Extended QCD(2) from dimensional projection of QCD(4)

We study an extended QCD model in (1+1) dimensions obtained from QCD in 4D by compactifying two spatial dimensions and projecting onto the zero-mode subspace. We work out this model in the large $N_c$ limit and using light cone gauge but keeping the equal-time quantization. This system is found to induce a dynamical mass for transverse gluons -- adjoint scalars in QCD(2), and to undergo a chiral symmetry breaking with the full quark propagators yielding non-tachyonic, dynamical quark masses, even in the chiral limit. We study quark-antiquark bound states which can be classified in this model by their properties under Lorentz transformations inherited from 4D. The scalar and pseudoscalar sectors of the theory are examined and in the chiral limit a massless ground state for pseudoscalars is revealed with a wave function generalizing the so called 't Hooft pion solution.Comment: JHEP class, 16 pages, 3 figures. Change in the title, some improvements in section 2, minors changes and comments added in introduction and conclusions. References added. Version appearing in JHE

Relation between Tunneling and Particle Production in Vacuum Decay

The field-theoretical description of quantum fluctuations on the background of a tunneling field $\sigma$ is revisited in the case of a functional Schrodinger approach. We apply this method in the case when quantum fluctuations are coupled to the $\sigma$ field through a mass-squared term, which is 'time-dependent' since we include the dynamics of $\sigma$ . The resulting mode functions of the fluctuation field, which determine the quantum state after tunneling, display a previously unseen resonance effect when their mode number is comparable to the curvature scale of the bubble. A detailed analysis of the relation between the excitations of the field about the true vacuum (interpreted as particle creation) and the phase shift coming from tunneling is presented.Comment: 20 pages, 4 figures, submitted to PR

Homogeneous Modes of Cosmological Instantons

We discuss the O(4) invariant perturbation modes of cosmological instantons. These modes are spatially homogeneous in Lorentzian spacetime and thus not relevant to density perturbations. But their properties are important in establishing the meaning of the Euclidean path integral. If negative modes are present, the Euclidean path integral is not well defined, but may nevertheless be useful in an approximate description of the decay of an unstable state. When gravitational dynamics is included, counting negative modes requires a careful treatment of the conformal factor problem. We demonstrate that for an appropriate choice of coordinate on phase space, the second order Euclidean action is bounded below for normalized perturbations and has a finite number of negative modes. We prove that there is a negative mode for many gravitational instantons of the Hawking-Moss or Coleman-De Luccia type, and discuss the associated spectral flow. We also investigate Hawking-Turok constrained instantons, which occur in a generic inflationary model. Implementing the regularization and constraint proposed by Kirklin, Turok and Wiseman, we find that those instantons leading to substantial inflation do not possess negative modes. Using an alternate regularization and constraint motivated by reduction from five dimensions, we find a negative mode is present. These investigations shed new light on the suitability of Euclidean quantum gravity as a potential description of our universe.Comment: 16 pages, compressed and RevTex file, including one postscript figure fil

de Sitter geodesics: reappraising the notion of motion

The de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de Sitter spacetime which cannot be joined to each other by any one of these geodesics. By taking into account the appropriate transitivity properties in the variational principle, a new family of maximizing trajectories is obtained, whose members are able to connect any two points of the de Sitter spacetime. These geodesics introduce a new notion of motion, given by a combination of translations and proper conformal transformations, which may possibly become important at very-high energies, where conformal symmetry plays a significant role.Comment: 9 pages. V2: Presentation changes aiming at clarifying the text; version accepted for publication in Gen. Rel. Gra

Fermion Propagators in Type II Fivebrane Backgrounds

The fermion propagators in the fivebrane background of type II superstring theories are calculated. The propagator can be obtained by explicitly evaluating the transition amplitude between two specific NS-R boundary states by the propagator operator in the non-trivial world-sheet conformal field theory for the fivebrane background. The propagator in the field theory limit can be obtained by using point boundary states. We can explicitly investigate the lowest lying fermion states propagating in the non-trivial ten-dimensional space-time of the fivebrane background: M^6 x W_k^(4), where W_k^(4) is the group manifold of SU(2)_k x U(1). The half of the original supersymmetry is spontaneously broken, and the space-time Lorentz symmetry SO(9,1) reduces to SO(5,1) in SO(5,1) x SO(4) \subset SO(9,1) by the fivebrane background. We find that there are no propagations of SO(4) (local Lorentz) spinor fields, which is consistent with the arguments on the fermion zero-modes in the fivebrane background of low-energy type II supergravity theories.Comment: 15 page

Gauge independence of the bubble nucleation rate in theories with radiative symmetry breaking

In field theories where a metastable false vacuum state arises as a result of radiative corrections, the calculation of the rate of false vacuum decay by bubble nucleation depends on the effective potential and the other functions that appear in the derivative expansion of the effective action. Beginning with the Nielsen identity, we derive a series of identities that govern the gauge dependence of these functions. Using these, we show, to leading nontrivial order, that even though these functions are individually gauge-dependent, one obtains a gauge-independent result for the bubble nucleation rate. Our formal arguments are complemented by explicit calculations for scalar electrodynamics in a class of $R_\xi$ gauges.Comment: 19 pages, 3 figures in uuencoded fil

Superconformal Multi-Black Hole Moduli Spaces in Four Dimensions

Quantum mechanics on the moduli space of N supersymmetric Reissner-Nordstrom black holes is shown to admit 4 supersymmetries using an unconventional supermultiplet which contains 3N bosons and 4N fermions. A near-horizon limit is found in which the quantum mechanics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes. This near-horizon theory is shown to have an enhanced D(2,1;0) superconformal symmetry. The bosonic symmetries are SL(2,R) conformal symmetry and SU(2)xSU(2) R-symmetry arising from spatial rotations and the R-symmetry of N=2 supergravity.Comment: 23 pages, harvmac. v2: many typos fixe

The (2+1)-dimensional Gross-Neveu model with a U(1) chiral symmetry at non-zero temperature

We present results from numerical simulations of the (2+1)-dimensional Gross-Neveu model with a U(1) chiral symmetry and N_f=4 fermion species at non-zero temperature. We provide evidence that there are two different chirally symmetric phases, one critical and one with finite correlation length, separated by a Berezinskii-Kosterlitz-Thouless transition. We have also identified a regime above the critical temperature in which the fermions acquire a screening mass even in the absence of chiral symmetry breaking, analogous to the pseudogap behaviour observed in cuprate superconductors.Comment: 12 pages, 6 figure

Self Excitation of the Tunneling Scalar Field in False Vacuum Decay

A method to determine the quantum state of a scalar field after $O(4)$-symmetric bubble nucleation has been developed recently. The method has an advantage that it concisely gives us a clear picture of the resultant quantum state. In particular, one may interpret the excitations as a particle creation phenomenon just as in the case of particle creation in curved spacetime. As an application, we investigate in detail the spectrum of quantum excitations of the tunneling field when it undergoes false vacuum decay. We consider a tunneling potential which is piece-wise quadratic, hence is simple enough to allow us an analytical treatment. We find a strong dependence of the excitation spectrum upon the shape of the potential on the true vacuum side. We then discuss features of the excitation spectrum common to general tunneling potentials not restricted to our simple model.Comment: 24 pages, uuencoded compressed postscript fil

Instantons and radial excitations in attractive Bose-Einstein condensates

Imaginary- and real-time versions of an equation for the condensate density are presented which describe dynamics and decay of any spherical Bose-Einstein condensate (BEC) within the mean field appraoch. We obtain quantized energies of collective finite amplitude radial oscillations and exact numerical instanton solutions which describe quantum tunneling from both the metastable and radially excited states of the BEC of 7Li atoms. The mass parameter for the radial motion is found different from the gaussian value assumed hitherto, but the effect of this difference on decay exponents is small. The collective breathing states form slightly compressed harmonic spectrum, n=4 state lying lower than the second Bogolyubov (small amplitude) mode. The decay of these states, if excited, may simulate a shorter than true lifetime of the metastable state. By scaling arguments, results extend to other attractive BEC-s.Comment: 6 pages, 3 figure