Five-Dimensional Supersymmetric Yang-Mills Theories and Random Plane Partitions

Five-dimensional $\mathcal{N}=1$ supersymmetric Yang-Mills theories are investigated from the viewpoint of random plane partitions. It is shown that random plane partitions are factorizable as q-deformed random partitions so that they admit the interpretations as five-dimensional Yang-Mills and as topological string amplitudes. In particular, they lead to the exact partition functions of five-dimensional $\mathcal{N}=1$ supersymmetric Yang-Mills with the Chern-Simons terms. We further show that some specific partitions, which we call the ground partitions, describe the perturbative regime of the gauge theories. We also argue their role in string theory. The gauge instantons give the deformation of the ground partition.Comment: 33 pages, 9 figures, typos correcte

Free Fermion and Seiberg-Witten Differential in Random Plane Partitions

A model of random plane partitions which describes five-dimensional $\mathcal{N}=1$ supersymmetric SU(N) Yang-Mills is studied. We compute the wave functions of fermions in this statistical model and investigate their thermodynamic limits or the semi-classical behaviors. These become of the WKB type at the thermodynamic limit. When the fermions are located at the main diagonal of the plane partition, their semi-classical wave functions are obtained in a universal form. We further show that by taking the four-dimensional limit the semi-classical wave functions turn to live on the Seiberg-Witten curve and that the classical action becomes precisely the integral of the Seiberg-Witten differential. When the fermions are located away from the main diagonal, the semi-classical wave functions depend on another continuous parameter. It is argued that they are related with the wave functions at the main diagonal by the renormalization group flow of the underlying gauge theory.Comment: 32 pages, 3 figures, typos correcte

Gravitational Quantum Foam and Supersymmetric Gauge Theories

We study K\"{a}hler gravity on local SU(N) geometry and describe precise correspondence with certain supersymmetric gauge theories and random plane partitions. The local geometry is discretized, via the geometric quantization, to a foam of an infinite number of gravitational quanta. We count these quanta in a relative manner by measuring a deviation of the local geometry from a singular Calabi-Yau threefold, that is a A_{N-1} singularity fibred over \mathbb{P}^1. With such a regularization prescription, the number of the gravitational quanta becomes finite and turns to be the perturbative prepotential for five-dimensional \mathcal{N}=1 supersymmetric SU(N) Yang-Mills. These quanta are labelled by lattice points in a certain convex polyhedron on \mathbb{R}^3. The polyhedron becomes obtainable from a plane partition which is the ground state of a statistical model of random plane partition that describes the exact partition function for the gauge theory. Each gravitational quantum of the local geometry is shown to consist of N unit cubes of plane partitions.Comment: 43 pages, 12 figures: V2 typos correcte

Association between shift work and the risk of death from biliary tract cancer in Japanese men

Background: There is increasing evidence suggesting that shift work involving night work may increase cancer risk. Methods: We examined the association between working rotating shifts and the risk of death from biliary tract cancer among Japanese men who participated in the Japan Collaborative Cohort Study. Of the 46, 395 men recruited, 22, 224 men aged 40-65 at baseline (1988-1990) who reported working full-time or were self-employed were included in the present analysis. The study subjects were followed through December 31, 2009. Information regarding occupation and lifestyle factors was collected using a self-administered questionnaire. Cox proportional hazard models were used to estimate the hazard ratio (HR) and 95 % confidence interval (CI) for the risk of death from biliary tract cancer in relation to shift work. Results: During a mean 17-year follow-up, we observed 94 biliary tract cancer deaths, including 23 deaths from gallbladder cancer and 71 deaths from extrahepatic bile duct cancer. Overall, shift work was associated with a statistically non-significant increase in the risk of biliary tract cancer, with an HR of 1.50 (95 % CI: 0.81-2.77), among rotating shift workers. When the analysis was limited to extrahepatic bile duct cancer, a significant association appeared, with a multivariable-adjusted HR of 1.93 (95 % CI: 1.00-3.72) for rotating shift workers. Conclusion: Our data indicate that shift work may be associated with increased risk of death from extrahepatic bile duct cancer in this cohort of Japanese men. The association with gallbladder cancer remains unclear because of the small number of deaths