The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
David Tong, Carl Turner
备注：
31 pages + appendices. 4 Figures. v2: references added and further comments on the chiral edge modes. v3: introduction and abstract rewritten for a condensed matter audience. More references added. Version to be published in Physical Review B
We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantise the vortices and, by relating their dynamics to a matrix model, show that their ground state wavefunction is in the same universality class as the Laughlin state. We further construct coherent state representations of the excitations of a finite number of vortices. These are quasi-holes. By an explicit computation of the Berry phase, without resorting to a plasma analogy, we show that these excitations have fractional charge and spin.
In this article it is studied the 3-brane world in the context of five-dimensional Einstein-Chern-Simons gravity. We started by considering Israel's junction condition for AdS-Chern-Simons gravity. Using the S-expansion procedure, we mapped the AdS-Chern-Simons junction conditions to Einstein-Chern-Simons gravity, allowing us to derive effective four-dimensional Einstein-Chern-Simons field equations.
Chern-Simons gravities and gravitational Chern-Simons densities are constructed using the non-Abelian Yang-Mills Chern-Simons densities. As such, they are defined only in odd dimensions. We propose instead an analogous construction employing what we term Higgs--Chern-Simons (HCS) densities, which are defined in $all\ dimensions$. This enables the definition of extended versions of Chern-Simons gravities in all dimensions. Employing the same prescription, the definition of gravitational Chern-Simons densities is extended to all even dimensions, but only to $4p-1$ $odd$ dimensions. All our consi…
Some of supersymmetric Chern-Simons theories are known to exhibit supersymmetry breaking when the Chern-Simons level is less than a certain number. The mechanism of the supersymmetry breaking is, however, not clear from the field theory viewpoint. In this paper, we discuss vacuum states of ${\cal N}=2$ pure Chern-Simons theory and ${\cal N}=2$ Chern-Simons-matter theories of quiver type using related theories in which Chern-Simons terms are replaced with (anti-)fundamental chiral multiplets. In the latter theories, supersymmetry breaking can be shown to occur by examining that the vacuum energ…
I present two calculations of the holographic Weyl anomalies induced by Chern-Simons gravity theories alternative to the ones presented in the literature. The calculations presented here rest on the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, which automatically yields the boundary terms suitable to regularize the theory. The procedure followed here sheds light in the structure of Chern-Simons gravities and their regularization.
We study the relation between the partition function of refined SU(N) and SO(2N) Chern-Simons on the 3-sphere and the universal Chern-Simons partition function in the sense of Mkrtchyan and Veselov. We find a four-parameter generalization of the integral representation of universal Chern-Simons that includes refined SU(N) and SO(2N) Chern-Simons for special values of parameters. The large N expansion of the integral representation of refined SU(N) Chern-Simons explicitly shows the replacement of the virtual Euler characteristic of the moduli space of complex curves with a refined Euler charact…
We search for vortices in a generalized Abelian Chern-Simons model with a nonstandard kinetic term. We illustrate our results, plotting and comparing several features of the vortex solution of the generalized model with those of the vortex solution found in the standard Chern-Simons model.
We develop the superfield background field method and study the effective action in the N=2, d3 supersymmetric Chern-Simons-matter systems. The one-loop low-energy effective action for non-Abelian supersymmetric Chern-Simons theory is computed to order $F^4$ by use of N = 2 superfield heat kernel techniques.
We derive the framing anomaly of four-dimensional holomorphic-topological Chern-Simons theory formulated on the product of a topological surface and the complex plane. We show that the presence of this anomaly allows one to couple four-dimensional Chern-Simons theory to holomorphic field theories with Kac-Moody symmetry, where the Kac-Moody level $k$ is critical $k=-h^{\vee}$. Applying this result to a holomorphic sigma model into a complex coadjoint orbit, we derive that four-dimensional Chern-Simons theory admits holomorphic monodromy defects.
We construct the $\mathcal{N}=2$ supersymmetric extensions of different models containing a Chern-Simons term and study their BPS structure. We find that the coupling of the Chern-Simons term to the general gauged nonlinear $σ$-model allows for general potentials depending on the Kähler metric and preserving two supersymmetries. We construct from supersymmetry the potentials that allow for BPS structures in different $\mathbb{C}P^{N}$ models coupled to Chern-Simons and Maxwell terms. We also couple the Chern-Simons term to a higher-derivative field theory (the baby Skyrme model) and study its …
