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Register a new userComplex structure of a DT surface with $T^2$ topology
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A method of defining the complex structure(moduli) for dynamically triangulated(DT) surfaces with torus topology is proposed. Distribution of the moduli parameter is measured numerically and compared with the Liouville theory for the surface coupled to c = 0, 1 and 2 matter. Equivalence between the dynamical triangulation and the Liouville theory is established in terms of the complex structure.
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The complex structure of a surface generated by the two-dimensional dynamical triangulation(DT) is determined by measuring the resistivity of the surface. It is found that surfaces coupled to matter fields have well-defined complex structures for cases when the matter central charges are less than or equal to one, while they become unstable beyond c=1. A natural conjecture that fine planar random network of resistors behave as a continuous sheet of constant resistivity is justified numerically for c<1.
We discuss the lattice formulation of the t Hooft surface, that is, the two-dimensional surface operator of a dual variable. The t Hooft surface describes the world sheets of topological vortices. We derive the formulas to calculate the expectation value of the t Hooft surface in the multiple-charge lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the first demonstration of the formula, we compute the intervortex potential in the charge-2 lattice Abelian Higgs model.
We perform dynamical QCD simulations with $n_f=2$ overlap fermions by hybrid Monte-Carlo method on $6^4$ to $8^3times 16$ lattices. We study the problem of topological sector changing. A new method is proposed which works without topological sector changes. We use this new method to determine the topological susceptibility at various quark masses.
We report on a Rosenbluth separation using previously published data by the CLAS collaboration in Hall B, Jefferson Lab for exclusive $pi^{0}$ deeply virtual electroproduction (DVEP) from the proton at a mean $Q^{2}$ of $approx$ 2 (GeV/c)$^{2}$. The central question we address is the applicability of factorization in $pi^0$ DVEP at these kinematics. The results of our Rosenbluth separation clearly demonstrate the dominance of the longitudinal contribution to the cross section. The extracted longitudinal and transverse contributions are in agreement with previous data from Hall A at Jefferson Lab, but over a much wider $-t$ range (0.12 - 1.8 (GeV/c)$^{2}$). The measured dominance of the longitudinal contribution at $Q^{2} approx$ 2 (GeV/c)$^{2}$ is consistent with the expectation of the handbag factorization theorem. We find that $sigma_L(t) sim 1/(-t)$ for $-t >$ 0.5 (GeV/c)$^2$. Determination of both longitudinal and transverse contributions to the deeply virtual $pi^{0}$ electroproduction cross section allows extraction of additional GPDs.
We analyze the vacuum structure of SU(2) lattice gauge theories in D=2,3,4, concentrating on the stability of t Hooft loops. High precision calculations have been performed in D=3; similar results hold also for D=4 and D=2. We discuss the impact of our findings on the continuum limit of Yang-Mills theories.
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