arXiv subjects

Frank Wilczek

Publications and source records attributed to Frank Wilczek.

At least 199 records · Page 11Linked to original sources

arXiv1996

Classical Hair in String Theory I: General Formulation

We discuss why classical hair is desirable for the description of black holes, and show that it arises generically in a wide class of field theories involving extra dimensions. We develop the canonical formalism for theories with the matter content that arises in string theory. General covariance and duality are used to determine the form of surface terms. We derive an effective theory (reduced Hamiltonian) for the hair in terms of horizon variables. % accessible to an observer at infinity. Solution of the constraints expresses these variables in terms of hair accessible to an observer at infinity. We exhibit some general properties of the resulting theory, including a formal identification of the temperature and entropy. The Cvetič-Youm dyon is described in some detail, as an important example.

hep-th↗

arXiv1996

Remarks on the Current-Carrying State of Hall Superfluids

I discuss in an elementary and self-contained way the nature of the current-carrying state in Hall superfluids. The explicit connection of fractional charge and rationality of the filling fraction $ν$ with quantization of angular momentum, and the discussion of the preferred velocity profile for bulk current flows may be new; the latter might provide an interesting experimental handle on a fundamental aspect of quantum superfluidity.

cond-mat↗

arXiv1996

Possible Electronic Structure of Domain Walls in Mott Insulators

We discuss the quantum numbers of domain walls of minimal length induced by doping Mott insulators, carefully distinguishing between holon and hole walls. We define a minimal wall hypothesis that uniquely correlates the observed spatial structure with the doping level for the low-temperature commensurate insulating state of La$_{2-x}$Ba$_x$CuO$_4$ and related materials at $x={1\over 8}$. We remark that interesting walls can be supported not only by conventional antiferromagnetic but also by orbital antiferromagnetic (staggered flux phase, $d$-density) bulk order. We speculate on the validity of the minimal wall hypothesis more generally, and argue that it plausibly explains several of the most striking anomalous features of the cuprate high-temperature superconductors.

cond-mat↗

arXiv1996

Aspects of d-Density Order

I briefly review the concept of d-density ordering, extend it to arbitrary dimensions, and speculate that it might describe Mott insulators. This ordering supports zero modes on domain walls, and quite plausibly dopants occupy such states. This phenomenon could induce quasi-one dimensional behavior in a two-dimensional electron system.

cond-mat↗

arXiv1995

Quantum Numbers of Textured Hall Effect Quasiparticles

We propose a class of variational wave functions with slow variation in spin and charge density and simple vortex structure at infinity, which properly generalize both the Laughlin quasiparticles and baby Skyrmions. We argue that the spin of the corresponding quasiparticle has a fractional part related in a universal fashion to the properties of the bulk state, and propose a direct experimental test of this claim. We show that certain spin-singlet quantum Hall states can be understood as arising from primary polarized states by Skyrmion condensation.

cond-mat↗

arXiv1995

Internal Structure of Black Holes

We present a number of qualitative arguments which strongly suggest that extremal dyonic black holes in the 4--dimensional low energy, classical field theory limit of toroidally compactified heterotic string theory represent largely degenerate classes of states in the quantum theory. We propose a simple expression for the full non--perturbative degeneracy, which contains no free continuous parameters and reproduces the Bekenstein-Hawking $S={A\over 4G_N}$ in the large-area limit (with the ${1\over 4}$ arising from microphysics). We sketch the elements of a physical picture leading to this expression: the holes support much hair, such that in counting it we are led to an effective string theory, and a matching condition whose solutions give the degeneracy.

hep-th↗

arXiv1995

Spin Singlet Ordering Suggested by Repulsive Interactions

We consider a correlated wavefunction including particle-hole pairing at half a reciprocal lattice vector for itinerant electrons hopping on a square lattice in two dimensions and subject both to on-site and nearest-neighbor repulsion. We find, within mean field theory, that in a suitable range of parameters there is a tendency toward a novel form of ordering characterized by discrete symmetry breaking and a gap at the magnetic zone boundary, which supports hole-like semiconductor behavior near half filling despite an apparently normal Fermi surface. The effective quasiparticle couplings to phonons includes a significant d-wave piece, which plausibly leads to an especially robust tendency toward superconductivity.

cond-mat↗

arXiv1995

Statistical Transmutation and Phases of Two-Dimensional Quantum Matter

After surveying the quantum kinematics and dynamics of statistical transmutation, I show how this concept suggests a phase diagram for the two-dimensional matter in a magnetic field, as a function of quantum statistics. I discuss the fundamental properties of quasiparticles in the different phases, and briefly suggest {\it gedanken\/} -- but not manifestly infeasible -- experiments to show up these properties.

cond-mat↗

arXiv1995

Spin-Singlet to Spin Polarized Phase Transition at $ν=2/3$: Flux-Trading in Action

We analyze the phase transition between spin-singlet and spin-polarized states which occurs at $ν=2/3$. The basic strategy is to use adiabatic flux-trading arguments to relate this transition to the analogous transition at $ν=2$. The transition is found to be similar to a transition in ferromagnets. In our analysis, we find two possible scenarios. In one, the transition is first-order, in agreement with experimental and numerical studies of the $ν=2/3$ transition. In the other, we find a second-order transition to a partially polarized state followed by a second-order transition to a fully polarized state. This picture is in qualitative agreement with experiments on the $ν=4/3$ state, the particle-hole conjugate of $ν=2/3$. We analyze the edge modes which propagate at the boundaries between regions of different phases and show that these do not support gapless excitations. Finally, we consider the possibility of a finite-temperature compressible state with a Fermi surface which would explain the non-zero $ρ_{xx}$ seen in experiments.

cond-mat↗

arXiv1995

Physical Properties of Metals from a Renormalization Group Standpoint

We derive the equilibrium and transport properties of metals using renormalization group equations and finite-size scaling. Particular attention is given to the well-known cases of Fermi and Luttinger liquids. An important subtlety is that the temperature dependence of many transport coefficients is determined by ``dangerous'' irrelevant operators. We also characterize violations of Fermi or Luttinger liquid behavior in terms of indices, analogous to the critical indices describing phase transitions. We briefly consider the normal-state properties of the cuprates from this standpoint.

cond-mat↗

arXiv1995

Renormalization of Black Hole Entropy and of the Gravitational Coupling Constant

The quantum corrections to black hole entropy, variously defined, suffer quadratic divergences reminiscent of the ones found in the renormalization of the gravitational coupling constant (Newton constant). We consider the suggestion, due to Susskind and Uglum, that these divergences are proportional, and attempt to clarify its precise meaning. Using a Euclidean formulation the proportionality is a fairly immediate consequence of basic principles -- a low-energy theorem. Thus in this framework renormalizing the Newton constant renders the entropy finite, and equal to its semiclassical value. As a partial check on our formal arguments we compare the one loop determinants, calculated using heat kernel regularization. An alternative definition of black hole entropy relates it to behavior at conical singularities in two dimensions, and thus to a suitable definition of geometric entropy. Geometric entropy permits the same renormalization, but it does not yield an intrinsically positive quantity. For scalar fields geometric entropy is subtly sensitive to curved space couplings, even in the limit of flat space. Fermions and gauge fields are considered as well. Their functional determinants are closely related to the determinants for non-minimally coupled scalar fields with specific values for the curvature coupling, and pose no further difficulties.

hep-th↗

arXiv1995

Quantum Numbers of Hall Effect Skyrmions

By carefully considering a family of wave functions for Skyrmions in simple quantum Hall states, whose members are labelled by a non-negative integer and which properly generalizes the traditional Laughlin quasiparticle, we argue that the spin of this particle has a fractional part related in a universal fashion to the properties of the bulk state, and propose a direct experimental test of this claim. We argue directly also for the fractional charge and fractional quantum statistics of these particles. We show that certain spin-singlet quantum Hall states can be understood as arising from primary polarized states by Skyrmion condensation.

cond-mat↗

arXiv1995

Indirect Neutrino Oscillations

We show how two different scales for oscillations between $e$ and $μ$ neutrinos, characterized by different mixing angles and effective mass scales, can arise in a simple and theoretically attractive framework. One scale characterizes direct oscillations, which can accommodate the MSW approach to the solar neutrino problem, whereas the other can be considered as arising indirectly, through virtual transitions involving the $τ$ neutrino with a mass $\sim$ 1 eV. This indirect transition allows the possibility of observable $\bar ν_μ\leftrightarrow \bar ν_e$ oscillations at accelerator and reactor energies. We discuss specifically the parameters suggested by a recent experiment at Los Alamos within this framework.

hep-ph↗

arXiv1995

Quantum Hall States of High Symmetry

We identify some hidden symmetries of Chern-Simons theories, such as appear in the effective theory for quantized Hall states. This allows us to determine which filling fractions admit spin-singlet quantum Hall states. Our results shed some light on states already observed at $ν=2/3$, and transitions between them. We identify SU(2), or higher, symmetries of many additional states -- including spin-polarized states. Our symmetries classify low-lying excited states and may be of use in the construction of trial wavefunctions, but are typically not present in the edge theory, where they are lifted by non-universal couplings.

cond-mat↗

arXiv1995

From the Standard Model to Dark Matter

The standard model of particle physics is marvelously successful. However, it is obviously not a complete or final theory. I shall argue here that the structure of the standard model gives some quite concrete, compelling hints regarding what lies beyond. Taking these hints seriously, one is led to predict the existence of new types of very weakly interacting matter, stable on cosmological time scales and produced with cosmologically interesting densities--that is, ``dark matter''.

hep-ph↗

arXiv1995

``Space Time Aspects of Quasiparticle Propagation''

Highly correlated states of electrons are thought to produce quasiparticles with very unusual properties. Here we consider how these properties are manifested in space-time propagation. Specifically, we discuss how spin-charge separation is realized in a simple double-layer geometry, how mass renormalization affects time-of-flight in compressible Hall states, and how quantum drifts can reveal the effective charge, mass, and quantum statistics in incompressible Hall states. We also discuss the possibility of observing the effect of fractional statistics directly in scattering. Finally we propose that, as a result of incompressibility and the fundamental charge-flux relation, charged probes induce macroscopic, measurable rotation of Hall fluids.

cond-mat↗

arXiv1994

Effect of Self-Interaction on Charged Black Hole Radiance

We extend our previous analysis of the modification of the spectrum of black hole radiance due to the simplest and probably most quantitatively important back-reaction effect, that is self-gravitational interaction, to the case of charged holes. As anticipated, the corrections are small for low-energy radiation when the hole is well away from extremality, butbecome qualitatively important near extremality. A notable result is that radiation which could leave the hole with mass and charge characteristic of a naked singularity, predicted in the usual approximation of fixed space-time geometry, is here suppressed. We discuss the nature of our approximations, and show how they work in a simpler electromagnetic analogue problem.

hep-th↗

arXiv1994

Liberating Exotic Slaves

The introduction of confined, ``slave'' fields is frequently useful as a formal device in models of condensed matter physics; it becomes a conceptual necessity for describing possible phases of matter where the slaves are liberated. Here I discuss some aspects of the fractional quantum Hall effect from this point of view, emphasizing analogies with phenomena in other areas of physics, particularly to the Meissner and Higgs mechanisms, and to confinement-deconfinement transitions. In this application, and in some recent attempts to model the normal state of copper oxide superconductors, it is important to employ slave anyon fields.

cond-mat↗