Berry-Chern monopoles and spectral flows

نویسندگان

چکیده

This lecture note adresses the correspondence between spectral flows, often associated to unidirectional modes, and Chern numbers degeneracy points. The notions of topological indices (Chern numbers, analytical indices) are introduced for non specialists with a wave physics or condensed matter background. is detailed several examples, including Dirac equations in two dimensions, Weyl fermions three shallow water model other generalizations.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Berry Phase and Monopoles in Gluodynamics

We introduce a gauge invariant definition of a monopole on the lattice. The construction is based on the observation that for each Wilson loop there exists an extra U(1) group which leaves the loop invariant. Since the lattice formulation utilizes the language of Wilson loops, the definition of the monopole charge in terms of this plaquette dependent U(1) is gauge invariant. The explicit constr...

متن کامل

Non-Abelian Berry Phases and BPS Monopoles

We study a simple quantum mechanical model of a spinning particle moving on a sphere in the presence of a magnetic field. The system has two ground states. As the magnetic field is varied, the ground states mix through a non-Abelian Berry phase. We show that this Berry phase is the path ordered exponential of the smooth SU(2) ’t Hooft-Polyakov monopole. We further show that, by adjusting a pote...

متن کامل

Hyperbolic monopoles, JNR data and spectral curves

A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. Thes...

متن کامل

Spectral curves of non-integral hyperbolic monopoles

In (??), a is an SUn-connection on the trivial bundle over H, Fa is its curvature, iφ (the Higgs field) is a section of the adjoint bundle, and ∗ is the Hodge ∗-operator on H. We regard two monopoles as the same if they are gauge-equivalent. (The reason for our apparently eccentric notation for the Higgs field will become clear in §3.) We shall develop the twistor description of solutions of (?...

متن کامل

Chern-Simons Level Shifts and M2-brane Flows

The Chern-Simons level k of ABJM gauge theory captures the orbifolding in the dual geometry. This suggests that if we move the membranes away from the tip of the orbifold to a smooth point, it should trigger an RG flow that changes the level to k = 1. We construct an explicit supergravity solution that is dual to this shift from generic k to k = 1. In the gauge theory side, we present arguments...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: SciPost physics lecture notes

سال: 2022

ISSN: ['2590-1990']

DOI: https://doi.org/10.21468/scipostphyslectnotes.39