119259824
Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain
In N = 2 super Yang-Mills theory, the Matone’s relation relates instanton corrections of the prepotential to instanton corrections of scalar field condensation < Trφ >. This relation has been proved to hold for Omega deformed theories too, using localization method. In this paper, we first give a case study supporting the relation, which does not rely on the localization technique. Especially, we show that the magnetic expansion also satisfies a relation of Matone’s type. Then we discuss implication of the relation for the spectrum of periodic Toda chain, in the context of recently proposed Nekrasov-Shatashvili scheme.
119664621
N =2 supersymmetric QCD and elliptic potentials
A bstractWe investigate the relation between the four dimensional N =2 SU(2) super Yang-Mills theory with four fundamental flavors and the quantum mechanics model with Treibich-Verdier potential described by the Heun equation in the elliptic form. We study the precise correspondence of quantities in the gauge theory and the quantum mechanics model. An iterative method is used to obtain the asymptotic expansion of the spectrum for the Schrödinger operator, we are able to fix the precise relation between the energy spectrum and the instanton partition function of the gauge theory. We also study asymptotic expansions for the spectrum which correspond to the strong coupling regions of the Seiberg-Witten theory.
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.
16000244
1/2-BPS Wilson-'t Hooft loops
We investigate the 1/2-BPS Wilson-'t Hooft loops in N=4 super-Yang-Mills theory. We use the bulk D-brane with both electric and magnetic charges to calculate the all-genus contribution of the circular loops. The expectation values of Wilson-'t Hooft loops are in perfect agreement with the result through supersymmetric condition and duality transformation in the gauge theory.
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.
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.
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.