Tom Banks

On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions

Abstract We present a systematic expansion for studying an infrared-stable fixed point of gauge theories with massless fermions. These results are combined with information from strong coupling and large-NF expansions to sketch the phase diagrams for lattice gauge theories with massless fermions. On the basis of these diagrams we conclude that a large class of continuum models with fermions in real representations of the gauge group do not have spontaneous chiral symmetry breaking. We also argue that the transition between chirally symmetric and asymmetric phases is generally first order.

Chiral Symmetry Breaking in Confining Theories

The behaviour of the chiral order parameter in gauge theories is analysed. It is shown that in the confining phase chiral symmetry is spontaneously broken. We employ a new lattice version of the Dirac equation which avoids spectral multiplication.

TCP, quantum gravity, the cosmological constant and all that...

Abstract We study cosmology from the point of view of quantum gravity. Some light is thrown on the nature of time, and it is suggested that the cosmological arrow of time is generated by a spontaneous breakdown of TCP . Conventional cosmological models in which quantum fields interact with a time-dependent gravitational field are shown to describe an approximation to the quantum gravitational wave function which is valid in the long-wavelength limit. Two problems with initial conditions are resolved in models in which a negative bare cosmological constant is cancelled by the classical excitation of a Bose field η with a very flat potential. These models can also give a natural explanation for the observed value of the cosmological constant.

Gauge invariance of string fields

Abstract We identify the gauge invariances of the linearized field theory of strings which give rise to the Yang-Mills and general coordinate invariance of this theory. We construct a kinetic energy term for string fields which is invariant to these gauge symmetries. By gauge-fixing, we derive from this action the expressions for the free string action, in particular gauges found by Kaku and Kikkawa and by Siegel. The structure of Stueckelberg auxilliary fields required to make the gauge-invariant action local is rather intricate; to clarify this structure, we develop a theory of differential forms on the space of strings. We conclude with some remarks on the origin of the dilaton and the appearance in the superstring of local supersymmetry.

Difficulties for the Evolution of Pure States Into Mixed States

Motivated by Hawkings proposal that the quantum-mechanical density matrix ϱ obeys an equation more general than the Schrodinger equation, we study the general properties of evolution equations for ϱ. We argue that any more general equation for ϱ violates either locality or energy-momentum conservation.

Finite-temperature behavior of the lattice abelian Higgs model

Abstract We study phase transitions in the lattice version of the abelian Higgs model, a model which can exhibit both spontaneous symmetry breaking and confinement. When the Higgs charge is the basic U(1) unit, we find that the Higgs and confinement regions are not separated by a phase transition and form a single homogenous phase which we call the total screening phase. The model does not undergo a symmetry restoring phase transition at finite temperature. If the Higgs charge is some multiple of the basic unit the model follows the conventional wisdom: there are 3 phases (normal, Higgs and confinement) at zero temperature, two of which disappear above some critical point. We apply the lessons learned from the lattice Higgs model to understand the behavior of the weak interactions at high temperature. In a long appendix we give an intuitive physical picture for the Polyakov-Susskind quark liberating phase transition and show that it is related to the Hagedorn spectrum of a confining model. We end with a collection of effective field theory approximations to various lattice theories.

Dilaton coupling and BRST quantization of bosonic strings

BRST quantization of the bosonic string on a flat world sheet in an arbitrary background field is discussed. It is shown that by demanding the nilpotence of the BRST charge we may obtain the equations of motion of all the massless fields in the theory, provided we couple the dilaton field to the divergence of the ghost number current in the α-model.

Deconfining and Chiral Phase Transitions in Quantum Chromodynamics at Finite Temperature

We give further arguments to support the claim of Svetitsky and Yaffe that the finite-temperature transition in 4-dimensional SU(N) gauge theories is in the universality class of 3-dimensional ZN spin models. We show that this implies a smoothing out of the transition when quarks are added to the system as long as N ≠ 3. For N = 3 the pure gauge transition is expected to be first order and will be smoothed by quarks only if the quark contribution to the internal energy is larger than the latent heat of transition.

BOSONIZATION OF THE SU(N) THIRRING MODELS

Abstract Bosonization is applied to the SU( N ) Thirring models, and interesting relations between various two-dimensional field theories arise. In particular, we show that the SU(2) model is equivalent to a version of the Sine-Gordon equation plus a free massless field.

All free string theories are theories of forms

Abstract We generalize the gauge-invariant theory of the free bosonic open string to treat closed strings and superstrings. All of these theories can be written as theories of string differential forms defined on suitable spaces. All of the bosonic theories have exactly the same structure; the Ramond theory takes an analogous first-order form. We show, explicitly, using simple and general manipulations, how to gauge-fix each action to the light-cone gauge and to the Feynman-Siegel gauge.