the decaying magnetohydrodynamic turbulence leads to a more rapid growth of the correlation length of a primordial magnetic field than that caused by the expansion of the Universe. As an example, we consider the magnetic fields created during the electroweak phase transition. The expansion of the universe alone would yield a correlation length at the present epoch of 1 AU, whereas we find that the correlation length is likely of order 100 AU, and cannot possibly be longer than $10^4$ AU for non-helical fields. If the primordial field is strongly helical, the correlation length can be much larger, but we show that even in this case it cannot exceed 100 pc. All these estimates make it hard to believe that the observed galactic magnetic fields can result from the amplification of seed fields generated at the electroweak phase transition by the standard galactic dynamo.
We derive, from first principle, the Fokker-Planck equation describing the non-perturbative real-time evolution of a gauge field at high temperatures on the spatial scale $(g^2T)^{-1}$ and the time scale $(g^4T)^{-1}$, where $g$ is the gauge coupling and $T$ is the temperature. The knowledge of the effective dynamics on such spatial and time scales is crucial for the understanding and quantitative calculation of the baryon number violation rate at high temperatures in the electroweak theory. The Fokker-Planck equation, which describes the diffusive motion of soft components of the gauge field in the space of field configurations, is shown to be gauge-invariant and consistent with the known thermodynamics of soft gauge modes. We discuss the ways the Fokker-Planck equation can be made useful for numerical simulations of long-distance dynamics of hot gauge theories.