arXiv subjects

Robert D. Pisarski

Publications and source records attributed to Robert D. Pisarski.

At least 73 records · Page 4Linked to original sources

arXiv2013

Gross-Witten-Wadia transition in a matrix model of deconfinement

We study the deconfining phase transition at nonzero temperature in a SU(N) gauge theory, using a matrix model which was analyzed previously at small N. We show that the model is soluble at infinite N, and exhibits a Gross-Witten-Wadia transition. In some ways, the deconfining phase transition is of first order: at a temperature $T_d$, the Polyakov loop jumps discontinuously from 0 to1/2, and there is a nonzero latent heat $\sim N^2$. In other ways, the transition is of second order: e.g., the specific heat diverges as $C \sim 1/(T-T_d)^{3/5}$ when $T \rightarrow T_d^+$. Other critical exponents satisfy the usual scaling relations of a second order phase transition. In the presence of a nonzero background field $h$ for the Polyakov loop, there is a phase transition at the temperature $T_h$ where the value of the loop =1/2, with $T_h < T_d$. Since $\partial C/\partial T \sim 1/(T-T_h)^{1/2}$ as $T \rightarrow T_h^+$, this transition is of third order.

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arXiv2013

Quasi-particle and matrix models of the semi Quark Gluon Plasma

We make a simple observation about two models used to treat the region near the critical temperature of QCD, quasiparticle and matrix models. While they appear very different, we show how these two models might be related. We also present results for the temperature dependence of the ratio of the shear viscosity to the entropy in a matrix model, and suggest that quasi-particle models may behave similarly.

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arXiv2013

The Roberge-Weiss transition and 't Hooft loops

Roberge and Weiss showed that for SU(N) gauge theories, phase transitions occur in the presence of an imaginary quark chemical potential. We show that at asymptotically high temperature, where the phase transition is of first order, that even with dynamical quarks 't Hooft loops of arbitrary Z(N) charge are well defined at the phase boundary. To leading order in weak coupling, the 't Hooft loop satisfies Casimir scaling in the pure glue theory, but not with quarks. Because the chemical potential is imaginary, typically the interaction measure is negative on one side of the phase transition. Using a matrix model to model the deconfining phase transition, we compute the phase diagram for heavy quarks, in the plane of temperature and imaginary chemical potential. In general we find intersecting lines of first order transitions. Using a modified Polyakov loop which is Roberge-Weiss symmetric, we suggest that the interface tension is related to the 't Hooft loop only at high temperature, where the imaginary part of this Polyakov loop, and not the real part, is discontinuous across the phase boundary.

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arXiv2013

Zero interface tension at the deconfining phase transition for a matrix model of a $SU(\infty)$ gauge theory

Using a matrix model, we model the deconfining phase transition at nonzero temperature for a SU(N) gauge theory at large $N$. At infinite $N$ the matrix model exhibits a Gross-Witten-Wadia transition. We show that as a consequence, both the order-disorder and the order-order interface tensions vanish identically at the critical temperature $T_d$. We estimate how these quantities vanish in the matrix model as $T \rightarrow T_d$ and as $N \rightarrow \infty$. The numerical solution of the matrix model suggests possible non-monotonic behavior in $N$ for relatively small values of $N \sim 5$.

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arXiv2012

Interweaving Chiral Spirals

We elaborate how to construct interweaving chiral spirals in (2+1) dimensions, defined as a superposition of chiral spirals oriented in different directions. We divide a two-dimensional Fermi sea into distinct wedges, characterized by the opening angle 2Theta and depth Q ~ pF, where pF is the Fermi momentum. In each wedge, the energy is lowered by forming a single chiral spiral. The optimal values for Theta and Q are chosen by balancing this gain in energy versus the cost of deforming the Fermi surface (which dominates at large Theta) and patch-patch interactions (dominant at small Theta). Using a non-local four-Fermi interaction model, we estimate the gain and cost in energy by expanding in terms of 1/Nc (where Nc is the number of colors), lqcd/Q, and Theta. Due to a form factor in our non-local model, at small 1/Nc the mass gap (chiral condensate) is large, and the interaction among quarks and the condensate local in momentum space. Consequently, interactions between different patches are localized near their boundaries, and it is simple to embed many chiral spirals. We identify the dominant and subdominant terms at high density and categorize formulate an expansion in terms of lqcd/Q or Theta. The kinetic term in the transverse directions is subdominant, so that techniques from (1+1)-dimensional systems can be utilized. To leading order in 1/Nc and lqcd/Q, the total gain in energy is ~ pF lqcd^2 with Theta ~ (lqcd/pF)^{3/5}. Since Theta decreases with increasing pF, there should be phase transitions associated with the change in the wedge number. We also argue the effects of subdominant terms at lower density where the large-Nc approximation is more reliable.

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arXiv2012

Electroweak Instantons, Axions, and the Cosmological Constant

If there is explicit violation of baryon plus lepton number at some energy scale, then the electroweak theory depends upon a θ-angle. Due to a singular integration over small scale size instantons, this θ-dependence is sensitive to very high momentum scales. Assuming that there is no new physics between the electroweak and Planck scales, for an electroweak axion the energy difference between the vacuum at θ /= 0, and that at θ = 0, is of the correct order of magnitude to be the dark energy observed in the present epoch.

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arXiv2012

Critical endpoint for deconfinement in matrix and other effective models

We consider the position of the deconfining critical endpoint, where the first order transition for deconfinement is washed out by the presence of massive, dynamical quarks. We use an effective matrix model, employed previously to analyze the transition in the pure glue theory. If the param- eters of the pure glue theory are unaffected by the presence of dynamical quarks, and if the quarks only contribute perturbatively, then for three colors and three degenerate quark flavors this quark mass is very heavy, m_de \sim 2.5 GeV, while the critical temperature, T_de, barely changes, \sim 1% below that in the pure glue theory. The location of the deconfining critical endpoint is a sensitive test to differentiate between effective models. For example, models with a logarithmic potential for the Polyakov loop give much smaller values of the quark mass, m_de \sim 1 GeV, and a large shift in T_de \sim 10% lower than that in the pure glue theory.

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arXiv2012

Effective matrix model for deconfinement in pure gauge theories

We construct matrix models for the deconfining phase transition in SU(N) gauge theories, without dynamical quarks, at a nonzero temperature T. We generalize models with zero and one free parameter to study a model with two free parameters: besides perturbative terms ~T^4, we introduce terms ~T^2 and ~T^0. The two N-dependent parameters are determined by fitting to data from numerical simulations on the lattice for the pressure, including the latent heat. Good agreement is found for the pressure in the semi-quark gluon plasma (QGP), which is the region from Tc, the critical temperature, to about ~4 Tc. Above ~1.2 Tc, the pressure is a sum of a perturbative term, ~ +T^4, and a simple non-perturbative term, essentially just a constant times ~ -Tc^2 T^2. For the pressure, the details of the matrix model only enter within a very narrow window, from Tc to ~1.2 Tc, whose width does not change significantly with N. Without further adjustment, the model also agrees well with lattice data for the 't Hooft loop. This is notable, because in contrast to the pressure, the 't Hooft loop is sensitive to the details of the matrix model over the entire semi-QGP. For the (renormalized) Polyakov loop, though, our results disagree sharply with those from the lattice. Matrix models provide a natural and generic explanation for why the deconfining phase transition in SU(N) gauge theories is of first order not just for three, but also for four or more colors. Lastly, we consider gauge theories where there is no strict order parameter for deconfinement, such as for a G(2) gauge group. To agree with lattice measurements, in the G(2) matrix model it is essential to add terms which generate complete eigenvalue repulsion in the confining phase.

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arXiv2011

The Dichotomous Nucleon: Some Radical Conjectures for the Large Nc Limit

We discuss some problems with the large Nc approximation for nucleons which arise if the axial coupling of the nucleon to pions is large, g_A \sim Nc. While g_A \sim Nc in non-relativistic quark and Skyrme models, it has been suggested that Skyrmions may collapse to a small size, r \sim 1/f_pi \sim Lambda_QCD^{-1}/sqrt(Nc). (This is also the typical scale over which the string vertex moves in a string vertex model of the baryon.) We concentrate on the case of two flavors, where we suggest that to construct a nucleon with a small axial coupling, that most quarks are bound into colored diquark pairs, which have zero spin and isospin. For odd Nc, this leaves one unpaired quark, which carries the spin and isospin of the nucleon. If the unpaired quark is in a spatial wavefunction orthogonal to the wavefunctions of the scalar diquarks, then up to logarithms of Nc, the unpaired quark only costs an energy \sim Lambda_QCD. This naturally gives g_A \sim 1 and has other attractive features. In nature, the wavefunctions of the paired and unpaired quarks might only be approximately orthogonal; then g_A depends weakly upon Nc. This dichotomy in wave functions could arise if the unpaired quark orbits at a size which is parametrically large in comparison to that of the diquarks. We discuss possible tests of these ideas from numerical simulations on the lattice, for two flavors and three and five colors; the extension of our ideas to more than three or more flavors is not obvious, though.

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arXiv2011

How Wide is the Transition to Deconfinement?

Pure SU(3) glue theories exhibit a deconfining phase transition at a nonzero temperature, Tc. Using lattice measurements of the pressure, we develop a simple matrix model to describe the transition region, when T > Tc. This model, which involves three parameters, is used to compute the behavior of the 't Hooft loop. There is a Higgs phase in this region, where off diagonal color modes are heavy, and diagonal modes are light. Lattice measurements of the latter suggests that the transition region is narrow, extending only to about 1.2 Tc. This is in stark contrast to lattice measurements of the renormalized Polyakov loop, which indicates a much wider width. The possible implications for the differences in heavy ion collisions between RHIC and the LHC are discussed.

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arXiv2010

Covering the Fermi Surface with Patches of Quarkyonic Chiral Spirals

We argue that in cold, dense quark matter, in the limit of a large number of colors the ground state is unstable with respect to creation of a complicated Quarkyonic Chiral Spiral (QCS) state, in which both chiral and translational symmetries are spontaneously broken. The entire Fermi surface is covered with patches of QCSs, whose number increases as the quark density does. The low energy excitations are gapless, given by Wess-Zumino-Novikov-Witten model plus transverse kinetic terms localized about different patches.

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arXiv2010

Small shear viscosity in the semi quark gluon plasma

At nonzero temperature in QCD, about the deconfining phase transition there is a "semi" quark gluon plasma (semi-QGP), where the expectation value of the (renormalized) Polyakov loop is less than one. This can be modeled by a semiclassical expansion about a constant field for the vector potential, A_0, which is diagonal in color. We compute the shear viscosity in the semi-QGP by using the Boltzmann equation in the presence of this background field. To leading, logarithmic order in weak coupling, the dominant diagrams are given by the usual scattering processes of 2 -> 2 particles. For simplicity we also assume that both the number of colors and flavors are large. Near the critical temperature T_c, where the expectation value of the Polyakov loop is small, the overall density of colored fields decreases according to their color representation, with the density of quarks vanishes linearly with the loop, and that of gluons, quadratically. This decrease in the overall density dominates changes in the transport cross section. As a result, relative to that in the perturbative QGP, near T_c the shear viscosity in the semi-QGP is suppressed by two powers of the Polyakov loop. In a semiclassical expansion, the suppression of colored fields depends only upon which color representation they lie in, and not upon their mass. That light and heavy quarks are suppressed in a common manner may help to explain the behavior of charm quarks at RHIC.

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arXiv2010

Quarkyonic Chiral Spirals

We consider the formation of chiral density waves in Quarkyonic matter, which is a phase where cold, dense quarks experience confining forces. We model confinement following Gribov and Zwanziger, taking the gluon propagator, in Coulomb gauge and momentum space, as 1/(p^2)^2. We assume that the number of colors, N, is large, and that the quark chemical potential, mu, is much larger than renormalization mass scale, Lambda_QCD. To leading order in 1/N and Lambda_QCD/mu, a gauge theory with Nf flavors of massless quarks in 3+1 dimensions naturally reduces to a gauge theory in 1+1 dimensions, with an enlarged flavor symmetry of SU(2Nf). Through an anomalous chiral rotation, in two dimensions a Fermi sea of massless quarks maps directly onto the corresponding theory in vacuum. A chiral condensate forms locally, and varies with the spatial position, z, as < psibar exp(2 i mu z gamma^0 gamma^z) psi >. Following Schon and Thies, we term this two dimensional pion condensate a (Quarkyonic) chiral spiral. Massive quarks also exhibit chiral spirals, with the magnitude of the oscillations decreasing smoothly with increasing mass. The power law correlations of the Wess-Zumino-Novikov-Witten model in 1+1 dimensions then generate strong infrared effects in 3+1 dimensions.

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arXiv2009

Zero Point Energy of Renormalized Wilson Loops

The quark antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero when terms for extrinsic curvature are included. At one loop order, the nonperturbative contribution to the zero point energy is negative, regardless of the sign of the extrinsic curvature term.

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arXiv2008

Suppression of the shear viscosity near the critical temperature in hot QCD

We consider QCD near but above critical temperature Tc. The pressure, susceptibilities and the renormalized Polyakov loop -- which is an order parameter for the deconfining phase transition -- dramatically change up to temperatures a few times Tc. We refer to this region as a "semi"-QGP, where partial confinement plays important role. We show that the shear viscosity ,eta, is suppressed by two powers of the Polyakov loop. This suggests that eta/T^3 decreases markedly as QCD cools down to temperatures near Tc. We also show a ratio of the viscosity to the entropy becomes small near Tc.

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arXiv2008

A Cornucopia of Experiment at RHIC

I outline experimental results on heavy ion collisions at the Relativistic Heavy Ion Collider for a non-technical audience. This includes: elliptic flow and nearly ideal hydrodynamics; the suppression of hard particles and the ratio R_AA; and electromagnetic signals, including dileptons and direct photons. Especially puzzling is why the behavior of heavy (charm) quarks appears to be so similar to that of light quarks.

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arXiv2008

Suppression of the Shear Viscosity in a "semi" Quark Gluon Plasma

We consider QCD at temperatures T near Tc, where the theory deconfines. We distinguish between a "complete" Quark Gluon Plasma (QGP), where the vacuum expectation value of the renormalized Polyakov loop is near unity, essentially constant with T, and the "semi"-QGP, where the loop changes strongly with T. Lattice simulations indicate that in QCD, there is a semi-QGP from below Tc to a few times that. Using a semi-classical model, we compute the shear viscosity, eta, to leading order in perturbation theory. We find that near Tc, where the expectation value of the Polyakov loop is small, that eta/T^3 is suppressed by two powers of the loop. For heavy ions, this suggests that during the initial stages of the collision, hydrodynamic behavior at the LHC will be characterized by a shear viscosity which is significantly larger than that at RHIC.

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arXiv2008

Baryons and the phase diagram for a large number of colors and flavors

We consider the possible phases of a non-Abelian gauge theory, as a function of temperature and quark chemical potential, when both the number of colors and flavors is very large. Generally, a large number of flavors washes out deconfining phase transitions. We show, however, that the degeneracy of even the lightest baryons is exponentially large. This implies that the baryon number (or fluctuations thereof, at zero chemical potential) is an order parameter in the limit of an infinite number of colors and flavors.

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