J. Greensite

Superstring amplitudes and contact interactions

Abstract We show that scattering amplitudes computed from light-cone superstring field theory are divergent at tree level. The divergences can be eliminated, and supersymmetry restored, by the addition of certain counter terms to the light-cone hamiltonian. These counter terms have the form of local contact interactions, whose existence we had previously deduced on grounds of vacuum stability and closure of the super-Poincare algebra. The quartic contact interactions required in type I and type IIB superstring theories are constructed in detail.

New interactions for superstrings

Abstract The supersymmetry relation {Q −A ,Q − B }=2Hδ A B implies the existence of a new quartic vertex in the open superstring light-cone hamiltonian, if the supercharges are cubic in the string fields. Green and Schwarz have argued that this vertex almost vanishes, due to exact cancellations among fermionic operators, with perhaps a non-local interaction remaining. In this article we show that these exact cancellations do not occur for certain contributions to the anticommutator, and that new local, and possibly divergent, 4-string interactions are generated. On the basis of vacuum stability, we argue that 4-string interaction terms should also exist for closed superstring hamiltonians.

Contact interactions in closed superstring field theory

We show that closed (type II and heterotic) superstring field theories, which are presently formulated without contact interactions in the light-cone gauge, do not have a stable vacuum state. States with arbitrary negative energy can be constructed in these theories; an explicit example is given. Negative energy states imply violation of the supersymmetry relation {Q−A, Q−B} = 2σABH. Using coherent state methods, we show that the super-Pioncare algebra is indeed violated by the standard light-cone gauge superstring hamiltonians, since the supercharge anticommulator generates local, 4-string contact interactions at O(λ2), where λ is the coupling of the 3-vertex. Contact interactions must therefore be added to the usual hamiltonian to restore supersymmetry and vacuum stability.

Variational computation of glueball masses in continuum QCD

Abstract We apply a field-theoretic Rayleigh-Ritz method to compute masses of the low-lying glueballs, with allowance for non-perturbative effects via condensate contributions to the gluon propagator. Since the gluon propagator is non-covariant, condensates of the form 〈Tr AA 〉 are allowed and must be introduced. Fitting the coupling constant and condensate parameter from the glueball candidates ι(1440) and θ(1690), we predict that mass (0 ++ ) = 1320 ± 20 MeV, mass (2 −+ ) = 1760 ± 40 MeV, at α s = 0.46 ± 0.05 (with an error estimated by using a variety of trial wavepackets). Our result has the 0 ++ glueball mass close to that of the isoscalar 0 ++ states e(1300) and g s (1240), suggesting that at least one of these states (presumably he g s (1240)) has a large-valence glue component.

A fifth-time action approach to the conformal instability problem in euclidean quantum gravity☆

Abstract The fifth-time action technique (a general method for defining bottomless action theories) is applied to euclidean quantum gravity, whose Einstein-Hilbert action is unbounded from below. A stabilized, diffeomorphism invariant action is generated, which has the same classical equations of motion as the unstable euclidean Einstein-Hilbert action. The stabilized action flips the sign of the “wrong-sign” mode in the kinetic term, and is non-local in the interaction terms. Equivalently, Green functions of the stabilized D = 4 theory can be computed from a D = 5 dimensional functional integral, whose “fifth-time” action is local, as well as diffeomorphism invariant and bounded from below. It is argued that the D = 4 Green functions defined in this way are also reflection positive. The D = 5 formulation thus appears to be a good starting point for latticization and numerical simulation.

Time and probability in quantum cosmology

A time function, an exactly conserved probability measure, and a time-evolution equation (related to the Wheeler-DeWitt equation) are proposed for quantum cosmology. The time-integral of the probability measure is the measure proposed by Hawking and Page. The evolution equation reduces to the Schrodinger equation, and probability measure to the Born measure, in the WKB approximation. The existence of this “Schrodinger-limit”, which involves a cancellation of time-dependencies in the probability density between the WKB prefactor and integration measure, is a consequence of laplacian factor ordering in the Wheeler-DeWitt equation.

Monte Carlo evidence for the gluon-chain model of QCD string formation

The Monte Carlo method is used to calculate the overlaps 〈Ψstring|n gluons〉, where Ψstring[A] is the Yang-Mills wave functional due to a static quark-antiquark pair, and |n gluons〉 are orthogonal trial states containing n = 0, 1, or 2 gluon operators multiplying the true ground state. The calculation is carried out for SU(2) lattice gauge theory in Coulomb gauge, in D = 4 dimensions. It is found that the string state is dominated, at small qq separations, by the vacuum (“no-gluon”) state, at larger separations by the one-gluon state, and, at the largest separations attempted, the two-gluon state begins to dominate. This behavior is in qualitative agreement with the gluon-chain model, which is a large-Ncolors motivated theory of QCD string formation.

Charge screening, large-N, and the abelian projection model of confinement

Abstract We point out that the abelian projection theory of quark confinement is in conflict with certain large- N predictions. According to both large- N and lattice strong-coupling arguments, the perimeter law behavior of adjoint Wilson loops at large scales is due to charge screening, and is suppressed relative to the area term by a factor of 1/ N 2 . In the abelian projection theory, however, the perimeter law is due to the fact that N − 1 out of N 2 − 1 adjoint quark degrees of freedom are (abelian) neutral and unconfined; the suppression factor relative to the area law is thus only 1/ N . We study numerically the behavior of Wilson loops and Polyakov lines with insertions of (abelian) charge projection operators, in maximal abelian gauge. It appears from our data that the forces between abelian charged, and abelian neutral adjoint quarks are not significantly different. We also show via the lattice strong-coupling expansion that, at least at strong couplings, QCD flux tubes attract one another, whereas vortices in type-II superconductors repel.

Stabilized quantum gravity stochastic interpretation and numerical simulation

Following the reasoning of Claudson and Halpern, it is shown that “fifth-time” stabilized quantum gravity is equivalent to Langevin evolution (i.e. stochastic quantization) between fixed non-singular, but otherwise arbituary, initial and final states. The simple restriction to a fixed final state at t5 → ∞ is sufficient to stabilize the theory. This equivalence fixes the integration measure, and suggests a particular operator-ordering, for the fifth-time action of quantum gravity. Results of a numerical simulation of stabilized, latticized Einstein-Cartan theory on some small lattices are reported. In the range of cosmological constant λ investigated, it is found that: (i) the system is always in the broken phase 〈det(e)〉 ≠ 0; and (ii) the negative free energy is large, possibly singular, in the vincinity of λ = 0. The second finding may be relevant to the cosmological-constant problem.

Ehrenfest's principle in quantum gravity

The Ehrenfest principle δt〈q〉 = 〈i[H, q]〉 is proposed as 〈part of 〉 a definition of the time variable in canonical quantum gravity. This principle selects a time direction in superspace, and provides a conserved, positive definite probability measure. An exact solution of the Ehrenfest condition is obtained, which leads to constant-time surfaces in superspace generated by the operator d/dτ = Δϑ·Δ, where Δ is the gradient operator in superspace, and ϑ is the phase of the Wheeler-DeWitt wavefunction ψ; the constant-time surfaces are determined by this solution up to a choice of initial t = 0 surface. This result holds throughout superspace, including classically forbidden regions and in the neighborhood of caustics; it also leads to ordinary quantum field theory and classical gravity in regions of superspace where the phase satisfies |δ,ϑ| ≫ |δt In(ψ≠ψ)| and (δtϑ)2 ≫ |δ2tϑ|.