arXiv subjects
Publications and source records attributed to James E. Hetrick.
We study small fluctuations of the stringy wormhole solutions of graviton-dilaton-axion system in arbitrary dimensions. We show under O($d$)-symmetric harmonic perturbation that the Euclidean wormhole solutions are unstable in flat space irrespective of dimensions and in anti de Sitter space of $d=3$.
We describe a calculation of heavy-light decay constants including virtual quark loop effects. We have generated dynamical gauge configurations at three $β$ values using two flavors of Kogut-Susskind quarks with a range of masses. These are analyzed with a Wilson valence quark action. Preliminary results based on a ``fat-link'' clover valence quark action are also reported. Results from the two methods differ by 30 to 50 MeV, which is presumably due to significant - but as yet unobserved - lattice spacing dependence in one or both of the approaches.
We calculate the light quark spectrum of lattice QCD in the quenched approximation using Kogut-Susskind quarks. By combining results for different lattice spacings, several volumes and five quark masses, we are able to take the light quark mass, infinite volume, continuum limit. When we use non-linear chiral extrapolations, we find that the nucleon to rho mass ratio is 1.254 +- 0.018 +- 0.027, where the errors are statistical and systematic (within the quenched approximation), respectively. This should be compared with the experimental value of 1.22. Our results indicate that the error due to quenching is less than about 5%.
We study on the lattice the topology of SU(2) and SU(3) Yang-Mills theories at zero temperature and of QCD at temperatures around the phase transition. To smooth out dislocations and the UV noise we cool the configurations with an action which has scale invariant instanton solutions for instanton size above about 2.3 lattice spacings. The corresponding "improved" topological charge stabilizes at an integer value after few cooling sweeps. At zero temperature the susceptibility calculated from this charge (about (195MeV)^4 for SU(2) and (185 MeV)^4 for SU(3)) agrees very well with the phenomenological expectation. At the minimal amount of cooling necessary to resolve the structure in terms of instantons and anti-instantons we observe a dense ensemble where the total number of peaks is by a factor 5-10 larger than the net charge. The average size observed for these peaks at zero temperature is about 0.4-0.45 fm for SU(2) and 0.5-0.6 fm for SU(3). The size distribution changes very little with further cooling, although in this process up to 90% of the peaks disappear by pair annihilation. For QCD we observe below T_c a reduction of the topological susceptibility as an effect of the dynamical fermions. Nevertheless also here the instantons form a dense ensemble with general characteristics similar to those of the quenched theory. A further drop in the susceptibility above T_c is also in rough agreement with what has been observed for pure SU(3). We see no clear signal for dominant formation of instanton - anti-instanton molecules.
Since gluons in QCD are interacting fundamental constituents just as quarks are, we expect that in addition to mesons made from a quark and an antiquark, there should also be glueballs and hybrids (bound states of quarks, antiquarks and gluons). In general, these states would mix strongly with the conventional q-bar-q mesons. However, they can also have exotic quantum numbers inaccessible to q-bar-q mesons. Confirmation of such states would give information on the role of "dynamical" color in low energy QCD. In the quenched approximation we present a lattice calculation of the masses of mesons with exotic quantum numbers. These hybrid mesons can mix with four quark (q-bar-q-bar-q-q) states. The quenched approximation partially suppresses this mixing. Nonetheless, our hybrid interpolating fields also couple to four quark states. Using a four quark source operator, we demonstrate this mixing for the 1-+ meson. Using the conventional Wilson quark action, we calculate both at reasonably light quark masses, intending to extrapolate to small quark mass, and near the charmed quark mass, where we calculate the masses of some c-bar-c-g hybrid mesons. The hybrid meson masses are large --- over 4 GeV for charmonium and more than twice the vector meson mass at our smallest quark mass, which is near the strange quark mass.
We have investigated QCD with two flavors of degenerate fermions using a Symanzik-improved lattice action for both the gauge and fermion actions. Our study focuses on the deconfinement transition on an $N_t=4$ lattice. Having located the thermal transition, we performed zero temperature simulations nearby in order to compute hadronic masses and the static quark potential. We find that the present action reduces lattice artifacts present in thermodynamics with the standard Wilson (gauge and fermion) actions. However, it does not bring studies with Wilson-type quarks to the same level as those using the Kogut--Susskind formulation.
Sigma models for the high temperature phase transition in quantum chromodynamics (QCD) suggest that at high temperature the SU(N_f) x SU(N_f) chiral symmetry becomes exact, but the anomalous axial U(1) symmetry need not be restored. In numerical lattice simulations, traditional methods for detecting symmetry restoration have sought multiplets in the screening mass spectrum. However, these methods were imprecise and the results, so far, incomplete. With improved statistics and methodology, we are now able to offer evidence for a restoration of the SU(2) x SU(2) chiral symmetry just above the crossover, but not of the axial U(1) chiral symmetry.
We study the effect of modifying the coupling of Kogut-Susskind quarks to the gauge field by replacing the link matrix in the quark action by a "fat link", or sum of link plus three-link paths. Flavor symmetry breaking, determined by the mass difference between the Goldstone and non-Goldstone local pions, is reduced by approximately a factor of two by this modification.
A progress report on experiences with a gauge fixing method proposed in LATTICE 94 is presented. In this algorithm, an SU(N) operator is diagonalized at each site, followed by gauge fixing the diagonal (Cartan) part of the links to Coulomb gauge using the residual abelian freedom. The Cartan sector of the link field is separated into the physical gauge field $α^{(f)}_μ$ responsible for producing $f^{\rm Cartan}_{μν}$, the pure gauge part, lattice artifacts, and zero modes. The gauge transformation to the physical gauge field $α^{(f)}_μ$ is then constructed and performed. Compactness of the lattice fields entails issues related to monopoles and zero modes which are addressed.
We digitally filter the Fourier modes of the link angles of an abelian lattice gauge field which produces the Fourier modes of a continuum $A_μ(x)$ that exactly reproduces the lattice links through their definition as phases of finite parallel transport. The constructed interpolation is smooth ($C^\infty$), free from transition functions, and gauge equivariant. After discussing some properties of this interpolation, we discuss the non-abelian generalization of the method, arriving for SU(2), at a Cayley parametrization of the links in terms of the Fourier modes of $A^c_μ(x)$. We then discuss the use of a maximum entropy type method to address gauge invariance in the non-abelian case.
We study lattice QCD in the limit that the quark mass and chemical potential are simultaneously made large, resulting in a controllable density of quarks which do not move. This is similar in spirit to the quenched approximation for zero density QCD. In this approximation we find that the deconfinement transition seen at zero density becomes a smooth crossover at any nonzero density, and that at low enough temperature chiral symmetry remains broken at all densities.
We examine the question of how baryogenesis can occur in lattice models of the Standard Model where there is a global $U(1)$ symmetry which is accompanied by an exactly conserved fermion number. We demonstrate that fermion creation and annihilation can occur in these models {\em despite} this exact fermion number conservation, by explicitly computing the spectral flow of the hamiltonian in the two dimensional U(1) axial model with Wilson fermions. For comparison we also study the closely related Schwinger model where a similar mechanism gives rise to anomalous particle creation and annihilation.
We study gauge fixing via the standard local extremization algorithm for 2-dimensional $U(1)$. On a lattice with spherical topology $S^2$ where all copies are lattice artifacts, we find that the number of these 'Gribov' copies diverges in the continuum limit. On a torus, we show that lattice artifacts can lead to the wrong evaluation of the gauge-invariant correlation length, when measured via a gauge-fixed procedure; this bias does not disappear in the continuum limit. We then present a new global approach, based on Hodge decomposition of the gauge field, which produces a unique smooth field in Landau gauge, and is economically powered by the FFT. We also discuss the use of this method for examining topological objects, and its extensions to non-abelian gauge fields.
Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit anomalous processes, such as electroweak baryogenesis in the early universe. One way to circumvent this problem is to formulate the theory such that this U(1) symmetry is explicitly broken. However we argue that in the framework of spectral flow, fermion creation and annihilation still in fact occurs, despite the exact fermion number conservation. The crucial observation is that fermions are excitations relative to the vacuum, at the surface of the Dirac sea. The exact global U(1) symmetry prohibits a state from changing its fermion number during time evolution, however nothing prevents the fermionic ground state from doing so. We illustrate our reasoning with a model in two dimensions which has axial-vector couplings, first using a sharp momentum cutoff, then using the lattice regulator with staggered fermions. The difference in fermion number between the time evolved state and the ground state is indeed in agreement with the anomaly. A study of the vacuum energy shows that the perturbative counterterm needed for restoration of gauge invariance is insufficient in a nonperturbative setting. For reference we also study a closely related model with vector couplings, the Schwinger model, and we examine the emergence of the $θ$-vacuum structure of both theories.
A nonperturbative regularization of the Standard Model may have a superficially undesirable exact global U(1) symmetry corresponding to exact fermion number conservation. We argue that such a formulation can still have the desired physics of fermion nonconservation, i.e. fermion particle creation and annihilation by sphaleron transitions. We illustrate our reasoning in massless axial QED in 1+1 dimensions.
Gauge fixing in general is incomplete, such that one solves some of the gauge constraints, quantizes, then imposes any residual gauge symmetries (Gribov copies) on the wavefunctions. While the Fadeev-Popov determinant keeps track of the local metric on this gauge fixed surface, the global topology of the reduced configuration space can be different depending on the treatment of the residual symmetries, which can in turn affect global properties of the theory such as the vacuum wavefunction. Pure $SU(N)$ gauge theory in two dimensions provides a simple yet non-trivial example where the above structure and effects can be elucidated explicitly, thus displaying physical effects of the treatment of Gribov copies.
%In order to understand how gauge fixing can be affected on the %lattice, we first study a simple model of pure Yang-mills theory on a %cylindrical spacetime [$SU(N)$ on $S^1 \times$ {\bf R}] where the %gauge fixed subspace is explicitly displayed. On the way, we find that %different gauge fixing procedures lead to different Hamiltonians and %spectra, which however coincide under a shift of states. The lattice %version of the model is compared and lattice gauge fixing issues are %discussed. (---TALK GIVEN AT LATTICE 92---AMSTERDAM, 15 SEPT. 92)
$SU(N)$ gauge fields on a cylindrical spacetime are canonically quantized via two routes revealing almost equivalent but different quantizations. After removing all continuous gauge degrees of freedom, the canonical coordinate $A_μ$ (in the Cartan subalgebra $\h$) is quantized. The compact route, as in lattice gauge theory, quantizes the Wilson loop $W$, projecting out gauge invariant wavefunctions on the group manifold $G$. After a Casimir energy related to the curvature of $SU(N)$ is added to the compact spectrum, it is seen to be a subset of the non-compact spectrum. States of the two quantizations with corresponding energy are shifted relative each other, such that the ground state on $G$, $χ_0(W)$, is the first excited state $Ψ_1(A_μ)$ on $\h$. The ground state $Ψ_0(A_μ)$ does not appear in the character spectrum as its lift is not globally defined on $G$. Implications for lattice gauge theory and the sum over maps representation of two dimensional QCD are discussed.