Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor

Non-Abelian strings are considered in non-supersymmetric theories with fermions in various appropriate representations of the gauge group U[Formula: see text]. We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases we observe a non-trivial [Formula: see text] dependence.

Download Full-text

Zero modes of various graphene configurations from the index theorem

The European Physical Journal Special Topics ◽

10.1140/epjst/e2007-00232-6 ◽

2007 ◽

Vol 148 (1) ◽

pp. 127-132 ◽

Cited By ~ 6

Author(s):

J. K. Pachos ◽

A. Hatzinikitas ◽

M. Stone

Keyword(s):

Index Theorem ◽

Zero Modes

Download Full-text

GENERALIZATION OF CHIRAL SYMMETRY FOR TILTED DIRAC CONES

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194512006046 ◽

2012 ◽

Vol 11 ◽

pp. 145-150 ◽

Cited By ~ 6

Author(s):

TOHRU KAWARABAYASHI ◽

YASUHIRO HATSUGAI ◽

TAKAHIRO MORIMOTO ◽

HIDEO AOKI

Keyword(s):

Differential Operator ◽

Chiral Symmetry ◽

Landau Level ◽

Index Theorem ◽

Dirac Cone ◽

Zero Modes ◽

Generalized Symmetry ◽

Dirac Hamiltonian

The notion of chiral symmetry for the conventional Dirac cone is generalized to include the tilted Dirac cones, where the generalized chiral operator turns out to be non-hermitian. It is shown that the generalized chiral symmetry generically protects the zero modes (n = 0 Landau level) of the Dirac cone even when tilted. The present generalized symmetry is equivalent to the condition that the Dirac Hamiltonian is elliptic as a differential operator, which provides an explicit relevance to the index theorem.

Download Full-text

Modular symmetry and zeros in magnetic compactifications

Journal of High Energy Physics ◽

10.1007/jhep10(2021)054 ◽

2021 ◽

Vol 2021 (10) ◽

Author(s):

Yoshiyuki Tatsuta

Keyword(s):

Boundary Conditions ◽

Zero Mode ◽

Index Theorem ◽

Homogeneous Magnetic Field ◽

Wave Functions ◽

Two Dimensional ◽

Dimensional Torus ◽

Zero Modes ◽

Modular Transformation ◽

Before And After

Abstract We discuss the modular symmetry and zeros of zero-mode wave functions on two-dimensional torus T2 and toroidal orbifolds T2/ℤN (N = 2, 3, 4, 6) with a background homogeneous magnetic field. As is well-known, magnetic flux contributes to the index in the Atiyah-Singer index theorem. The zeros in magnetic compactifications therefore play an important role, as investigated in a series of recent papers. Focusing on the zeros and their positions, we study what type of boundary conditions must be satisfied by the zero modes after the modular transformation. The consideration in this paper justifies that the boundary conditions are common before and after the modular transformation.

Download Full-text