Vol 190, No 3 (2017)

We discuss the universal soft behavior of form factors in the N=4 maximally supersymmetric Yang–Mills theory in the limit where the momentum of one of the particles tends to zero. We present details of how the tree-level form factors of this theory are related to eigenfunctions of a gl(4|4) integrable spin chain.

For the first time, we present a field theory description of the phase transition in an amorphous magnet with the effects of both random anisotropy and structural defects in the two-loop approximation with the fixed dimension d = 3. For this multivertex model, we determine the system of fixed points of the renormalization group equations and calculate the stability exponents using the Padé–Borel summation method. We show the role of structural defects as stabilizing factors in second-order phase transitions.

We formulate a model of quark–antiquark interaction related to the limit transition to the light-front Hamiltonian in quantum chromodynamics. As ultraviolet regularization, we use a lattice in the space of transverse coordinates, and we additionally introduce a longitudinal light-front coordinate cutoff and also corresponding periodic boundary conditions. We regard the zero mode with respect to this coordinate as an independent dynamical variable. The state space of the model is limited to a quark and an antiquark that interact only via the zero mode of the gluon field on the light front. In this framework, we obtain a discrete mass spectrum of bound states. This spectrum is determined by an equation that with respect to the longitudinal coordinate turns out to be analogous to the’ t Hooft equation in two-dimensional quantum chromodynamics. The equation also contains a quark–antiquark potential that ensures confinement in the transverse space.

We present the method and results of a renormalization group description of nonequilibrium critical relaxation of model A with evolution from an initial high-temperature state. We calculate the two-time dependence of the correlation function and response function and find a violation of the fluctuationdissipation theorem in the nonequilibrium critical regime. For the limit fluctuation-dissipation relation, which is a universal property of the nonequilibrium critical dynamics, we calculate the fluctuation and impurity corrections in the two-loop approximation at the fixed space dimension d = 3 using Padé–Borel summation for asymptotic series.

We consider reference systems of uniformly accelerated observers in anti-de Sitter space. We construct coordinate transformations for the transition from an inertial reference system to a uniformly accelerated reference system for all acceleration values, both greater and less than critical. The basis for the construction are the Beltrami coordinates, natural coordinates for describing a uniformly accelerated motion because geodesics in anti-de Sitter space in these coordinates become straight lines, i.e., can be described by linear functions. Because translations of space–time coordinates in anti-de Sitter space are non-Abelian, a nontrivial problem of defining the comoving inertial reference system arises. Constructing the coordinate system of an accelerated observer using this auxiliary comoving inertial reference system requires additional transformations that not only equalize the velocities of the two systems but also equalize the system origins. The presence of a critical acceleration in anti-de Sitter space leads to a difference in explicit expressions in passing to an accelerated coordinate system for accelerations greater and less than critical.

We study the dynamics of a massive pointlike particle coupled to gravity in four space–time dimensions. It has the same degrees of freedom as an ordinary particle: its coordinates with respect to a chosen origin (observer) and the canonically conjugate momenta. The effect of gravity is that such a particle is a black hole: its momentum becomes spacelike at a distances to the origin less than the Schwarzschild radius. This happens because the phase space of the particle has a nontrivial structure: the momentum space has curvature, and this curvature depends on the position in the coordinate space. The momentum space curvature in turn leads to the coordinate operator in quantum theory having a nontrivial spectrum. This spectrum is independent of the particle mass and determines the accessible points of space–time.

We analyze properties of unstable vacuum states from the standpoint of quantum theory. Some suggestions can be found in the literature that some false (unstable) vacuum states can survive up to times when their survival probability takes a nonexponential form. At asymptotically large times, the survival probability as a function of the time t has an inverse power-law form. We show that in this time region, the energy of false vacuum states tends to the energy of the true vacuum state as 1/t² as t→∞. This means that the energy density in the unstable vacuum state and hence also the cosmological constant Λ = Λ(t) should have analogous properties. The conclusion is that Λ in a universe with an unstable vacuum should have the form of a sum of the “bare” cosmological constant and a term of the type 1/t²: Λ(t) ≡ Λ_bare + d/t² (where Λ_bare is the cosmological constant for a universe with the true vacuum).