# Gauge interactions and topological phases of matter

Progress of Theoretical and Experimental Physics, Sep 2016

We study the effects of strongly coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time-reversal symmetry. We first derive a sufficient condition for the introduction of a dynamical Yang–Mills field to preserve the topological phase of matter, and then show how the massless pions capture in the infrared the topological properties of the fermions in the ultraviolet. Finally, we use the S-duality of <mml:math display="inline"><mml:mrow><mml:mi mathvariant="script" class="MJX-tex-caligraphic">N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>N=2 supersymmetric <mml:math display="inline"><mml:mrow><mml:mtext>SU</mml:mtext><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>SU(2) gauge theory with <mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math>Nf=4 flavors to show that the <mml:math display="inline"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:math>ν=16 phase of Majorana fermions can be continuously connected to the trivial <mml:math display="inline"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>ν=0 phase.

This is a preview of a remote PDF: http://ptep.oxfordjournals.org/content/2016/9/093B07.full.pdf

Yuji Tachikawa, Kazuya Yonekura. Gauge interactions and topological phases of matter, Progress of Theoretical and Experimental Physics, 2016, DOI: 10.1093/ptep/ptw131