Abstract
We study the physics of 3d supersymmetric abelian gauge theories (with small supersymmetry breaking perturbations) at finite density. Using mirror symmetry, which provides a natural generalization of the duality between the XY model and the abelian Higgs model but now including fermionic fields, we see many dynamical phenomena conjectured to be of relevance in condensed matter systems. In particular, we find examples of the emergence of a Fermi surface at low energies from hybridization of fermions localized at magnetic defects at high energies, as well as fractionalization of charged fermions into spinon-holon pairs with the concomitant appearance of emergent gauge fields. We also find dual descriptions for Fermi surfaces coupled to critical bosons, which give rise to non-Fermi liquids.
Highlights
We study the physics of 3d supersymmetric abelian gauge theories at finite density
Using mirror symmetry, which provides a natural generalization of the duality between the XY model and the abelian Higgs model but including fermionic fields, we see many dynamical phenomena conjectured to be of relevance in condensed matter systems
This theory exhibits a type of particle-vortex duality called “mirror symmetry” that turns out to be extremely useful for analyzing the IR physics at finite density
Summary
The theory flows to a nontrivial conformal field theory that admits a mirror dual description in terms of free vortices with the same amount of supersymmetry [10,11,12]. We will explain in detail the mapping of external sources and global symmetries, which will be important for adding electric and magnetic impurities to the theory. Let us recall first the fact that in 2 + 1 dimensions a gauge field Aμ is dual to a scalar γ — the “dual photon”. The abelian gauge field gives rise to a global U(1)J current that shifts the dual photon, Jμ =. Note that current conservation follows from the Bianchi identity for the gauge field. The U(1)J current plays an important role in particle/vortex dualities, because its charge is carried by sources of magnetic flux, i.e. vortices or monopoles
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