119121164
Mathieu Equation and Elliptic Curve
We present a relation between the Mathieu equation and a particular elliptic curve. We find that the Floquet exponent of the Mathieu equation, for both q 1 and q 1, can be obtained from the integral of a differential one form along the two homology cycles of the elliptic curve. Certain higher order differential operators are needed to generate the WKB expansion. We make a few conjectures about the general structure of these differential operators.
119319431
Combinatorial approach to Mathieu and Lamé equations
Based on some recent progress on a relation between four dimensional super Yang-Mills gauge theory and quantum integrable system, we study the asymptotic spectrum of the quantum mechanical problems described by the Mathieu equation and the Lame equation. The large momentum asymptotic expansion of the eigenvalue is related to the instanton partition function of supersymmetric gauge theories which can be evaluated by a combinatorial method. The electro-magnetic duality of gauge theory indicates that in the parameter space, there are three asymptotic expansions for the eigenvalue, and we confirm this fact by performing the Wentzel–Kramers–Brillouin (WKB) analysis in each asymptotic expansion region. The results presented here give some new perspective on the Floquet theory about periodic differential equation.
119623293
M5-branes and Wilson surfaces
We investigate the M5-brane description of the Wilson surface operators in six-dimensional (2,0) superconformal field theory from AdS/CFT correspondence. We consider the Wilson surface operators in high-dimensional representation, whose description could be M5-brane string soliton solutions in AdS(7) x S' background. We construct such string soliton solutions from the covariant M5-brane equations of motion and discuss their properties. The supersymmetry analysis shows that these solutions are half-BPS. We also discuss the subtle issue on the boundary terms.
123383330
Sine-Gordon quantum mechanics on the complex plane and N=2 gauge theory
We study the relation between the $\mathcal{N}=2$ gauge theory in the $\ensuremath{\Omega}$ background and the quantized integral system recently proposed by Nekrasov and Shatashvili. We focus on the simplest case, the pure Yang-Mills theory with the $SU(2)$ gauge group and the corresponding sine-Gordon integral model on the complex plane. We analyze the periodic wave function and the corresponding energy spectrum of the sine-Gordon quantum mechanics, and find this model contains information of the low energy effective theory of the gauge theory.
117830006
A note on W symmetry of N=2 gauge theory
The AGT correspondence indicates $\mathcal{N}=2$ gauge theory possesses of W algebra symmetry. We study how the conformal block of Toda CFT gives the expectation value of Casimir operators of gauge theory. The $A_2$ Toda CFT with $W_3$ symmetry is taken as the main example.
121263480
New test and analysis of position-sensitive-silicon-detector
We have tested and analyzed the properties of two-dimensional Position-Sensitive-silicon-Detector (PSD) with new integrated preamplifiers. The test demonstrates that the best position resolution for 5.5 MeV α particles is 1.7 mm (FWHM), and the best energy resolution is 2.1%, which are notably better than the previously reported results. A scaling formula is introduced to make the absolute position calibration.