119304812
Application of abelian holonomy formalism to the elementary theory of numbers
We consider an abelian holonomy operator in two-dimensional conformal field theory with zero-mode contributions. The analysis is made possible by use of a geometric-quantization scheme for abelian Chern-Simons theory on S1 × S1 × R. We find that a purely zero-mode part of the holonomy operator can be expressed in terms of Riemann's zeta function. We also show that a generalization of linking numbers can be obtained in terms of the vacuum expectation values of the zero-mode holonomy operators. Inspired by mathematical analogies between linking numbers and Legendre symbols, we then apply these results to a space of Fp = Z/pZ, where p is an odd prime number. This enables us to calculate “scattering amplitudes” of identical odd primes in the holonomy formalism. In this framework, the Riemann hypothesis can be interpreted by means of a physically obvious fact, i.e., there is no notion of “scattering” for a single-particle system. Abelian gauge theories described by the zero-mode holonomy operators will be usef...
16024304
Noncommutative gravity: Fuzzy sphere and others
Gravity on noncommutative analogues of compact spaces can give a finite mode truncation of ordinary commutative gravity. We obtain the actions for gravity on the noncommutative two-sphere and on the noncommutative ${\mathbf{CP}}^{2}$ in terms of finite dimensional $(N\ifmmode\times\else\texttimes\fi{}N)$ matrices. The commutative large N limit is also discussed.
118650221
Holonomies of gauge fields in twistor space 3: Gravity as a square of N=4 theory
Abstract In a recent paper, we show that an S-matrix functional for graviton amplitudes can be described by an N = 8 supersymmetric gravitational holonomy operator in twistor space. In this paper, we obtain an alternative expression for the gravitational holonomy operator such that it can be interpreted as a square of an N = 4 holonomy operator for frame fields, by taking a sum of certain shuffles over ordered indices. The new expression leads to amplitudes of not only spin-2 gravitons but also spin-0 massless particles. We discuss that the squared model is favored as a theory of quantum gravity.
119222076
On the deconfining limit in (2+1)-dimensional Yang–Mills theory
Abstract We consider ( 2 + 1 ) -dimensional Yang–Mills theory on S 1 × S 1 × R in the framework of a Hamiltonian approach developed by Karabali, Kim and Nair. The deconfining limit in the theory can be discussed in terms of one of the S 1 radii of the torus ( S 1 × S 1 ), while the other radius goes to infinity. We find that the limit agrees with the previously known result for a dynamical propagator mass of a gluon. We also make comparisons with numerical data.
119406982
Emergence of longitudinal 7-branes and fuzzy S 4 in compactification scenarios of M(atrix) theory
In M(atrix) theory, there exist membranes and longitudinal 5-branes (L5-branes) as extended objects. Transverse components of these brane solutions are known to be described by fuzzy ${\mathbf{C}\mathbf{P}}^{k}$ ($k=1$, 2), where $k=1$ and $k=2$ correspond to spherical membranes and L5-branes of ${\mathbf{C}\mathbf{P}}^{2}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ world-volume geometry, respectively. In addition to these solutions, we here show the existence of L7-branes of ${\mathbf{C}\mathbf{P}}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ geometry, introducing extra potentials to the M(atrix) theory Lagrangian. As in the cases of $k=1$, 2, the L7-branes (corresponding to $k=3$) also break the supersymmetries of M(atrix) theory. The extra potentials are introduced such that the energy of a static L7-brane solution becomes finite in the large $N$ limit where $N$ represents the matrix dimension of fuzzy ${\mathbf{C}\mathbf{P}}^{3}$. As a consequence, fluctuations from the L7-branes are suppressed, which effectively describes compactification of M(atrix) theory down to 7 dimensions. We show that one of the extra potentials can be considered as a matrix-valued 7-form. The presence of the 7-form in turn supports a possibility of Freund-Rubin type compactification. This suggests that our modification of M(atrix) theory can also lead to a physically interesting matrix model in four dimensions. In hope of such a possibility, we further consider compactification of M(atrix) theory down to fuzzy ${S}^{4}$ which can be defined in terms of fuzzy ${\mathbf{C}\mathbf{P}}^{3}$. Along the way, we also find a new L5-brane solution to M(atrix) theory which has purely spherical geometry in the transverse directions.
119278846
Holonomies of gauge fields in twistor space 4: Functional MHV rules and one-loop amplitudes
Abstract We consider generalization of the Cachazo–Svrcek–Witten (CSW) rules to one-loop amplitudes of N = 4 super Yang–Mills theory in a recently developed holonomy formalism in twistor space. We first reconsider off-shell continuation of the Lorentz-invariant Nair measure for the incorporation of loop integrals. We then formulate an S-matrix functional for general amplitudes such that it implements the CSW rules at quantum level. For one-loop MHV amplitudes, the S-matrix functional correctly reproduces the analytic expressions obtained in the Brandhuber–Spence–Travaglini (BST) method. Motivated by this result, we propose a novel regularization scheme by use of an iterated-integral representation of polylogarithms and obtain a set of new analytic expressions for one-loop NMHV and N 2 MHV amplitudes in a conjectural form. We also briefly sketch how the extension to one-loop non-MHV amplitudes in general can be carried out.
121916152
On stochastic approaches of nuclear dynamics
Abstract We present recent developments of stochastic descriptions of nuclear dynamics. We focus on the newly introduced microscopic descriptions, such as stochastic extensions of currently used kinetic equations, as well as on more phenomenological, macroscopic approaches. We show to what extent these stochastic descriptions may offer a proper picture of nuclear dynamics both in strongly out of equilibrium situations, such as the ones encountered in energetic heavy-ion collisions or in closer to equilibrium situations such as the deexcitation of hot nuclei by thermal fission. In Section 1 we present a pedestrian introduction to the stochastic description of dynamical systems. We start from the elementary Brownian motion and introduce the Langevin and Fokker-Planck descriptions of the motion on that occasion. A few words are then spent to discuss the numerical methods developed for simulating stochastic equations. Section 2 of the paper is devoted to a formal introduction and discussion of both macroscopic and microscopic stochastic descriptions of nuclear dynamics. After a brief introduction reminding general concepts of equilibrium statistical physics we focus on microscopic descriptions of the many-body problem. We introduce here the Boltzmann Langevin equation which will provide a basis for many subsequent discussions. After having discussed the obtention of this equation from various points of view (from density matrix and Green's function techniques in particular), we consider reduced versions of this equation as well as a Fokker-Planck alternative. Section 3 is devoted to an analysis of fission by means of Langevin or Fokker-Planck-like approaches. We mainly discuss phenomenological approaches and spend some time in a detailed presentation of the ingredients entering these models. We present results obtained in these dynamical calculations when a proper account of particle evaporation is included for describing the fission of hot nuclei. Critical comparisons with experimental data are also provided. In Section 4 we focus on the application of the Boltzmann Langevin Equation to various situations encountered in energetic nuclear collisions. We first remind some typical examples for which this stochastic approach is both necessary and well suited. Typical applications are nuclear multifragmentation and subthreshold particle production, such as in particular kaon production. We discuss possible simulations of this equation and present some results in realistic calculations of collisions. We particularly focus on the dynamics of collective variables such as the quadrupole moment of the momentum distribution. We finally discuss other numerical simulations developed in the field. The last section before conclusion is devoted to extensions presently developed in the field of microscopic stochastic descriptions of nuclear dynamics. We present as a first step a relativistic version of the theory, then focus on fluid dynamics reductions. We finally discuss in some detail the recently introduced Stochastic time-dependent Hartree-Fock theory, which could provide new interesting developments.
53482561
Inverse Kramers formula and fusion dynamics of heavy ions
Abstract.Fusion probability of colliding heavy ions is evaluated by exactly solving a Langevin equation with a parabolic potential barrier. The model, which accommodates dissipation in the approaching phase, leads to an inverse Kramers formula and an expression of the extra-push energy. In the very specific case of an overdamped regime, an Arrhenius-type formula is obtained.
14579423
Theory of fusion hindrance and synthesis of the superheavy elements
Abstract The two-step model for fusion reactions of massive systems is briefly reminded. By the use of fusion probabilities obtained by the model and of survival probabilities obtained by the new statistical code, we predict xn residue cross sections for 48 Ca+actinide systems leading to superheavy elements with Z=114, 116 and 118.
14734856
Theoretical predictions of residues cross sections of superheavy elements
Dynamical reaction theories are reviewed for synthesis of superheavy elements. Characteristic features of formation and surviving are discussed with reference to possible incident channels. Theoretical predictions are presented on favorable incident channels and on optimum energies for synthesis of Z=114.
118635536
Analysis of the fusion hindrance in mass-symmetric heavy ion reactions
The fusion hindrance, which is also denominated by the term extra-push, is studied on mass-symmetric systems by the use of the liquid drop model with the two-center parameterization. Following the idea that the fusion hindrance exists only if the liquid drop barrier (saddle point) is located at the inner side of the contact point after overcoming the outer Coulomb barrier, the reactions in which two barriers are overlapped with each other are determined. It is shown that there are many systems where the fusion hindrance does not exist for the atomic number of projectile or target nucleus Z ⩽ 43, while for Z> 43, all of the mass-symmetric reactions are fusion-hindered.