17808614
Construction of supersymmetric nonlinear sigma models on noncompact Calabi-Yau manifolds with isometry
Abstract We propose a class of N = 2 supersymmetric nonlinear sigma models on the noncompact Ricci-flat Kahler manifolds, interpreted as the complex line bundles over the hermitian symmetric spaces. Kahler potentials and Ricci-flat metrics for these manifolds with isometries are explicitly constructed by using the techniques of supersymmetric gauge theories. Each of the metrics contains a resolution parameter which controls the size of these base manifolds, and the conical singularity appears when the parameter vanishes.
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.
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.
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.
651290
A note on conifolds
Abstract We present the Ricci-flat metric and its Kahler potential on the conifold with the O ( N ) isometry, whose conical singularity is repaired by the complex quadric surface Q N −2 = SO ( N )/ SO ( N −2)× U (1).
15429929
Supersymmetric nonlinear sigma models on Ricci-flat Kähler manifolds with O(N) symmetry
Abstract We propose a class of N =2 supersymmetric nonlinear sigma models on the Ricci-flat Kahler manifolds with O( N ) symmetry.
20098388
Characters of Lattice Fermions Based on the Hyperdiamond Lattice
We study minimal-doubling fermion actions on hyperdiamond and deformed hyperdiamond lattices, with emphasis on the real-space construction of them and Lorentz covariance of excitations from fermion poles. We propose the improved spatial construction of Creutz fermion action on a deformed hyperdiamond lattice, and discuss conditions for a hyperdiamond-lattice action to produce Lorentz-covariant excitations from poles of fermion propagators. It is pointed out that the non-nearest-site hoppings are essential for the correct excitations. We propose a class of minimal-doubling actions defined on a deformed hypercubic lattice as a generalization of Creutz-type actions. In addition we introduce a two-parameter class of Wilczek-type minimal-doubling actions.
119289018
Current reflection and transmission at conformal defects: Applying BCFT to transport process
Abstract We study reflection/transmission process at conformal defects by introducing new transport coefficients for conserved currents. These coefficients are defined by using BCFT techniques thanks to the folding trick, which turns the conformal defect into the boundary. With this definition, exact computations are demonstrated to describe reflection/transmission process for a class of conformal defects. We also compute the boundary entropy based on the boundary state.
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.
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.
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.