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.
44215083
Fuzzy S(4) and its construction
We present construction of fuzzy S, utilizing the fact that CP is an S bundle over S. Fuzzy S is obtained by imposing an additional algebraic constraint on fuzzy CP. Hence, as in the case of fuzzy CP = SU(4)/U(3), fuzzy S is globally defined on R with the additional constraint on top of the construction of fuzzy CP. We consider the commutative limit of fuzzy S and find that it naturally gives commutative S in terms of homogeneous coordinates on CP. We also discuss exact matrix-function correspondence of fuzzy S. In conclusion, it is proposed that fuzzy S is described by a certain form of block-diagonal matrix whose embedding square matrix represents fuzzy CP.
56161879
Construction of Fuzzy Spaces and Their Applications to Matrix Models
Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in mathematics and physics. Shedding some light on such an interplay is the main theme of this dissertation. The dissertation roughly separates into two parts. In the first part, we consider a mathematical aspect of fuzzy spaces, namely, their construction. We begin with a review of the construction of fuzzy complex projective spaces CP^k (k=1,2,...) in relation to geometric quantization. We then present the construction of fuzzy S^4, utilizing the fact that CP^3 is an S^2 bundle over S^4. This method is also applicable to the case of fuzzy S^8. In the second part, we consider applications of fuzzy spaces to physics. We first consider gravitational theories on fuzzy spaces, anticipating that they may offer a novel way of regularizing spacetime dynamics. Particularly we obtain actions for gravity on fuzzy S^2 and fuzzy CP^2. We also discuss application to M(atrix) theory. Introducing extra potentials, we show that the theory has new brane solutions whose transverse directions are described by fuzzy S^4 and fuzzy CP^3. The extra potentials can be interpreted as fuzzy versions of differential forms or fluxes, which enable us to discuss compactification models of M(atrix) theory. Compactification down to fuzzy S^4 is discussed and a physically interesting matrix model in four-dimensions is proposed.
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.
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.
118361299
Stochastic approaches to dynamics of heavy ion collisions, the case of thermal fission
In order to study the influence of fluctuations on various phenomena linked to heavy ion collisions, a Langevin equation has been derived from a microscopic model. Parameters entering this equation are completely determined from microscopic quantities characterizing nuclear matter. This equation has been applied to various phenomena at intermediate energies. This paper focuses on large amplitude motions and especially thermal fission. Fission rate is calculated and compared to experimental results.
53058436
WHAT CAN WE LEARN FROM THE FISSION TIME OF THE SUPER-HEAVY ELEMENTS?
Recent experiments performed at GANIL with a crystal blocking technique have shown direct evidences of long fission times in the Super-Heavy Elements (SHE) region. Aimed to localize the SHE island of stability, can these experiments give access to the fission barrier and then to the shell-correction energy? In this paper, we calculate the fission time of heavy elements by using a new code, KEWPIE2, devoted to the study of the SHE. We also investigate the effect of potential structure beyond the saddle on the fission time.
317018
Spin Alignments in Heavy-ion Resonances
Recent particle-particle-$\gamma$ coincident measurements on a $^{28}\rm Si+{}^{28}Si$ resonance have suggested ''vanishing spin alignments''. New analyses for spin alignments by using a molecular model are reported. Different aspects between di-nuclear systems with prolate deformed nuclei and those with oblate deformed nuclei are clarified.
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.
42188849
KEWPIE: A dynamical cascade code for decaying exited compound nuclei
A new dynamical cascade code for decaying hot nuclei is proposed and specially adapted to the synthesis of super-heavy nuclei. For such a case, the interesting channel is of the tiny fraction that will decay through particles emission, thus the code avoids classical Monte-Carlo methods and proposes a new numerical scheme. The time dependence is explicitely taken into account in order to cope with the fact that fission decay rate might not be constant. The code allows to evaluate both statistical and dynamical observables. Results are successfully compared to experimental data.