Quantum mechanics

Theoretical physics

Algorithm

Magnetic field

Riemann surface

Pure mathematics

Mathematical physics

Sigma model

Field (mathematics)

Plane (geometry)

Skyrmion

Economics

Physics

Nonlinear system

Riemann hypothesis

Mathematics

Political science

Unitary state

Holomorphic function

Condensed matter physics

Mathematical analysis

Geometry

Connection (principal bundle)

Finance

Riemann sphere

Order (exchange)

Sigma

SciPost Physics

We define a gauged non-linear sigma model for a 2-sphere valued field and a SU(2) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math> connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary Dzyaloshinskii-Moriya interaction, for a suitably chosen gauge field. We use the interplay of unitary and holomorphic structures to derive a general solution of the first order Bogomol’nyi equation of the model for any given connection. We illustrate this formula with examples, and also point out applications to the study of impurities.

Gauged sigma models and magnetic Skyrmions