Vacuum structure of gauge theory on lattice with two parallel plaquette action

We perform Monte Carlo simulations of a lattice gauge system with an action which contains two parallel plaquettes. The action is defined as a product of gauge group variables over two parallel plaquettes belonging to a given three-dimensional cube. The peculiar property of this system is that it has strong degeneracy of the vacuum state inherited from corresponding gonihedric $Z_2$ gauge spin system. These vacuua are well separated and can not be connected by a gauge transformation. We measure different observables in these vacuua and compare their properties.Comment: 9 pages, 6 figures, Late

Two and Three-Dimensional Spin Systems with Gonihedric Action

We perform numerical simulations of the two and three-dimensional spin systems with competing interaction. They describe the model of random surfaces with linear-gonihedric action.The degeneracy of the vacuum state of this spin system is equal to $~~d \cdot 2^{N}~~$ for the lattice of the size $~N^{d}~$. We observe the second order phase transition of the three-dimensional system, at temperature $\beta_{c} \simeq 0.43932$ which almost coincides with $\beta_{c}$ of the 2D Ising model. This confirms the earlier analytical result for the case when self-interaction coupling constant $k$ is equal to zero. We suggest the full set of order parameters which characterize the structure of the vacuum states and of the phase transition.Comment: 10 pages,Latex,The figures are availabl

Interaction Hierarchy. Gonihedric String and Quantum Gravity

We have found that the Regge gravity \cite{regge,sorkin}, can be represented as a $superposition$ of less complicated theory of random surfaces with $Euler~character$ as an action. This extends to Regge gravity our previous result \cite{savvidy}, which allows to represent the gonihedric string \cite{savvidy1} as a superposition of less complicated theory of random paths with $curvature$ action. We propose also an alternative linear action $A(M_{4})$ for the four and high dimensional quantum gravity. From these representations it follows that the corresponding partition functions are equal to the product of Feynman path integrals evaluated on time slices with curvature and length action for the gonihedric string and with Euler character and gonihedric action for the Regge gravity. In both cases the interaction is proportional to the overlapping sizes of the paths or surfaces on the neighboring time slices. On the lattice we constructed spin system with local interaction, which have the same partition function as the quantum gravity. The scaling limit is discussed.Comment: 11 pages,Late

Gonihedric String Equation

We discuss the basic properties of the gonihedric string and the problem of its formulation in continuum. We propose a generalization of the Dirac equation and of the corresponding gamma matrices in order to describe the gonihedric string. The wave function and the Dirac matrices are infinite-dimensional. The spectrum of the theory consists of particles and antiparticles of increasing half-integer spin lying on quasilinear trajectories of different slope. Explicit formulas for the mass spectrum allow to compute the string tension and thus demonstrate the string character of the theory.Comment: 40 pages, Latex, 9 figure

Phase structure of four-dimensional gonihedric spin system

We perform Monte Carlo simulations of a gauge invariant spin system which describes random surfaces with gonihedric action in four dimensions. The Hamiltonian is a mixture of one-plaquette and additional two- and three-plaquette interaction terms with specially adjusted coupling constants. For the system with the large self-intersection coupling constant $k$ we observe the second-order phase transition at temperature $\beta_{c}\simeq 1.75$. The string tension is generated by quantum fluctuations as it was expected theoretically. This result suggests the existence of a noncritical string in four dimensions. For smaller values of $k$ the system undergoes the first order phase transition and for $k$ close to zero exhibits a smooth crossover.Comment: 14 pages, Latex, 10 figure

Neutrino-nucleus reactions and their role for supernova dynamics and nucleosynthesis

The description of nuclear reactions induced by supernova neutrinos has witnessed significant progress during the recent years. At the energies and momentum transfers relevant for supernova neutrinos neutrino-nucleus cross sections are dominated by allowed transitions, however, often with non-negligible contributions from (first) forbidden transitions. For several nuclei allowed Gamow-Teller strength distributions could be derived from charge-exchange reactions and from inelastic electron scattering data. Importantly the diagonalization shell model has been proven to accurately describe these data and hence became the appropriate tool to calculate the allowed contributions to neutrino-nucleus cross sections for supernova neutrinos. Higher multipole contributions are usually calculated within the framework of the Quasiparticle Random Phase Approximation, which describes the total strength and the position of the giant resonances quite well. This manuscript reviews the recent progress achieved in calculating supernova-relevant neutrino-nucleus cross sections and discusses its verification by data. Moreover, the review summarizes also the impact which neutrino-nucleus reactions have on the dynamics of supernovae and on the associated nucleosynthesis. These include the absorption of neutrinos by nuclei (the inverse of nuclear electron capture which is the dominating weak-interaction process during collapse), inelastic neutrino-nucleus scattering and nuclear de-excitation by neutrino-pair emission. We also discuss the role of neutrino-induced reactions for the recently discovered $\nu p$ process, for the r-process and for the neutrino process, for which neutrino-nucleus reactions have the largest impact. Finally, we briefly review neutrino-nucleus reactions important for the observation of supernova neutrinos by earthbound detectors. (Abridged)Comment: 77 pages, 29 figures, 4 tables, submitted to Progress in Particle and Nuclear Physic

T violation in radiative β\beta decay and electric dipole moments

In radiative $\beta$ decay, $T$ violation can be studied through a spin-independent $T$-odd correlation. We consider contributions to this correlation by beyond the standard model (BSM) sources of $T$-violation, arising above the electroweak scale. At the same time such sources, parametrized by dimension-6 operators, can induce electric dipole moments (EDMs). As a consequence, the manifestations of the $T$-odd BSM physics in radiative $\beta$ decay and EDMs are not independent. Here we exploit this connection to show that current EDM bounds already strongly constrain the spin-independent $T$-odd correlation in radiative $\beta$ decay.Comment: 11 pages, 2 figure