Unstable Vacuum Research Articles

Effective energy–momentum tensor of strong-field QED with unstable vacuum

We study the influence of a vacuum instability on the effective energy-momentum tensor (EMT) of QED, in the presence of a quasiconstant external electric field, by means of the relevant Green functions. In the case when the initial vacuum, |0,in>, differs essentially from the final vacuum, |0,out>, we find explicitly and compared both the vacuum average value of EMT, <0,in|T_{\mu \nu}|0,in>, and the matrix element, <0,out|T_{\mu \nu}|0,in>. In the course of the calculation we solve the problem of the special divergences connected with infinite time T of acting of the constant electric field. The EMT of pair created by an electric field from the initial vacuum is presented. The relations of the obtained expressions to the Euler-Heisenberg's effective action are established.

GRAVITATIONAL INSTABILITY OF THE VACUUM AND THE COSMOLOGICAL CONSTANT PROBLEM

A mechanism for suppressing the cosmological constant is described, using a superconducting analogy in which fermions coupled perturbatively to gravitons are in an unstable false vacuum. The coupling of the fermions to gravitons and a screened attractive interaction among pairs of fermions generates fermion condensates with zero momentum and a phase transition induces a non-perturbative transition to a true vacuum state. This produces a positive energy gap Δ in the vacuum energy identified with [Formula: see text] where Λ is the cosmological constant. In the strong coupling limit, a large cosmological constant induces a period of inflation in the early universe, followed by a weak coupling limit in which [Formula: see text] vanishes exponentially fast as the universe expands due to the dependence of the energy gap on the density of Fermi surface fermions, predicting a small cosmological constant in the early universe.

Gravitational Shielding Effect in Gauge Theory of Gravity

In 1992, E.E. Podkletnov and R. Nieminen found that under certain conditions, ceramic superconductor with composite structure reveals weak shielding properties against gravitational force. In classical Newton's theory of gravity and even in Einstein's general theory of gravity, there are no grounds of gravitational shielding effects. But in quantum gauge theory of gravity, the gravitational shielding effects can be explained in a simple and natural way. In quantum gauge theory of gravity, gravitational gauge interactions of complex scalar field can be formulated based on gauge principle. After spontaneous symmetry breaking, if the vacuum of the complex scalar field is not stable and uniform, there will be a mass term of gravitational gauge field. When gravitational gauge field propagates in this unstable vacuum of the complex scalar field, it will decays exponentially, which is the nature of gravitational shielding effects. The mechanism of gravitational shielding effects is studied in this paper, and some main properties of gravitational shielding effects are discussed.

UNITARITY OF NONCOMMUTATIVE FIELD THEORIES FROM STRING THEORY

We improve the study of the lack of perturbative unitarity of noncommutative space-time quantum field theories derived from open string theory in electric backgrounds, enforcing the universality of the mechanism by which a tachyonic branch cut appears when the Seiberg-Witten limit freezes the string in an unstable vacuum. The main example is realized in the context of the on-shell four-tachyon amplitude of the bosonic string, and the dependence of the phenomenon on the brane-worldvolume dimension is analysed. We discuss the possibility of a proof in superstring theory, and finally mention the NCOS limit in this framework.

Tachyon kinks on non-BPS D-branes

We consider solitonic solutions of the DBI tachyon effective action for a non-BPS brane. When wrapped on a circle, these solutions are regular and have a finite energy. We show that in the decompactified limit, these solitons give Sen's infinitely thin finite energy kink—interpreted as a BPS brane—provided that some conditions on the potential hold. In particular, if for large T the potential is exponential, V=e−Ta, then Sen's solution is only found for a<1. For power-law potentials V=1/Tb, one must have b>1. If these conditions are not satisfied, we show that the lowest energy configuration is the unstable tachyon vacuum with no kinks. We examine the stability of the solitons and the spectrum of small perturbations.

A perturbative analysis of tachyon condensation

Tachyon condensation in the open bosonic string is analyzed using a perturbative expansion of the tachyon potential around the unstable D25-brane vacuum. Using the leading terms in the tachyon potential, Pad\'e approximants can apparently give the energy of the stable vacuum to arbitrarily good accuracy. Level-truncation approximations up to level 10 for the coefficients in the tachyon potential are extrapolated to higher levels and used to find approximants for the full potential. At level 14 and above, the resulting approximants give an energy less than -1 in units of the D25-brane tension, in agreement with recent level-truncation results by Gaiotto and Rastelli. The extrapolated energy continues to decrease below -1 until reaching a minimum near level 26, after which the energy turns around and begins to approach -1 from below. Within the accuracy of this method, these results are completely consistent with an energy which approaches -1 as the level of truncation is taken to be arbitrarily large.

QUANTUM SPINOR FIELD IN THE FRW UNIVERSE WITH A CONSTANT ELECTROMAGNETIC BACKGROUND

This paper is a natural continuation of our paper Quantum Scalar Field in FRW Universe with Constant Electromagnetic Background, Int. J. Mod. Phys.A12, 4837 (1997). We generalize our previous work to the case of a massive spinor field, which is placed in a FRW universe of a special type with a constant electromagnetic field. So as to achieve this, special sets of exact solutions of the Dirac equation in the background under consideration are constructed and classified. Using these solutions representations for out–in, in–in, and out–out spinor Green functions are explicitly constructed as proper-time integrals over the corresponding contours in the complex proper-time plane. The vacuum-to-vacuum transition amplitude and the number of created particles are found and vacuum instability is discussed. The mean values of the current and of the energy–momentum tensor are evaluated, and different approximations for them are presented. The back reaction related to particle creation and to unstable vacuum polarization is estimated in different regimes.

One loop partition function in the presence of tachyon background and corrections to tachyon condensation

We compute the one-loop partition function for quadratic tachyon background in open string theory. Both closed and open string representations are developed. Using these representations we study the one-loop divergences in the partition function in the presence of the tachyon background. The divergences due to the open and closed string tachyons are treated by analytic continuation in the tachyon mass squared. We pay particular attention to the imaginary part of the analytically continued expressions. The last one gives the decay rate of the unstable vacuum. The dilaton tadpole is also given some partial consideration. The partition function is further used to study corrections to tachyon condensation processes describing brane descent relations. Assuming the boundary string field theory prescription for construction of the string field action via partition function holds at one loop level we study the one-loop corrections to the tachyon potential and to the tensions of lower-dimensional branes.

Erratum: Determination of the quantum part of the truly nonperturbative Yang-Mills vacuum energy density in covariant gauge QCD [Phys. Rev. D62, 076008 (2000)

Using the effective potential approach for composite operators, we have formulated a general method of calculation of the truly nonperturbative Yang-Mills vacuum energy density in the covariant gauge QCD ground state quantum models. It is defined as an integration of the truly nonperturbative part of the full gluon propagator over the deep infrared region (soft momentum region). A nontrivial minimization procedure makes it possible to determine the value of the soft cutoff in terms of the corresponding nonperturbative scale parameter, which is inevitably present in any nonperturbative model for the full gluon propagator. We have shown for specific models of the full gluon propagator explicitly that the use of the infrared enhanced and finite gluon propagators lead to the vacuum energy density which is finite, always negative and it has no imaginary part (stable vacuum), while the infrared vanishing propagators lead to unstable vacuum and therefore they are physically unacceptable.

D-brane effective field theory from string field theory

Open string field theory is considered as a tool for deriving the effective action for the massless or tachyonic fields living on D-branes. Some simple calculations are performed in open bosonic string field theory which validate this approach. The level truncation method is used to calculate successive approximations to the quartic terms \phi^4, (A^\mu A_\mu)^2 and [A_\mu, A_\nu]^2 for the zero momentum tachyon and gauge field on one or many bosonic D-branes. We find that the level truncation method converges for these terms within 2-4% when all massive fields up to level 20 are integrated out, although the convergence is slower than exponential. We discuss the possibility of extending this work to determine the structure of the nonabelian Born-Infeld theory describing the gauge field on a system of many parallel bosonic or supersymmetric D-branes. We also describe a brane configuration in which tachyon condensation arises in both the gauge theory and string field theory pictures. This provides a natural connection between recent work of Sen and Zwiebach on tachyon condensation in string field theory and unstable vacua in super Yang-Mills and Born-Infeld field theory.

Determination of the quantum part of the truly nonperturbative Yang-Mills vacuum energy density in covariant gauge QCD

Using the effective potential approach for composite operators, we formulate a general method of calculation of the truly nonperturbative Yang-Mills vacuum energy density in the covariant gauge QCD ground state quantum models. It is defined as an integration of the truly nonperturbative part of the full gluon propagator over the deep infrared region (soft momentum region). A nontrivial minimization procedure makes it possible to determine the value of the soft cutoff in terms of the corresponding nonperturbative scale parameter, which is inevitably present in any nonperturbative model for the full gluon propagator. We have shown for specific models of the full gluon propagator explicitly that the use of the infrared-enhanced and finite gluon propagators leads to the vacuum energy density which is finite, always negative, and has no imaginary part (stable vacuum), while the infrared vanishing propagators lead to an unstable vacuum and therefore they are physically unacceptable.

Level truncation and the tachyon in open bosonic string field theory

The tachyonic instability of the open bosonic string is analyzed using the level truncation approach to string field theory. We have calculated all terms in the cubic action of the string field theory describing zero-momentum interactions of up to level 20 between scalars of level 10 or less. These results are used to study the tachyon effective potential and the nonperturbative stable vacuum. We find that the energy gap between the unstable and stable vacua converges much more quickly than the coefficients of the effective tachyon potential. By including fields up to level 10, 99.91% of the energy from the bosonic D-brane tension is cancelled in the nonperturbative stable vacuum. It appears that the perturbative expansion of the effective tachyon potential around the unstable vacuum has a small but finite radius of convergence. We find evidence for a critical point in the tachyon effective potential at a small negative value of the tachyon field corresponding to this radius of convergence. We study the branch structure of the effective potential in the vicinity of this point and speculate that the tachyon effective potential is globally non-negative.

Timelike T-duality, de Sitter space, large N gauge theories and topological field theory

T-Duality on a timelike circle does not interchange IIA and IIB string theories, but takes the IIA theory to a type $IIB^*$ theory and the IIB theory to a type $IIA^*$ theory. The type $II^*$ theories admit E-branes, which are the images of the type II D-branes under timelike T-duality and correspond to imposing Dirichlet boundary conditions in time as well as some of the spatial directions. The effective action describing an E$n$-brane is the $n$-dimensional Euclidean super-Yang-Mills theory obtained by dimensionally reducing 9+1 dimensional super-Yang-Mills on $9-n$ spatial dimensions and one time dimension. The $IIB^*$ theory has a solution which is the product of 5-dimensional de Sitter space and a 5-hyperboloid, and the E4-brane corresponds to anon-singular complete solution which interpolates between this solution and flat space. This leads to a duality between the large $N$ limit of the Euclidean 4-dimensional U(N) super-Yang-Mills theory and the $IIB^*$ string theory in de Sitter space, and both are invariant under the same de Sitter supergroup. This theory can be twisted to obtain a large $N$ topological gauge theory and its topological string theory dual. Flat space-time may be an unstable vacuum for the type $II^*$ theories, but they have supersymmetric cosmological solutions.

Gluon condensation in nonperturbative flow equations

We employ nonperturbative flow equations for an investigation of the effective action in Yang-Mills theories. We compute the effective action $\Gamma[B]$ for constant color magnetic fields $B$ and examine Savvidy's conjecture of an unstable perturbative vacuum. Our results indicate that the absolute minimum of $\Gamma[B]$ occurs for B=0. Gluon condensation is described by a nonvanishing expectation value of the regularized composite operator $F_{\mu\nu}F^{\mu\nu}$ which agrees with phenomenological estimates.

Comment on a mechanism for dynamical breaking of supersymmetry

We re-examine the so-called Nambu-Jona-Lasinio mechanism suggested by Song, Xu and Chin in breaking the supersymmetry in the Wess-Zumino model and show that this mechanism cannot be justified without assuming special effects between fermions. The fermion condensation suggested by them corresponds to an unstable vacuum configuration. As a result, there is no fermion condensation and no supersymmetry breaking in the model discussed by them.

CONCERNING THE DOUBLE SCALING LIMIT IN THE O(N) VECTOR MODEL IN FOUR DIMENSIONS

The 1/N expansion for the O(N) vector model in four dimensions is reconsidered. It is emphasized that the effective potential for this model becomes everywhere complex just at the critical point, which signals an unstable vacuum. Thus a critical O(N) vector model cannot be consistently defined in the 1/N expansion for four dimensions, which makes the existence of a double-scaling limit for this theory doubtful.

GEOMETRIZED INSTANTONS AND THE CREATION OF THE UNIVERSE

A nonsingular cosmological scenario is presented in which the currently observed Riemannian configuration of spacetime originates from a primordial Weylian “stiff matter” phase driven by a geometrized inflaton-like field. In the particular case of a Friedman-Robertson-Walker line element, it is shown that an unstable original Minkowski vacuum starts to collapse adiabatically at a remote past and bounces when a minimum radius is attained. Throughout the collapsing stage, this matter-free Universe is accelerated (or “inflationary”). As in models of spontaneous quantum creation, the bouncing phase can be shown to correspond to the propagation of a Weyl instanton in an Euclideanized, classically forbidden region. In the course of the bouncing period, concurrent to the maximal deviation of the Riemannian configuration, a geometry-driven amplification mechanism operates causing the exponential increase of entropy and matter fluctuations. Once the environment temperature is always bounded, this nonadiabatical process stands for a “ Big — but finite — Bang” creation event, followed by a standard radiation-dominated era. The model describes an eternal, Friedman-like open Universe, free of many problems that hinder standard cosmology; the observed existence of a baryon excess also fits naturally within the proposed scheme.

QUANTUM EFFECTS IN A COMBINATION OF A CONSTANT UNIFORM FIELD AND A PLANE WAVE FIELD

Quantum effects are considered in the external field, which is a superposition of a constant uniform electromagnetic field and a plane wave field. The complete and orthonormal sets of solutions to the Klein-Gordon and Dirac equations are constructed for this field. The probabilities of scattering and pair creation are calculated. The representations of various Green functions, which are used in quantum electrodynamics with unstable vacuum, are obtained. The radiative processes are explored for the field under consideration.

Vacuum stability, wormholes, cosmic rays and the cosmological bounds on mt and mH

In the standard model, if the top quark mass m t is larger than some critical value depending on the Higgs mass m H, then we live in an unstable vacuum state corresponding to a local minimum of the effective potential. An experimental discovery of the top quark with m t above this critical value would invalidate the standard version of the wormhole theory, according to which the vacuum energy should be zero at the absolute minimum of the effective potential. However, unless the top quark is much heavier than this, the lifetime is much heavier than this, the lifetime of the unstable vacuum state is greater than the age of our part of the universe. In this paper we develop a stochastic approach to tunneling and apply it to examine the possibility that cosmic ray collisions may trigger vacuum decay and derive improved cosmological bounds on m H and m t.

Optical Theorem in Quantum electrodynamics with Unstable Vacuum

All the results reffering to the relations of the optical theorem in QED with an external electromagnetic field with unstable vacuum are consistently given in this paper. The results obtained are true in all orders of perturbation theory. A generating functional is introduced for calculating total probabilities of any processes in QED with unstable vacuum.