Ghost-free higher-derivative theory

We present an example of the quantum system with higher derivatives in the Lagrangian, which is ghost-free: the spectrum of the Hamiltonian is bounded from below and unitarity is preserved.     

Supermembrane monopole vacua

The supermembrane classical solutions with non-trivial circle bundles, i.e. supermembrane monopole vacua, are derived. The hamiltonian of the fermion fluctuations about the monopole vacuum configuration is weakly hermitian, in contrast with the same problem in QED. The electrically charged and dyon analogues to the monopole vacua are also discussed.     

Non-Abelian higher-derivative Chern-Simons theories

The canonical and path-integral quantization of the non-Abelian higher-derivative Chem-Simons model in three dimensions coupled to a matter field is constructed. The expression of the gauge field propagator in the momentum space for this higher-derivative model is computed. In the framework of the perturbative formalism, the diagrammatic and the Feynman rules are analyzed. Among other results, we conclude that higher-derivative terms added to the Lagrangian improve the ultraviolet behavior, rendering the model less divergent.     

Lattice θ vacua

We study some aspects of θ vacua by Monte-Carlo simulations of the SU(2) lattice gauge theory using a definition proposed recently for the total lattice topological charge. We find no phase transition up to θ = 0.8π. Beyond this point, limited statistical accuracy prevents a definite conclusion. Our results are in surprisingly good agreement with the dilute gas picture.     

Fermion helicity flip in higher-derivative electromagnetism

It is shown that massive fermions have their helicity flipped on account of their interaction with an electromagnetic field described by Podolsky’s generalized electrodynamics. Massless fermions, in turn, seem to be unaffected by the electromagnetic field as far as their helicity is concerned.     

Quantization of higher-derivative field theories

A free-scalar field satisfying a wave equation with any number of time derivatives is expanded in terms of creation and annihilation operators that are quantized by replacing the classical Poisson brackets of Ostrogradski by the commutator. Regardless of the coefficients in the wave equation, various algebraic identities make it possible to explicitly carry out the quantization, construct the Hamiltonian, and evaluate the propagator. There are always states of negative norm. A wave equation whose highest time derivative is order 2N can have N single-particle states with positive, real energy. Of these, the number of negative-norm states will be N/2 if N is even and (N−1)/2 if N is odd.     

Canonical transformations in a higher-derivative field theory

It has been suggested that the chiral symmetry can be implemented only in classical Lagrangians containing higher covariant derivatives of odd order. Contrary to this belief, it is shown that one can construct an exactly soluble two-dimensional higher-derivative fermionic quantum field theory containing only derivatives of even order whose classical Lagrangian exhibits chiralgauge invariance. The original field solution is expressed in terms of usual Dirac spinors through a canonical transformation, whose generating function allows the determination of the new Hamiltonian. It is emphasized that the original and transformed Hamiltonians are different because the mapping from the old to the new canonical variables depends explicitly on time. The violation of cluster decomposition is discussed and the general Wightman functions satisfying the positive-definiteness condition are obtained.     

Fixed points of higher-derivative gravity

We recalculate the beta functions of higher-derivative gravity in four dimensions using the one-loop approximation to an exact renormalization group equation. We reproduce the beta functions of the dimensionless couplings that were known in the literature, but we find new terms for the beta functions of Newton's constant and of the cosmological constant. As a result, the theory appears to be asymptotically safe at a non-Gaussian fixed point rather than perturbatively renormalizable and asymptotically free.     

Black hole evaporation and higher-derivative gravity

We examine the role which higher-derivative gravity interactions may play in black hole evaporation. The thermodynamic properties of black holes in Lovelock gravity are described. In certain cases, the specific heat of a black hole becomes positive at a small mass. This results in an infinite lifetime for the black hole (and also allows it to achieve stable equilibrium with a thermal environment). Thus no conflict with unitary time evolution would arise in such theories.This essay received the fourth award from the Gravity Research Foundation for the year 1988.-Ed.     

Plausible black hole solutions in higher-derivative gravity

Here we obtain explicit black hole solutions in Extension Gravity models with high-order derivative terms, while the Lichnerowicz-type theorem simplifies our analysis by vanishing Ricci's scalar curvature. We find out two explicit static, spherical solutions that satisfy the presented action: the first one is the same usual Schwarzschild solution and the other one is the new non-Schwarzschild solution. It means that Schwarzschild's solution following the no-hair theorem can describe any black hole object on each gravity theory. Without considering the first law of thermodynamics for it, we show that the non-Schwarzschild solution is depending on its set of constants, and then we consider its entropy and other thermodynamic parameters for specific values of the constants.     

Speed of light in non-trivial vacua

We unify all existing results on the change of the speed of low-energy photons due to modifications of the vacuum, finding that it is given by a universal constant times the quotient of the difference of energy densities between the usual and modified vacua over the mass of the electron to the fourth power. Whether photons move faster or slower than c depends only on the lower or higher energy density of the modified vacuum, respectively. Physically, a higher energy density is characterized by the presence of additional particles (real or virtual) in the vacuum whereas a lower one stems from the absence of some virtual modes. We then carry out a systematic study of the speed of propagation of massless particles for several field theories up to two loops on a thermal vacuum. Only low-energy massless particles corresponding to a massive theory show genuine modifications of their speed while remaining massless. All other modifications are mass related, or running mass-related. We also develop a formalism for the Casimir vacuum which parallels the thermal one and check that photons travel faster than c between plates.     

Spinor-vector duality in heterotic string vacua

Classification of the N=1 space–time supersymmetric fermionic Z₂×Z₂ heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S_t↔V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor-vector duality exists also in fermionic Z₂ heterotic string models, which preserve N=2 space–time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S_t↔V duality map. We present a novel basis to generate the free fermionic models in which the ten-dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non-trivial sectors, and due to the triality property of the SO(8) representations. Thus, while in the new basis the appearance of GUT symmetries is more cumbersome, it may be more instrumental in revealing the duality symmetries that underly the string vacua.     

Infrared sensitivity of unstable vacua

We discover that some unstable vacua have long memory. By that we mean that even in the theories containing only massive particles, there are correllators and expectation values which grow with time. We examine the cases of instabilities caused by the constant electric fields, expanding and contracting universes and, most importantly, the global de Sitter space. In the last case the interaction leads to a remarkable UV/IR mixing and to a large back reaction. This gives reasons to believe that the cosmological constant problem could be resolved by the infrared physics.