119276315
Vortices on orbifolds
The Abelian and non-Abelian vortices on orbifolds are investigated based on the moduli matrix approach, which is a powerful method to deal with the BPS equation. The moduli space and the vortex collision are discussed through the moduli matrix as well as the regular space. It is also shown that a quiver structure is found in the Kähler quotient, and a half of ADHM is obtained for the vortex theory on the orbifolds as the case before orbifolding.
117091130
Hall and spin Hall viscosity ratio in topological insulators
We study responses to metric perturbation in topological insulator models. In this paper we introduce a novel quantity, Hall viscosity to particle density ratio, which is analogous to the viscosity to entropy ratio suggested by AdS/CFT correspondence. This quantity corresponds to the filling fraction which characterizes the quantum Hall states, and hence it could be discussed in Haldane's zero-field quantum Hall system. We also consider dissipationless viscosity in the time reversal invariant quantum spin Hall system, which is related to a spin current.
106401419
Phase structure of two-dimensional topological insulators by lattice strong-coupling expansion
The phase structure of 2-dimensional topological insulators under a sufficiently strong electron- electron interaction is investigated. The effective theory is constructed by extending the idea of the Kane-Mele model on the graphenelike honeycomb lattice, in terms of U(1) lattice gauge theory (quantum electrodynamics, QED). We analyze the phase structure by the techniques of strong coupling expansion of lattice gauge theory. As a result, we find that the topological phase structure of the system is modified by the electron-electron interaction. There evolves a new phase with the antiferromagnetism not parallel to the direction pointed by the spin-orbit coupling, in between the conventional and the topological insulator phases. We also discuss the physical implication of the new phase structure found here, in analogy to the parity-broken phase in lattice quantum chromodynamics (QCD), known as "Aoki phase".
7646194
Index theorem and overlap formalism with naive and minimally doubled fermions
We present a theoretical foundation for the Index theorem in naive and minimally doubled lattice fermions by studying the spectral flow of a Hermitean version of Dirac operators. We utilize the point splitting method to implement flavored mass terms, which play an important role in constructing proper Hermitean operators. We show the spectral flow correctly detects the index of the would-be zero modes which is determined by gauge field topology. Using the flavored mass terms, we present new types of overlap fermions from the naive fermion kernels, with a number of flavors that depends on the choice of the mass terms. We succeed to obtain a single-flavor naive overlap fermion which maintains hypercubic symmetry.
119324754
Duality and integrability of a supermatrix model with an external source
We study the Hermitian supermatrix model involving an external source. We derive the determinantal formula for the supermatrix partition function, and also for the expectation value of the characteristic polynomial ratio, which yields the duality between the characteristic polynomial and the external source with an arbitrary matrix potential function. We also show that the supermatrix integral satisfies the one and two dimensional Toda lattice equations as well as the ordinary matrix model.
55474215
Phase structure of topological insulators by lattice strong-coupling expansion
The effect of the strong electron correlation on the topological phase structure of 2-dimensional (2D) and 3D topological insulators is investigated, in terms of lattice gauge theory. The effective model for noninteracting system is constructed similarly to the lattice fermions with the Wilson term, corresponding to the spin-orbit coupling. Introducing the electron-electron interaction as the coupling to the gauge field, we analyze the behavior of emergent orders by the strong coupling expansion methods. We show that there appears a new phase with the in-plane antiferromagnetic order in the 2D topological insulator, which is similar to the so-called "Aoki phase" in lattice QCD with Wilson fermions. In the 3D case, on the other hand, there does not appear such a new phase, and the electron correlation results in the shift of the phase boundary between the topological phase and the normal phase.
9052236
Zero-mode Spectrum of Eleven-dimensional Theory on the Plane-wave Background
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 AdS_4 x S^7 and AdS_7 x S^4. 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 on the plane-wave background suggested by Berenstein, Maldacena and Nastase. We construct the Hamiltonian, 32 supercharges and their commutation relations. We discuss a spectrum of one specific supermultiplet which represents the center of mass degrees of freedom of N D0-branes. This supermultiplet would also represent a superparticle of the eleven-dimensional supergravity in the large-N limit. Second, we study the linearized supergravity on the plane-wave background in eleven dimensions. Fixing the bosonic and fermionic fields in the light-cone gauge, we obtain the spectrum of physical modes. We obtain the fact that the energies of the states in Matrix theory completely correspond to those of fields in supergravity. Thus, we find that the Matrix theory on the plane-wave background contains the zero-mode spectrum of the eleven-dimensional supergravity completely. Through this result, we can argue the Matrix theory on the plane-wave as a candidate of quantum extension of eleven-dimensional supergravity, or as a candidate which describes M-theory.
119194039
Canonical approach to Courant brackets for D-branes
A bstractWe present an extension of the Courant bracket to the ones for Dp-branes by analyzing Hamiltonians and local superalgebras. Contrast to the basis of the bracket for a fundamental string which consists of the momentum and the winding modes, the ones for Dp-branes contain higher rank R-R coupling tensors. We show that the R-R gauge transformation rules are obtained by these Courant brackets for Dp-branes where the Dirac-Born-Infeld gauge field and the “two-vierbein field” play an essential role. Canonical analysis of the worldvolume theories naturally gives the basis of the brackets and the target space backgrounds keeping T-duality manifest at least for NS-NS sector. In a D3-brane analysis S-duality is manifest as a symmetry of interchanging the NS-NS coupling and the R-R coupling.
118395821
Type IIA orientifolds and orbifolds on non-factorizable tori
Abstract We investigate type II orientifolds on non-factorizable torus with and without its oribifolding. We explicitly calculate the Ramond–Ramond tadpole from string one-loop amplitudes, and confirm that the consistent number of orientifold planes is directly derived from the Lefschetz fixed point theorem. We furthermore classify orientifolds on non-factorizable Z N × Z M orbifolds, and construct new supersymmetric type IIA orientifold models on them.
10988502
Spectrum of eleven-dimensional supergravity on a pp -wave background
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 an ${\mathrm{AdS}}_{4}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{7}$ background.
8177695
Gauged linear sigma models for noncompact Calabi-Yau varieties
Abstract We study gauged linear sigma models for noncompact Calabi–Yau manifolds described as a line bundle on a hypersurface in a projective space. This gauge theory has a unique phase if the Fayet–Iliopoulos parameter is positive, while there exist two distinct phases if the parameter is negative. We find four massless effective theories in the infrared limit, which are related to each other under the Calabi–Yau/Landau–Ginzburg correspondence and the topology change. In the T-dual theory, on the other hand, we obtain two types of exact massless effective theories: one is the sigma model on a newly obtained Calabi–Yau geometry as a mirror dual, while the other is given by a Landau–Ginzburg theory with a negative power term, indicating N = 2 superconformal field theory on SL ( 2 , R ) / U ( 1 ) . We argue that the effective theories in the original gauged linear sigma model are exactly realized as N = 2 Liouville theories coupled to well-defined Landau–Ginzburg minimal models.