arXiv subjects
Publications and source records attributed to K. G. Savvidy.
Searches for WIMP Dark Matter particle at the LHC are considered from the point of view of the existence of a Dark Matter particle which couples primarily through the heavy gauge boson Z, as suggested by recent tentative evidence for a 130 GeV gamma line in the FermiLAT data. We compare three models in which the WIMP is a neutrino-like particle and consider the limits on such particle and interactions from LHC.
The recent WMAP and Planck data have confirmed that exotic dark matter together with the vacuum energy (cosmological constant) dominate in the flat Universe. Many extensions of the standard model provide dark matter candidates, in particular Weakly Interacting Massive Particles (WIMPs). %Supersymmetry provides a natural dark matter candidate, the lightest supersymmetric particle (LSP). Thus the direct dark matter detection is central to particle physics and cosmology. Most of the research on this issue has hitherto focused on the detection of the recoiling nucleus. In this paper we study transitions to the excited states, possible in some nuclei, which have sufficiently low lying excited states. Good examples are the first excited states of I-127 and Xe-129. %focusing on the first excited state at 50 keV of Iodine A=127. We find appreciable branching ratios for the inelastic scattering mediated by the spin cross sections. %find that the transition rate to this excited state is about 5 %percent of the transition to the ground state for low mass WIMPS, but the branching ratio can be much larger in the case pf heaver WIMPS. So, in principle, the extra signature of the gamma ray following the de-excitation of these states can, in principle, be exploited experimentally.
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.
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 $β_{c}\simeq 1.75$. 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.
We analyse the curvature representation of the gonihedric action $A(M)$ for the cases when the dependence on the dihedral angle is arbitrary.
Using the Steiner-Weyl expansion formula for parallel manifolds and the so called gonihedric principle we find a large class of discrete integral invariants which are defined on simplicial manifolds of various dimensions. These integral invariants include the discrete version of the Hilbert-Einstein action found by Regge and alternative actions which are linear with respect to the size of the manifold. In addition the concept of generalized deficit angles appear in a natural way and is related to higher order curvature terms. These angles may be used to introduce various aspects of rigidity in simplicial 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.
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 $β_{c} \simeq 0.43932$ which almost coincides with $β_{c}$ 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.
We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a two-plaquette gauge Hamiltonian. The duality transformation is constructed in geometrical and algebraic language. The dual Hamiltonian represents a new type of spin system with local gauge invariance. At each vertex $ξ$ there are $d(d-1)/2$ Ising spins $Λ_{μ,ν}= Λ_{ν,μ}$, $μ\neq ν= 1,..,d$ and one Ising spin $Γ$ on every link $(ξ,ξ+e_μ)$. For the frozen spin $Γ\equiv 1$ the dual Hamiltonian factorizes into $d(d-1)/2$ two-dimensional Ising ferromagnets and into antiferromagnets in the case $Γ\equiv -1$. For fluctuating $Γ$ it is a sort of spin glass system with local gauge invariance. The generalization to $p$-branes is given.
We analyse a new class of statistical systems, which simulate different systems of random surfaces on a lattice. Geometrical hierarchy of the energy functionals on which these theories are based produces corresponding hierarchy of the surface dynamics and of the phase transitions. We specially consider 3D gonihedric system and have found that it is equivalent to the propagation of almost free 2D Ising fermions. We construct dual statistical system with new matchbox spin variable $G_ξ$, high temperature expansion of which equally well describe these surfaces.
We analyse statistical system with interface energy proportional to the length of the edges of interface. We have found the dual system high temperature expansion of which equally well generates surfaces with linear amplitude. These dual systems are in the same relation as 3D Ising ferromagnet to the 3D Gauge spin system.
We classify different theories of self-intersecting random surfaces assigning special weights to intersections. When self-intersection coupling constant $κ$ tends to zero, then the surface can freely inetrsect and it is completely self-avoiding when $κ$ tends to infinity. Equivalent spin systems for this general case were constructed. In two-dimension the system with $κ= 0$ is in complete disorder as it is in the case of 2D gauge Ising system.
Few natural basic principles allow to extend Feynman integral over the paths to an integral over the surfaces so, that they coincide at long time scale, that is when the surface degenerates into a single particle world line. In the first approximation the loop Green functions have perimeter behavior. That corresponds to the case when free quarks interact through one gluon exchange. Quantum fluctuations of the surface generate the area low. Thus in this string theory asymptotic freedom and confinement can coexist.