arXiv subjects

Benjamin Svetitsky

Publications and source records attributed to Benjamin Svetitsky.

At least 55 records · Page 3Linked to original sources

arXiv2005

Localization of lattice fermions: lessons for overlap

Lattice fermions in a fluctuating gauge field can show localization, much like electrons in a disordered potential. We study the spectrum of localized and extended states of supercritical Wilson fermions in gauge ensembles generated with plaquette and improved actions. When the Wilson fermion operator is used to construct the overlap kernel, the mobility edge, that is the boundary between the localized and extended states, determines the range of the kernel.

hep-lat↗

arXiv2005

Localization properties of lattice fermions with plaquette and improved gauge actions

We determine the location $λ_c$ of the mobility edge in the spectrum of the hermitian Wilson operator in pure-gauge ensembles with plaquette, Iwasaki, and DBW2 gauge actions. The results allow mapping a portion of the (quenched) Aoki phase diagram. We use Green function techniques to study the localized and extended modes. Where $λ_c>0$ we characterize the localized modes in terms of an average support length and an average localization length, the latter determined from the asymptotic decay rate of the mode density. We argue that, since the overlap operator is commonly constructed from the Wilson operator, its range is set by the value of $λ_c^{-1}$ for the Wilson operator. It follows from our numerical results that overlap simulations carried out with a cutoff of 1 GeV, even with improved gauge actions, could be afflicted by unphysical degrees of freedom as light as 250 MeV.

hep-lat↗

arXiv2005

Instability of Bubbles Near the Hadron--Quark-Gluon-Plasma Phase Transition

The small surface tension of the interface between hadronic and quark-gluon-plasma domains, along with a negative curvature tension, implies that the uniform plasma is unstable against spontaneous formation of hadronic bubbles. We furthermore show that spherical bubbles are not stable against small perturbations.

hep-ph↗

arXiv2005

Divergent chiral condensate in the quenched Schwinger model

We calculate numerically the eigenvalue distribution of the overlap Dirac operator in the quenched Schwinger model on a lattice. The distribution does not fit any of the three universality classes of spontaneous chiral symmetry breaking, and its strong volume dependence indicates that the chiral condensate in the quenched theory is an ill-defined and divergent quantity. When we reweight configurations with the Dirac determinant to study the theory with N_f=1, we obtain a distribution of eigenvalues that is well-behaved and consistent with the theory of explicit symmetry breaking due to the anomaly.

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arXiv2005

Mobility edge in lattice QCD

We determine the location $λ_c$ of the mobility edge in the spectrum of the hermitian Wilson operator on quenched ensembles. We confirm a theoretical picture of localization proposed for the Aoki phase diagram. When $λ_c>0$ we also determine some key properties of the localized eigenmodes with eigenvalues $|λ|<λ_c$. Our results lead to simple tests for the validity of simulations with overlap and domain-wall fermions.

hep-lat↗

arXiv2004

Anisotropic Goldstone bosons of strong-coupling lattice QCD at high density

We calculate the spectrum of excitations in strong-coupling lattice QCD in a background of fixed baryon density, at a substantial fraction of the saturation density. We employ a next-nearest-neighbor fermion formulation that possesses the SU(N_f)xSU(N_f) chiral symmetry of the continuum theory. We find two types of massless excitations: type I Goldstone bosons with linear dispersion relations and type II Goldstone bosons with quadratic dispersion relations. Some of the type I bosons originate as type II bosons of the nearest-neighbor theory. Bosons of either type can develop anisotropic dispersion relations, depending on the value of N_f and the baryon density.

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arXiv2003

Spontaneous symmetry breaking in strong-coupling lattice QCD at high density

We determine the patterns of spontaneous symmetry breaking in strong-coupling lattice QCD in a fixed background baryon density. We employ a next-nearest-neighbor fermion formulation that possesses the SU(N_f)xSU(N_f) chiral symmetry of the continuum theory. We find that the global symmetry of the ground state varies with N_f and with the background baryon density. In all cases the condensate breaks the discrete rotational symmetry of the lattice as well as part of the chiral symmetry group.

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arXiv2002

Lattice gauge theory with baryons at strong coupling

We study the effective Hamiltonian for strong-coupling lattice QCD in the case of non-zero baryon density. In leading order the effective Hamiltonian is a generalized antiferromagnet. For naive fermions, the symmetry is U(4N_f) and the spins belong to a representation that depends on the local baryon number. Next-nearest-neighbor (nnn) terms in the Hamiltonian break the symmetry to U(N_f) x U(N_f). We transform the quantum problem to a Euclidean sigma model which we analyze in a 1/N_c expansion. In the vacuum sector we recover spontaneous breaking of chiral symmetry for the nearest-neighbor and nnn theories. For non-zero baryon density we study the nearest-neighbor theory only, and show that the pattern of spontaneous symmetry breaking depends on the baryon density.

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arXiv2001

Effective Lagrangian for strongly coupled domain wall fermions

We derive the effective Lagrangian for mesons in lattice gauge theory with domain-wall fermions in the strong-coupling and large-N_c limits. We use the formalism of supergroups to deal with the Pauli-Villars fields, needed to regulate the contributions of the heavy fermions. We calculate the spectrum of pseudo-Goldstone bosons and show that domain wall fermions are doubled and massive in this regime. Since we take the extent and lattice spacing of the fifth dimension to infinity and zero respectively, our conclusions apply also to overlap fermions.

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arXiv2000

Exact topological density in the lattice Skyrme model

We propose using the Skyrme model on a lattice as an effective field theory of meson-baryon interactions. To this end we construct a local topological density that involves the volumes of tetrahedra in the target space S^3 and we make use of Coxeter's formula for the Schlafli function to implement it. We calculate the mean-square radius of a skyrmion in the three-dimensional Skyrme model, and find some surprises.

hep-lat↗

arXiv2000

Topology and metastability in the lattice Skyrme model

We offer the Skyrme model on a lattice as an effective field theory - fully quantized - of baryon-meson interactions at temperatures below the chiral phase transition. We define a local topological density that involves the volumes of tetrahedra in the target space S^3 and we make use of Coxeter's formula for the Schlafli function to implement it. This permits us to calculate the mean-square radius of a skyrmion in the three-dimensional lattice Skyrme model, which may be viewed as a Ginzburg-Landau effective theory for the full quantum theory at finite temperature. We find that, contrary to expectations, the skyrmion shrinks as quantum and thermal fluctuations are enhanced. We ascribe this to a large number of metastable states that become accessible as the temperature is raised.

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arXiv2000

Hamiltonian domain wall fermions at strong coupling

We apply strong-coupling perturbation theory to gauge theories containing domain-wall fermions in Shamir's surface version. We construct the effective Hamiltonian for the color-singlet degrees of freedom that constitute the low-lying spectrum at strong coupling. We show that the effective theory is identical to that derived from naive, doubled fermions with a mass term, and hence that domain-wall fermions at strong coupling suffer both doubling and explicit breaking of chiral symmetry. Since we employ a continuous fifth dimension whose extent tends to infinity, our result applies to overlap fermions as well.

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arXiv1999

Interaction potential in compact three-dimensional QED with mixed action

We use a variational wave function to calculate the energy of the interaction between external charges in the compact Abelian gauge theory in 2+1 dimensions with mixed action. Our variational wave functions preserve the compact gauge invariance of the theory both in the vacuum and in the charged sectors. We find that a good estimate of the interaction energy is obtained only when we allow more variational parameters in the charged sector than in the vacuum sector. These extra parameters are the profile of an induced electric field. We find that the theory has a two-phase structure: When the charge-2 coupling is large and negative there is no mass gap in the theory and no confinement, while otherwise a mass gap is generated dynamically and the theory confines charges. The pure Wilson theory is in the confining phase.

hep-lat↗

arXiv1999

The flux-tube model of particle creation in nuclear collisions

I review some of the history of the flux-tube model, concentrating on work done by the Los Alamos-Tel Aviv collaboration on particle creation and back-reaction in uniform fields and in the central rapidity region. I discuss the incorporation of more realistic geometry and structure of the flux tube via application of the dual superconductor model of confinement.

hep-ph↗

arXiv1999

Flux tube dynamics in the dual superconductor

We have studied plasma oscillations in a flux tube created in a dual superconductor. Starting from a static flux tube configuration, with electric charges at either end, we release a fluid of electric charges in the system that accelerate and screen the electric field. The weakening of the electric field allows the flux tube to collapse, and the inertia of the charges forces it open again. We find strong radiation of electric flux into the superconductor in all regimes of couplings.

hep-ph↗

arXiv1999

Flux tube dynamics in the dual superconductor

We study plasma oscillations in a flux tube of the dual superconductor model of 't Hooft and Mandelstam. A magnetic condensate is coupled to an electromagnetic field by its dual vector potential, and fixed electric charges set up a flux tube. An electrically charged fluid (a quark plasma) flows in the tube and screens the fixed charges via plasma oscillations. We investigate both Type I and Type II superconductors, with plasma frequencies both above and below the threshold for radiation into the Higgs vacuum. We find strong radiation of electric flux into the superconductor in all regimes, and argue that this invalidates the use of the simplest dual superconductor model for dynamical problems.

hep-ph↗

arXiv1998

Effective spin models for the confinement phase transition

Spatial correlations - bubbles, domain walls, etc. - can best be studied by concentrating on the degrees of freedom most relevant to the problem. For the finite temperature confinement transition, I integrate out all gauge degrees of freedom, leaving only spins - Ising or Potts - related to the Wilson line. I present problems that arise in the course of this transformation and some results for the effective spin action.

hep-lat↗

arXiv1997

Charm -- a thermometer of the mixed phase

A charmed quark experiences drag and diffusion in the quark-gluon plasma, as well as strong interaction with the plasma surface. Our simulations indicate that charmed quarks created in heavy ion collisions will be trapped in the mixed phase and will come to equilibrium in it. Their momentum distribution will thus reflect the temperature at the confinement phase transition.

hep-ph↗