Description:
<jats:title>A<jats:sc>bstract</jats:sc>
</jats:title>
<jats:p>We explicitly find representations for different large <jats:italic>N</jats:italic> phases of Chern-Simons matter theory on <jats:italic>S</jats:italic>
<jats:sup>2</jats:sup> × <jats:italic>S</jats:italic>
<jats:sup>1</jats:sup>. These representations are characterised by Young diagrams. We show that no-gap and lower-gap phase of Chern-Simons-matter theory correspond to integrable representations of SU(<jats:italic>N</jats:italic>)<jats:sub>
<jats:italic>k</jats:italic>
</jats:sub> affine Lie algebra, where as upper-cap phase corresponds to integrable representations of SU(<jats:italic>k</jats:italic> − <jats:italic>N</jats:italic>)<jats:sub>
<jats:italic>k</jats:italic>
</jats:sub> affine Lie algebra. We use phase space description of [1] to obtain these representations and argue how putting a cap on eigenvalue distribution forces corresponding representations to be integrable. We also prove that the Young diagrams corresponding to lower-gap and upper-cap representations are related to each other by transposition under level-rank duality. Finally we draw phase space droplets for these phases and show how information about eigenvalue and Young diagram descriptions can be captured in topologies of these droplets in a unified way.</jats:p>