Related papers: Dirac Operator on Fuzzy AdS_2
We give results about the L^2 kernel and the spectrum of the Dirac operator on a complete Riemannian manifold which is conformally equivalent to the interior of a Riemannian manifold with nonempty boundary.
We prove the Bari-Markus property for spectral projectors of non-self-adjoint Dirac operators on a finite interval with square-integrable matrix-valued potentials and some separated boundary conditions.
Non-chiral operators with positive anomalous dimensions can have interesting applications to supersymmetric model building. Motivated by this, we develop a new method for obtaining the anomalous dimensions of non-chiral double-trace…
This article presents a survey of recent developments on pseudodifferential operators on noncommutative tori. We describe currently available constructions of those operators: by means of a $C^*$--dynamical system, by using an analogue of…
Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.
A new class of lattice Dirac operators which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands…
Let G be a compact connected semisimple Lie group and let H\subset G be a closed connected subgroup such that rank(G)=rank(H) and G/H is a symmetric space. Given an irreducible representation of H, we define a Dirac operator D and determine…
Callias-type (or Dirac-Schr\"odinger) operators associated to abstract semifinite spectral triples are introduced and their indices are computed in terms of an associated index pairing derived from the spectral triple. The result is then…
We construct an $O(a^2)$-improved overlap-Dirac operator by designing an improved overlap kernel, based on the Symanzik improvement program. Field rotation terms are also identified to improve off-shell amplitudes for both massless and…
In this paper, Dirac operator with some integral type nonlocal boundary conditions is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we give an algorithm for the…
We describe a novel implementation of non-relativistic fermions in AdS/CFT by imposing Lorentz violating boundary conditions for a Dirac spinor in AdS4. The dual boundary theory is scale invariant and exhibits a number of interesting…
We use the conjectured strong-weak coupling worldsheet duality between the SL(2)/U(1) and Sine-Liouville conformal field theories to study some properties of degenerate operators and to compute correlation functions in CFT on AdS_3. The…
We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac…
We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's…
In this article we develop a functional model for a general maximal dissipative operator. We construct the selfadjoint dilation of such operators. Unlike previous functional models, our model is given explicitly in terms of parameters of…
We give the description of self-adjoint regular Dirac operators, on $[0, \pi]$, with the same spectra.
We study the spectrum of the Dirac operator on hyperbolic manifolds of finite volume. Depending on the spin structure it is either discrete or the whole real line. For link complements in S^3 we give a simple criterion in terms of linking…
We discuss the continuum limit of discrete Dirac operators on the square lattice in $\mathbb R^2$ as the mesh size tends to zero. To this end, we propose the most natural and simplest embedding of $\ell^2(\mathbb Z_h^d)$ into $L^2(\mathbb…
Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…
In this second part of the paper, we define spectral spacetimes, a noncommutative generalization of Lorentzian orientable spacetimes of even dimension with a spin structure. There are two main differences with spectral triples: the…