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تسجيل مستخدم جديدIntroducing Dynamical Triangulations to the Type IIB Superstrings
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In order to consider non-perturbative effects of superstrings, we try to apply dynamical triangulations to the type IIB superstrings. The discretized action is constructed from the type IIB matrix model proposed as a constructive definition of superstring theory. The action has the local N=2 supersymmetry explicitly, and has no extra fermionic degrees of freedom. We evaluate the partition function for some simple configurations and discuss constraints required from the finiteness of partition functions.
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We consider random superstrings of type IIB in $d$-dimensional space. The discretized action is constructed from the supersymetric matrix model, which has been proposed as a constructive definition of superstring theory. Our action is invariant under
the local N=2 super transformations, and doesnt have any redundant fermionic degrees of freedom.
In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheet conformal invariance for superstrings in type IIB R-R plane-wave in semi-light-cone gauge. Here we give further justification to the results found in that work through alternati
ve arguments using dynamical supersymmetries. We show that by using the susy algebra the same quantum definition of the energy-momentum (EM) tensor can be derived. Furthermore, using certain Jacobi identities we indirectly compute the Virasoro anomaly terms by calculating second order susy variation of the EM tensor. Certain integrated form of all such terms are shown to vanish. In order to deal with various divergences that appear in such computations we take a point-split definition of the same EM tensor. The final results are shown not to suffer from the ordering ambiguity as noticed in the previous work provided the coincidence limit is taken before sending the regularization parameter to zero at the end of the computation.
The dynamical triangulations approach to quantum gravity is investigated in detail for the first time in five dimensions. In this case, the most general action that is linear in components of the f-vector has three terms. It was suspected that the co
rresponding space of couplings would yield a rich phase structure. This work is primarily motivated by the hope that this new viewpoint will lead to a deeper understanding of dynamical triangulations in general. Ultimately, this research programme may give a better insight into the potential application of dynamical triangulations to quantum gravity. This thesis serves as an exploratory study of this uncharted territory. The five dimensional (k,l) moves used in the Monte Carlo algorithm are proven to be ergodic in the space of combinatorially equivalent simplicial 5-manifolds. A statement is reached regarding the possible existence of an exponential upper bound on the number of combinatorially equivalent triangulations of the 5-sphere. Monte Carlo simulations reveal non-trivial phase structure which is analysed in some detail. Further investigations deal with the geometric and fractal nature of triangulations. This is followed by a characterisation of the weak coupling limit in terms of stacked spheres. Simple graph theory arguments are used to reproduce and generalise a well-known result in combinatorial topology. Finally, a comprehensive study of singular structures in dynamical triangulations is presented. It includes a new understanding of their existence, which appears to be consistent with the non-existence of singular vertices in three dimensions. The thesis is concluded with an overview of results, general discussion and suggestions for future work.
We study Kahler-Dirac fermions on Euclidean dynamical triangulations. This fermion formulation furnishes a natural extension of staggered fermions to random geometries without requring vielbeins and spin connections. We work in the quenched approxima
tion where the geometry is allowed to fluctuate but there is no back-reaction from the matter on the geometry. By examining the eigenvalue spectrum and the masses of scalar mesons we find evidence for a four fold degeneracy in the fermion spectrum in the large volume, continuum limit. It is natural to associate this degeneracy with the well known equivalence in continuum flat space between the Kahler-Dirac fermion and four copies of a Dirac fermion. Lattice effects then lift this degeneracy in a manner similar to staggered fermions on regular lattices. The evidence that these discretization effects vanish in the continuum limit suggests both that lattice continuum Kahler-Dirac fermions are recovered at that point, and that this limit truly corresponds to smooth continuum geometries. One additional advantage of the Kahler-Dirac action is that it respects an exact $U(1)$ symmetry on any random triangulation. This $U(1)$ symmetry is related to continuum chiral symmetry. By examining fermion bilinear condensates we find strong evidence that this $U(1)$ symmetry is not spontaneously broken in the model at order the Planck scale. This is a necessary requirement if models based on dynamical triangulations are to provide a valid ultraviolet complete formulation of quantum gravity.
For dynamical triangulations in dimensions d<=4 the most general action has two couplings. We note that the most general action for d=5 has three couplings. We explore this larger coupling space using Monte Carlo simulations. Initial results indicate evidence for non-trivial phase structure.
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