We study the proposed duality between the 5-dimensional supergravity/superstring on AdS3×S and the 2-dimensional N = (0, 4) SCFT defined on the boundary of AdSspace. We construct explicitly the N = (0, 4) SCFT by imposing the “quiver projection” developed by Douglas-Moore [14] on the N = (4, 4) SCFT of symmetric orbifold, which is proposed to be the dual of the 6-dimensional supergravity/supers...

In this doctoral thesis we study zero-mode spectra of Matrix theory and eleven-dimensional supergravity on the plane-wave background. This background is obtained via the Penrose limit of AdS4 × S7 and AdS7 × S4. The plane-wave background is a maximally supersymmetric spacetime supported by non-vanishing constant four-form flux in eleven-dimensional spacetime. First, we discuss the Matrix theory...

We show that adding a vacuum expectation value to a gauge field left over from a dimensional reduction of three-dimensional pure supersymmetric YangMills theory generates mass terms for the fundamental fields in the two-dimensional theory while supersymmetry stays intact. This is similar to the adjoint mass term that is generated by a Chern-Simons term in this theory. We study the spectrum of t...

The spectral analysis of uniform or nonuniform sampling signal is one of the hot topics in digital signal processing community. Theories and applications of uniformly and nonuniformly sampled one-dimensional or two-dimensional signals in the traditional Fourier domain have been well studied. But so far, none of the research papers focusing on the spectral analysis of sampled signals in the line...

We study the proposed duality between the 5-dimensional supergravity/superstiring on AdS3×S and the 2-dimensional N = (0, 4) SCFT defined on the boundary of AdSspace. We construct explicitely the N = (0, 4) SCFT by imposing the “quiver projection” developed by Douglas-Moore [12] on the N = (4, 4) SCFT of symmetric orbifold, which is proposed to be the dual of the 6-dimensional supergravity/supe...

Abstract. We consider the spectral problem for the two-dimensional Schrödinger operator of a charged particle in strong uniform magnetic and periodic electric fields. The related classical problem is first analyzed by the Krylov–Bogolyubov–Alfven and Neishtadt averaging methods. This allows us to prove the almost integrability of the original two-dimensional classical Hamiltonian system and red...

We consider a semi-periodic two-dimensional Schr\"odinger operator which is cut at an angle. When the commensurate with periodic lattice, spectrum of has band-gap Bloch structure. prove that in incommensurable case, there are no gaps: gaps bulk filled edge spectrum.

We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov-Zakharov (KZ) spectrum in weak three-wave turbulence. In the finite-capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a conse...

We study the entanglement spectrum (ES) of the Bose-Hubbard model on the two-dimensional square lattice at unit filling, both in the Mott insulating and in the superfluid phase. In the Mott phase, we demonstrate that the ES is dominated by the physics at the boundary between the two subsystems. On top of the boundary-local (perturbative) structure, the ES exhibits substructures arising from one...

We calculate the spectrum of the linearized supergravity around the maximally supersymmetric pp-wave background in eleven dimensions. The resulting spectrum agrees with that of zero-mode Hamiltonian of a supermembrane theory on the pp-wave background. We also discuss the connection with the Kaluza-Klein zero modes of AdS4 × S background.