P.G. Tinyakov

Infrared-modified gravities and massive gravitons

We review some theoretical and phenomenological aspects of massive gravities in 4 dimensions. We start from the Fierz–Pauli theory with Lorentz-invariant mass terms and then proceed to Lorentz-violating masses. Unlike the former theory, some models with Lorentz violation have no pathologies in the spectrum in flat and nearly flat backgrounds and lead to an interesting phenomenology.

Brane world: disappearing massive matter

In a brane (domain wall) scenario with an infinite extra dimension and localized gravity, bulk fermions and scalars often have bound states with zero 4-dimensional mass. In this way massless matter residing on the brane may be obtained. We consider what happens when one tries to introduce small, but non-vanishing mass to these matter fields. We find that the discrete zero modes turn into quasi-localized states with finite 4-dimensional mass and finite width. The latter is due to tunneling of massive matter into extra dimension. We argue that this phenomenon is generic to fields that can have bulk modes. We also point out that in theories meant to describe massive scalars, the 4-dimensional scalar potential has, in fact, power-law behavior at large distances.

Instanton induced cross sections below the sphaleron

Abstract We study the S-matrix and the total cross section of high-energy collisions in the one-instanton sector of purely bosonic theories with instantons. Making use of the coherent state formalism, we develop the perturbation theory around the instanton. We find that in the limit g2 → 0, E/Esph fixed, the leading behaviour of the total cross section is σtot ∼ exp[g−2(−2S0 + F(E/Esph))], where S0 is the instanton action. In the eelectroweak theory at E/Esph ⪡ 1, the function F(E/Esph) is determined by the gauge boson part of the instanton configuration and its explicit form is found. Our results suggest that there may exist a semiclassical type of procedure for evaluating the leading behaviour of the one-instanton total cross section at E≳Esph and g2 → 0.

Periodic instantons and scattering amplitudes

Abstract We discuss the role of periodic euclidean solutions with two turning points and zero winding number (periodic instantons) in instanton-induced processes below the sphaleron energy E sph . We find that the periodic instantons describe certain multiparticle scattering events leading to the transitions between topologically distinct vacua. Both the semiclassical amplitudes and initial and final states of these transitions are determined by the periodic instantons. Furthermore, the corresponding probabilities are maximal among all states of a given energy. We show that at E ⪡ E sph , the periodic instantons can be approximated by infinite chains of ordinary instantons and anti-instantons, and they naturally emerge as deformations of the zero-energy instanton. In the framework of the two-dimensional abelian Higgs model and four-dimensional electroweak theory we show, however, that there is no obvious relation between periodic instantons and two-particle scattering amplitudes.

Is the electric charge conserved in brane world

We discuss whether electric charge conservation may not hold in four-dimensional world in models with infinite extra dimensions, i.e., whether escape of charged particles from our brane is consistent with effectively four-dimensional electrodynamics on the brane. We introduce a setup with photon localized on the brane and show that charge leakage into extra dimension is allowed within this setup. The electric field induced on the brane by escaping charge does not obey four-dimensional Maxwells equations; this field gradually disappears in a causal way. We also speculate on the possibility of the escape of colored particles and formation of colorless free quark states on the brane.

What becomes of vortices in theories with flat directions

Abstract In many theories with flat directions of scalar potential, static vortex solutions do not exist for a generic choice of vacuum. In tow Euclidean dimensions, we find their substitutes — constrained instantons consisting of compact core formed by Abrikosov-Nielsen-Olesen vortex and long-ranged cloud of modulus field. In (3 + 1) dimensions, an initial compact configuration of string topology evolves in such a way that at every point in space the modulus relaxes, in a universal manner, to one and the same value characteristic to the theory.

Galactic anisotropy as signature of CDM related ultrahigh-energy cosmic rays

We show that “top-down” mechanisms of ultrahigh-energy cosmic rays which involve heavy relic particle-like objects predict a Galactic anisotropy of the highest-energy cosmic rays at the level of minimum ∼ 20%. This anisotropy is large enough to be either observed or ruled out in the next generation of experiments.

Bumpy black holes from spontaneous Lorentz violation

We consider black holes in Lorentz violating theories of massive gravity. We argue that in these theories black hole solutions are no longer universal and exhibit a large number of hairs. If they exist, these hairs probe the singularity inside the black hole providing a window into quantum gravity. The existence of these hairs can be tested by future gravitational wave observatories. We generically expect that the effects we discuss will be larger for the more massive black holes. In the simplest models the strength of the hairs is controlled by the same parameter that sets the mass of the graviton (tensor modes). Then the upper limit on this mass coming from the inferred gravitational radiation emitted by binary pulsars implies that hairs are likely to be suppressed for almost the entire mass range of the super-massive black holes in the centers of galaxies.

Towards the semiclassical calculability of high energy instanton cross sections

Abstract We argue that the baryon number violating cross sections of two-particle collisions at high energies can be evaluated by studying the rate of instanton-like transitions for multiparticle “semiclassical” states. In the limit g 2 →0, where g is the coupling constant, this transition rate has a semiclassical form, σ ( E )∼exp[(1/ g 2 ) F ( E / E sph )], while by an appropriate choice of the initial state, σ ( E ) can be made close to the two-particle cross section at CM energy E . Therefore, the two-particle cross section is argued to have the same exponential form, with the function F ( E / E sph ) calculable by semiclassical methods.

Instanton induced cross-section at high-energies: Leading order and beyond

We study the total cross-section of high energy collisions in the one-instanton sector of purely bosonic theories with instantons. We find that in the limit g2 → 0, E/Esph = fixed, the leading behavior of the total cross-section is σlot ~ exp [1/g2(−2S0 + F(E/Esph))], where S0 is the instanton action. In the electroweak theory at E/Esph ≪ 1, the function F(E/Esph) is determined by the gauge boson part of the instanton configuration and its explicit form is found.