Search

Summary

We define Chern–Simons gauge fields in 2+1 dimensions, and the quantization of their “level” k. We show that the CS action in a material define a topological response, and gives an integer quantum Hall effect. We show how a CS field emerges, as a statistical field, in materials. We define anyons and show how they can appear from a CS field in the fractional Quantum Hall effect.

Summary

We describe vector theories in 2+1 dimensions, Maxwell, Proca, with topological mass terms, and finally the “self-dual” action. We generalize the “self-duality” to odd dimensions. We show the duality of the self-dual action to the one with topological mass term, through the intermediary of a master action. We generalize the proof to odd dimensions. We then describe the basic 1+1 dimensional example of duality, the “T-duality”, and finish with comments on CS fields in higher odd dimensions.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

33 - Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics

Summary

34 - Chern–Simons and Self-Duality in Odd Dimensions, Its Duality to Topologically Massive Theory and Dualities in General

Summary

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

33 - Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics

Summary

34 - Chern–Simons and Self-Duality in Odd Dimensions, Its Duality to Topologically Massive Theory and Dualities in General

Summary