Abstract
We consider SU(N) Chern-Simons theory coupled to a scalar field in the fundamental representation at strictly zero temperature and finite chemical potential for the global U(1)B particle number or flavour symmetry. In the semiclassical regime we identify a Bose condensed ground state with a vacuum expectation value (VEV) for the scalar accompanied by noncommuting background gauge field matrix VEVs. These matrices coincide with the droplet ground state of the Abelian quantum Hall matrix model. The ground state spontaneously breaks U(1)B and Higgses the gauge group whilst preserving spatial rotations and a colour-flavour locked global U(1) symmetry. We compute the perturbative spectrum of semiclassical fluctuations for the SU(2) theory and show the existence of a single massless state with a linear phonon dispersion relation and a roton minimum (and maximum) determining the Landau critical superfluid velocity. For the massless scalar theory with vanishing self interactions, the semiclassical dispersion relations and location of roton extrema take on universal forms.
Highlights
Scalar coupled to Chern-Simons gauge fields in the presence of a chemical potential for particle number
In the semiclassical regime we identify a Bose condensed ground state with a vacuum expectation value (VEV) for the scalar accompanied by noncommuting background gauge field matrix VEVs
We find that the theory with SU(N ) gauge group, Chern-Simons level k and nonzero chemical potential for particle number, exhibits a zero temperature ground state where the scalar field condenses and all gauge fields acquire noncommuting background expectation values
Summary
We have found a one-parameter family of gauge field solutions parametrised by the variables (a1, a2), satisfying a constraint (2.20). The transformation acts on the background gauge fields Ai = A(ia) ta exactly as a rotation (R) by a constant angle θ in the x-y plane: U(1)C : Ax Ay. the vacuum gauge configuration is invariant under a global U(1)B+C+R symmetry which can be viewed as a linear combination of global colour, flavour (or baryon number) and SO(2) rotations in the x-y plane. The above observation has an important consequence It implies that the ground state does not break rotational invariance, since the action of rotations can be undone by a gauge transformation. This is naturally reflected in the expectation values of all gauge invariant operators built from field strengths.
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