Heavy Quark Potential from Gauge/Gravity Duality: A Large D Analysis

The heavy-quark potential is calculated in the framework of gauge/gravity duality using the large-D approximation, where D is the number of dimensions transverse to the flux tube connecting a quark and an antiquark in a flat D+2-dimensional spacetime. We find that in the large-D limit the leading correction to the ground-state energy, as given by an effective Nambu-Goto string, arises not from the heavy modes but from the behavior of the massless modes in the vicinity of the quark and the antiquark. We estimate this correction and find that it should be visible in the near-future lattice QCD calculations of the heavy-quark potential.Comment: 22 pages, 5 Figures. v2: references added, typos corrected and, Sec. 4 rewritten with an expanded non-perturbative discussion of the corrections to the Arvis potential arising from the massless modes near the boundary of the qcd strin

Fermionization, Convergent Perturbation Theory, and Correlations in the Yang-Mills Quantum Field Theory in Four Dimensions

We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a convergent perturbation expansion. To zeroth order in this perturbation expansion, the correlation function $E(x,y)$ of generic components of pairs of connections is given by an explicit, finite-dimensional integral formula, which we conjecture will behave as $$E(x,y) \sim |x - y|^{-2 - 2 d_G},$$ \noindent for $|x-y|>>0,$ where $d_G$ is a positive integer depending on the gauge group $G.$ In the case where $G=SU(n),$ we conjecture that $$d_G = {\rm dim}SU(n) - {\rm dim}S(U(n-1) \times U(1)),$$ \noindent so that the rate of decay of correlations increases as $n \to \infty.$Comment: Minor corrections of notation, style and arithmetic errors; correction of minor gap in the proof of Proposition 1.4 (the statement of the Proposition was correct); further remark and references adde

Assessing Legal Responses to Prenatal Drug Use: Can Therapeutic Responses Produce More Positive Outcomes than Punitive Responses

Expressing a growing concern for fetal well being, the 2006 Idaho Senate passed legislation that permits criminal charges to be brought against women who abuse illegal drugs while pregnant. This bill allows for the potential incarceration of violators for up to five years, as well as a possible $50,000 fine. In some locations, women have the option of choosing to go to drug court instead of serving time in jail or prison. These drug courts provide drug treatment, case management, drug testing, and supervision, while requiring women who abuse illegal drugs to regularly report to scheduled status hearings before a judge. Legislators, such as Idaho Senator Kate Kelly, have criticized these laws for being punitive. Such critics believe that addiction to methamphetamine is an illness and not a crime. Some critics are also concerned about the law\u27s effects on families. Senator Kelly also said, [c]riminalization of substance abuse, [and] the separation of infants from their mother, is not in the best interest of Idaho families. In other words, punitive measures are not necessarily the best policies; other options should be considered first. Also, Senator Denton Darrington stated [t]he goal of this legislation is to avoid the birth of meth babies. . . . While the current legal actions taken against prenatal substance abusers are intended to produce positive outcomes, such as healthier fetuses and mothers, negative results are possible. Avoidance of prenatal care, constitutional infringements, and discrimination are just a few of the possible negative effects. For example, while legislatures hope the new Idaho law will prevent prenatal drug abuse, experts fear that pregnant drug users will not seek prenatal care for fear of being prosecuted

Assessing Legal Responses to Prenatal Drug Use: Can Therapeutic Responses Produce More Positive Outcomes than Punitive Responses

Expressing a growing concern for fetal well being, the 2006 Idaho Senate passed legislation that permits criminal charges to be brought against women who abuse illegal drugs while pregnant. This bill allows for the potential incarceration of violators for up to five years, as well as a possible $50,000 fine. In some locations, women have the option of choosing to go to drug court instead of serving time in jail or prison. These drug courts provide drug treatment, case management, drug testing, and supervision, while requiring women who abuse illegal drugs to regularly report to scheduled status hearings before a judge. Legislators, such as Idaho Senator Kate Kelly, have criticized these laws for being punitive. Such critics believe that addiction to methamphetamine is an illness and not a crime. Some critics are also concerned about the law\u27s effects on families. Senator Kelly also said, [c]riminalization of substance abuse, [and] the separation of infants from their mother, is not in the best interest of Idaho families. In other words, punitive measures are not necessarily the best policies; other options should be considered first. Also, Senator Denton Darrington stated [t]he goal of this legislation is to avoid the birth of meth babies. . . . While the current legal actions taken against prenatal substance abusers are intended to produce positive outcomes, such as healthier fetuses and mothers, negative results are possible. Avoidance of prenatal care, constitutional infringements, and discrimination are just a few of the possible negative effects. For example, while legislatures hope the new Idaho law will prevent prenatal drug abuse, experts fear that pregnant drug users will not seek prenatal care for fear of being prosecuted

Regularized Green's Function for the Inverse Square Potential

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version of the model. The application of Sturm-Liouville theory yields a closed expression for the radial energy Green's function. Finally, the equivalence with a recent path-integral treatment of the same problem is explicitly shown.Comment: 10 pages. The final section was expande

Vacuum decay and internal symmetries

We study the effects of internal symmetries on the decay by bubble nucleation of a metastable false vacuum. The zero modes about the bounce solution that are associated with the breaking of continuous internal symmetries result in an enhancement of the tunneling rate into vacua in which some of the symmetries of the initial state are spontaneously broken. We develop a general formalism for evaluating the effects of these zero modes on the bubble nucleation rate in both flat and curved space-times.Comment: LaTex, 11 pages, No figures, one minor chang

S1×S2S^1 \times S^2 wormholes and topological charge

I investigate solutions to the Euclidean Einstein-matter field equations with topology $S^1 \times S^2 \times R$ in a theory with a massless periodic scalar field and electromagnetism. These solutions carry winding number of the periodic scalar as well as magnetic flux. They induce violations of a quasi-topological conservation law which conserves the product of magnetic flux and winding number on the background spacetime. I extend these solutions to a model with stable loops of superconducting cosmic string, and interpret them as contributing to the decay of such loops.Comment: 18 pages (includes 6 figs.), harvmac and epsf, CU-TP-62

Minisuperspace Model for Revised Canonical Quantum Gravity

We present a reformulation of the canonical quantization of gravity, as referred to the minisuperspace; the new approach is based on fixing a Gaussian (or synchronous) reference frame and then quantizing the system via the reconstruction of a suitable constraint; then the quantum dynamics is re-stated in a generic coordinates system and it becomes dependent on the lapse function. The analysis follows a parallelism with the case of the non-relativistic particle and leads to the minisuperspace implementation of the so-called {\em kinematical action} as proposed in \cite{M02} (here almost coinciding also with the approach presented in \cite{KT91}). The new constraint leads to a Schr\"odinger equation for the system. i.e. to non-vanishing eigenvalues for the super-Hamiltonian operator; the physical interpretation of this feature relies on the appearance of a ``dust fluid'' (non-positive definite) energy density, i.e. a kind of ``materialization'' of the reference frame. As an example of minisuperspace model, we consider a Bianchi type IX Universe, for which some dynamical implications of the revised canonical quantum gravity are discussed. We also show how, on the classical limit, the presence of the dust fluid can have relevant cosmological issues. Finally we upgrade our analysis by its extension to the generic cosmological solution, which is performed in the so-called long-wavelength approximation. In fact, near the Big-Bang, we can neglect the spatial gradients of the dynamical variables and arrive to implement, in each space point, the same minisuperspace paradigm valid for the Bianchi IX model.Comment: 16 pages, no figures, to appear on International Journal of Modern Physics