197438672
A new treatment for some periodic Schr\"odinger operators
We revise some aspects of the asymptotic solution for the eigenvalues for Schr\"odinger operators with periodic potential, from the perspective of the Floquet theory. In the context of classical Floquet theory, when the periodic potential can be treated as small perturbation we give a new method to compute the asymptotic spectrum. For elliptic potentials a generalized Floquet theory is needed. In order to produce other asymptotic solutions consistent with known results, new relations for the Floquet exponent and the monodromy of wave function are proposed. Many Schr\"odinger equations of this type, such as the Hill's equation and the ellipsoidal wave equation, etc., can be treated by this method.
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.
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.
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.
118518339
Magnetic expansion of Nekrasov theory: The SU(2) pure gauge theory
It is recently claimed by Nekrasov and Shatashvili that the N=2 gauge theories in the {Omega} background with {epsilon}{sub 1}=({h_bar}/2{pi}), {epsilon}{sub 2}=0 are related to the quantization of certain algebraic integrable systems. We study the special case of SU(2) pure gauge theory; the corresponding integrable model is the A{sub 1} Toda model, which reduces to the sine-Gordon quantum mechanics problem. The quantum effects can be expressed as the WKB series written analytically in terms of hypergeometric functions. We obtain the magnetic and dyonic expansions of the Nekrasov theory by studying the property of hypergeometric functions in the magnetic and dyonic regions on the moduli space. We also discuss the relation between the electric-magnetic duality of gauge theory and the action-action duality of the integrable system.
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.