119227659
Spinless basis for spin-singlet FQH states
We investigate an alternative description of the SU(M)-singlet FQH state by using the spinless basis. The SU(M)-singlet Halperin state is obtained via the q-deformation of the Laughlin state and its root of unity limit, by applying the Yangian Gelfand-Zetlin basis for the spin Calogero-Sutherland model. The squeezing rule for the SU(M) state is also investigated in terms of the spinless basis.
119232647
Bulk angular momentum and Hall viscosity in chiral superconductors
We establish the Berry-phase formulas for the angular momentum (AM) and the Hall viscosity (HV) to investigate chiral superconductors (SCs) in two and three dimensions. The AM is defined by the temporal integral of the anti-symmetric momentum current induced by an adiabatic deformation, while the HV is defined by the symmetric momentum current induced by the symmetric torsional electric field. Without suffering from the system size or geometry, we obtain the macroscopic AM Lz = hmN0=2 at zero temperature in full-gap chiral SCs, wherem is the magnetic quantum number andN0 is the total number of electrons. We also find that the HV is equal to half the AM at zero temperature not only in full-gap chiral SCs as is well-known but also in nodal ones, but its behavior at finite temperature is different from each other in the both cases.
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.
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".
84177735
Viscoelastic-electromagnetism and Hall viscosity
We introduce a kind of electromagnetism, which we call viscoelastic-electromagnetism, to investigate viscoelastic transport phenomena. It is shown that Cartan’s formalism of general relativity is essential for viscoelastic theory, and then the corresponding electric and magnetic fields are regarded as a velocity gradient and a Burgers vector density, respectively. As an application of this formalism, the Styreda formula for the Hall viscosity is obtained.
118872049
Worldsheet description of exotic five-brane with two gauged isometries
A bstractWe study the string worldsheet description of the background geometry of the exotic $ 5_2^2 $-brane where two isometries are gauged. This is an extension of the gauged linear sigma model (GLSM) for the exotic $ 5_2^2 $-brane with a single gauged isometry. The new GLSM with two gauged isometries has only $ \mathcal{N} $ = (2, 2) supersymmetry rather than $ \mathcal{N} $ = (4, 4) supersymmetry of the original GLSM. This is caused by a conflict between two different SU(2)R associated with the two gauge symmetries. However, if we take a certain limit, we can find the genuine string sigma model of the background geometry of the exotic $ 5_2^2 $-brane with $ \mathcal{N} $ = (4, 4) supersymmetry. We also investigate the worldsheet instanton corrections to the background geometry of the exotic $ 5_2^2 $-brane. The worldsheet instanton corrections to the string sigma model can be traced in terms of the two gauge fields in the new GLSM. This new GLSM gives rise to a different feature of the quantum corrections from the one in the GLSM with the single gauged isometry.
121903928
Index theorems on torsional geometries
We investigate the Atiyah-Singer index theorems with torsion given by Neveu-Schwarz three-form flux H under the condition dH = 0 in flux compactification scenarios with non-trivial background fields in string theories. Using an identification between the Clifford algebra on the geometry and the canonical quantization condition in quantum mechanics, we explicitly reformulate the Dirac index on manifolds with torsion, which will provides a fundamental information to effective theories derived from string theory. In the same analogy we also reformulate the Euler characteristics and the Hirzebruch signatures in the framework of quantum mechanics.
13806519
Gauge Theoretical Construction of Non-compact Calabi–Yau Manifolds
Abstract We construct the non-compact Calabi–Yau manifolds interpreted as the complex line bundles over the Hermitian symmetric spaces. These manifolds are the various generalizations of the complex line bundle over C P N −1 . Imposing an F-term constraint on the line bundle over C P N −1 , we obtain the line bundle over the complex quadric surface Q N −2 . On the other hand, when we promote the U (1) gauge symmetry in C P N −1 to the non-abelian gauge group U ( M ), the line bundle over the Grassmann manifold is obtained. We construct the non-compact Calabi–Yau manifolds with isometries of exceptional groups, which we have not discussed in the previous papers. Each of these manifolds contains the resolution parameter which controls the size of the base manifold, and the conical singularity appears when the parameter vanishes.
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.