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.
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.
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.
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.
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).
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.
16648280
Lattice fermions based on higher-dimensional hyperdiamond lattices
In this paper we generalize to higher dimensions several types of fermion actions on the hyperdiamond lattice including a two-parameter class of minimal-doubling fermions "Creutz fermion" and a simple fermion with sufficient discrete symmetry "BBTW fermion". Then it is shown that they possess some properties in common with the four-dimensional case: BBTW fermions in higher even dimensions inevitably yield unphysical degrees of freedom. Creutz fermions are defined on the distorted lattices, and they lose the high discrete symmetry of the original lattices. We also find properties specific to the higher-dimensional cases. The parameter range for Creutz action to yield minimal-doubling and physical fermions becomes narrower with the dimension getting higher, thus it becomes more and more difficult to realize minimal-doubling. In addition, we generalize the subspecies of Creutz and BBTW actions including a new class of minimal-doubling actions "Appended Creutz action".
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.
9078238
VORTEX DESCRIPTION OF QUANTUM HALL FERROMAGNETS
We study particle states of quantum Hall ferromagnet from the viewpoint of the incompressible fluid description. It is shown that phase space of Chern–Simons matrix theory which is an effective theory for the incompressible fluid is equivalent to moduli space of vortex theory. According to this correspondence, elementary excitations in vortex theory are identified as particle states in quantum Hall ferromagnet, and thus we propose that a pure electron state is absent from the strong coupling region but only a composite particle state is present.
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".
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.