arXiv subjects
Publications and source records attributed to Frank Wilczek.
I discuss the general principles underlying quantum field theory, and attempt to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality. I mention a few of its most striking successes, both achieved and prospective. Possible limitations of quantum field theory are viewed in the light of its history.
It is shown how a metric structure can be induced in a simple way starting with a gauge structure and a preferred volume, by spontaneous symmetry breaking. A polynomial action, including coupling to matter, is constructed for the symmetric phase. It is argued that assuming a preferred volume, in the context of a metric theory, induces only a limited modification of the theory.
The membrane paradigm is the remarkable view that, to an external observer, a black hole appears to behave exactly like a dynamical fluid membrane, obeying such pre-relativistic equations as Ohm's law and the Navier-Stokes equation. It has traditionally been derived by manipulating the equations of motion. Here we provide an action formulation of this picture, clarifying what underlies the paradigm, and simplifying the derivations. Within this framework, we derive previous membrane results, and extend them to dyonic black hole solutions. We discuss how it is that an action can produce dissipative equations. Using a Euclidean path integral, we show that familiar semi-classical thermodynamic properties of black holes also emerge from the membrane action. Finally, in a Hamiltonian description, we establish the validity of a minimum entropy production principle for black holes.
These are the essence of two lectures given at the Ettore Majorana Summer School, 1997, and the discussion sections which followed them. The title indicates their content: some reasoned expectations for physics beyond the Standard Model, and an annotated list of major open questions.
We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at $ν=1$ is an $SU(2)_2$ Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chern-Simons theory with coupling constant $k=2$. The effective field theories for other Pfaffian states, such as the fermionic one at $ν=1/2$ are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.
I briefly discuss three phenomena arising in recent work where the realization of symmetries in quantum mechanics is unusual. The first of these is, I believe, the very simplest realization of non-trivial confinement by a mechanism of charge-flux frustration. It arises in models having several coupled abelian Chern-Simons gauge symmetries, which closely resemble effective theories used for the quantum Hall effect. The second is symmetry obstruction by non-abelian flux, which has implications for 2+1 dimensional supergravity. Third is the possibility of new varieties of quantum statistics: non-abelian and projective.
The long-range fields associated with non-abelian vortices generally obstruct full realization, in the spectrum, of the symmetry of the ground state. In the context of 2+1 dimensional field theories, we show how this effect manifests itself concretely in altered conditions for the angular momentum and in the energy spectrum. A particularly interesting case is supersymmetry, which is obstructed by the gravitational effect of any mass.
We identify a class of 2+1 dimensional models, involving multiple Chern-Simons gauge fields, in which a form of classical confinement occurs. This confinement is not cumulative, but allows finite mass combinations of individually confined objects, as in baryons. The occurrence and nature of the phenomena depends on number theoretic properties of the couplings and charges.
Taking the reported high-Q^2 anomaly at HERA as a signal of new physics, we show that several independent considerations point towards s-channel leptoquark production as the most attractive interpretation. We argue that even this option is highly constrained by flavor-changing processes: the couplings must be accurately diagonal in the quark and lepton mass eigenstate basis and should preserve individual quark and lepton family numbers. We propose a dynamical mechanism that might produce this pattern; it has distinctive experimental consequences.
In the first part of the talk, I give a low-resolution overview of the current state of particle physics - the triumph of the Standard Model and its discontents. I review and re-endorse the remarkably direct and (to me) compelling argument that existing data, properly interpreted, point toward a unified theory of fundamental particle interactions and toward low-energy supersymmetry as the near-term future of high energy physics as a natural science. I then attempt, as requested, some more `visionary' - i.e. even lower resolution - comments about the farther future. In that spirit, I emphasize the continuing importance of condensed matter physics as a source of inspiration and potential application, in particular for expansion of symmetry concepts, and of cosmology as a source of problems, applications, and perhaps ultimately limitations.
Several experiments suggest that the charge carriers in the normal state of certain cuprate superconductors reside on domain walls. In an earlier paper, we suggested that several aspects of the anomalous dynamical behavior of these materials could be explained, at least qualitatively, on this basis. Here, using results on the ground state energy of the 1-dimensional Hubbard model (soluble by Bethe ansatz techniques) as a function of charge density, we argue that a non-zero charge density localized to domain walls is a very plausible consequence of strong short-range electron-electron repulsion. We also suggest a method to suppress meandering of the walls, and thereby enhance their signature in neutron diffraction.
We show that a class of 3+1 dimensional Friedmann-Robertson-Walker cosmologies can be embedded within a variety of solutions of string theory. In some realizations the apparent singularities associated with the big bang or big crunch are resolved at non-singular horizons of higher-dimensional quasi-black hole solutions (with compactified real time); in others plausibly they are resolved at D-brane bound states having no conventional space-time interpretation.
We calculate the low-lying spectrum of new particles expected in a minimal model wherein supersymmetry breaking at < 100 TeV is indirectly transmitted to the Standard Model. We calculate the couplings of these particles relevant to their most nearly accessible experimental signatures, and estimate those signatures quantitatively. Running of various couplings plays a crucial role in the phenomenology, specifically in generating an adequate $\neutralino_1 - \slepton_R$ splitting.
I discuss how the basic phenomenon of asymptotic freedom in QCD can be understood in elementary physical terms. Similarly, I discuss how the long-predicted phenomenon of ``gluonization of the proton'' -- recently spectacularly confirmed at HERA -- is a rather direct manifestation of the physics of asymptotic freedom. I review the broader significance of asymptotic freedom in QCD in fundamental physics: how on the one hand it guides the interpretation and now even the design of experiments, and how on the other it makes possible a rational, quantitative theoretical approach to problems of unification and early universe cosmology.
After emphasizing the importance of obtaining a space-time understanding of black hole entropy, we further elaborate our program to identify the degrees of freedom of black holes with classical space-time degrees of freedom. The Cvetič-Youm dyonic black holes are discussed in some detail as an example. In this example hair degrees of freedom transforming as an effective string can be identified explicitly. We discuss issues concerning charge quantization, identification of winding, and tension renormalization that arise in counting the associated degrees of freedom. The possibility of other forms of hair in this example, and the prospects for making contact with D-brane ideas, are briefly considered.
I discuss some central issues in particle physics which are potentially relevant to cosmology. I first briefly review the present (glorious) experimental status of the Standard Model, emphasizing that it provides a firm foundation both for early Universe cosmology and for further exploration toward the basic laws of Nature. I then provide a critique, arguing that while there are no clear discrepancies, there are several major, specific deficiencies of the Standard Model which clearly point up its provisional character. I elaborate on the story theorists have made up to address one of these problems, the problem of scattered multiplets, and show how upon following it out one finds, within existing experiments, encouragement -- bordering on evidence -- for certain ambitious ideas regarding unification and supersymmetry. I briefly describe and contrast two paradigms of supersymmetry breaking, which have markedly different experimental and cosmological consequences. I call attention to specific connections with cosmology where appropriate throughout; and near the end I make some more global remarks. Finally I venture a speculation suggesting, in a fairly concrete way, the possibility that the laws of physics cannot, in principle, be disentangled from cosmology.
By explicitly identifying a basis valid for any number of electrons, we demonstrate that simple multi-quasihole wavefunctions for the $ν=1/2$ Pfaffian paired Hall state exhibit an exponential degeneracy at fixed positions. Indeed, we conjecture that for $2n$ quasiholes the states realize a spinor representation of an expanded (continuous) nonabelian statistics group $SO(2n)$. In the four quasihole case, this is supported by an explicit calculation of the corresponding conformal blocks in the $c={1\over2}+1$ conformal field theory. We present an argument for the universality of this result, which is significant for the foundations of fractional statistics generally. We note, for annular geometry, an amusing analogue to black hole entropy. We predict, as a generic consequence, glassy behavior. Many of our considerations also apply to a form of the (3,3,1) state.
We consider how two classes of heavy particles: extra vector-like families, and strongly interacting superpartners, manifest themselves below threshold, by interference of virtual loops with normal QCD processes. Quantitative estimates are presented.