Fermionization and boundary states in 1+1 dimensions
Yoshiki Fukusumi, Yuji Tachikawa, Yunqin Zheng
Abstract
In the last few years it was realized that every fermionic theory in 1+1 dimensions is a generalized Jordan-Wigner transform of a bosonic theory with a non-anomalous \mathbb{Z}_2} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mstyle mathvariant="double-struck"> <mml:mi>ℤ</mml:mi> </mml:mstyle> <mml:mn>2</mml:mn> </mml:msub> </mml:math> symmetry. In this note we determine how the boundary states are mapped under this correspondence. We also interpret this mapping as the fusion of the original boundary with the fermionization interface.
Topics & Concepts
Boundary (topology)PhysicsMathematicsTheoretical physicsState (computer science)Boundary value problemAlgebra over a fieldClass (philosophy)Duality (order theory)Feature (linguistics)Pure mathematicsCurrent (fluid)Advanced Operator Algebra ResearchSpectral Theory in Mathematical PhysicsAlgebraic structures and combinatorial models