Supersymmetric Chern-Simons Theory Research Articles

Superstrings on AdS4× ℂℙ3as a coset sigma-model

According to the recent proposal by Aharony, Bergman, Jafferis and Maldacena the N=6 supersymmetric Chern-Simons theory in three dimensions has a 't Hooft limit whose holographic dual is described by type IIA superstings on AdS_4 x CP^3 background. We argue that the Green-Schwarz action for type IIA string theory on AdS_4 x CP^3 with kappa-symmetry partially fixed can be understood as a coset sigma-model on the same space supplied with a proper Wess-Zumino term. We construct the corresponding sigma-model Lagrangian and show that it is invariant under a local fermionic symmetry which for generic bosonic string configurations allows one to remove 8 out of 24 fermionic degrees of freedom. The remaining 16 fermions together with their bosonic partners should describe the physical content of AdS_4 x CP^3 superstring. As further evidence, we demonstrate that in the plane-wave limit the quadratic action arising from our model reproduces the one emerging from the type IIA superstring. The coset sigma-model is classically integrable which opens up the possibility to investigate its dynamics in a way very similar to the case of AdS_5 x S^5 superstrings.

Membranes on an Orbifold

We provide an M theory interpretation of the recently discovered N=8 supersymmetric Chern-Simons theory with SO(4) gauge symmetry. The theory is argued to describe two membranes moving in the orbifold R8/Z2. At level k=1 and k=2, the classical moduli space M coincides with the infrared moduli space of SO(4) and SO(5) super Yang-Mills theory, respectively. For higher Chern-Simons level, the moduli space is a quotient of M. At a generic point in the moduli space, the massive spectrum is proportional to the area of the triangle formed by the two membranes and the orbifold fixed point.

Notes on superconformal Chern-Simons-Matter theories

The three dimensional = 2 supersymmetric Chern-Simons theory coupled to matter fields, possibly deformed by a superpotential, give rise to a large class of exactly conformal theories with Lagrangian descriptions. These theories can be arbitrarily weakly coupled, and hence can be studied perturbatively. We study the theories in the large N limit, and compute the two-loop anomalous dimension of certain long operators. Our result suggests that various = 2 U(N) Chern-Simons theories coupled to suitable matter fields are dual to open or closed string theories in AdS4, which are not yet constructed.

Five-dimensional supersymmetric Chern–Simons action as a hypermultiplet quantum correction

Abstract Building on the covariant supergraph techniques in 4D N = 2 harmonic superspace, we develop a manifestly 5D N = 1 supersymmetric and gauge covariant formalism to compute the one-loop effective action for a hypermultiplet coupled to a background vector multiplet. As a simple application, we demonstrate the generation of a supersymmetric Chern–Simons action at the quantum level, both in the Coulomb and the non-Abelian phases. These superfield results are in agreement with the earlier component considerations of Seiberg et al. Our analysis suggests that similar calculations in terms of hybrid 4D superfields or within the 5D projective superspace approach may allow one to extract suitable formulations for the non-Abelian 5D supersymmetric Chern–Simons theory.

Supersymmetric Chern-Simons theory and supersymmetric quantum Hall liquid

We develop a supersymmetric extension of Chern-Simons theory and Chern-Simons-Landau-Ginzburg theory for the supersymmetric quantum Hall liquid. Supersymmetric counterparts of topological and gauge structures peculiar to the Chern-Simons theory are inspected in the supersymmetric Chern-Simons theory. We also explore an effective field theoretical description for the supersymmetric quantum Hall liquid. The key observation is the charge-flux duality. Based on the duality, we derive a dual supersymmetric Chern-Simons-Landau-Ginzburg theory, and discuss physical properties of the topological excitations in the supersymmetric quantum Hall liquid.

ℵ0-extended supersymmetric Chern-Simons theory for arbitrary gauge groups

We present a model of supersymmetric non-Abelian Chern-Simons theories in three-dimensions with arbitrarily many supersymmetries, called alephnull-extended supersymmetry. The number of supersymmetry N equals the dimensionality of any non-Abelian gauge group G as N = dim G. Due to the supersymmetry parameter in the adjoint representation of a local gauge group G, supersymmetry has to be local. The minimal coupling constant is to be quantized, when the homotopy mapping is nontrivial: \pi_3(G) = Z. Our results indicate that there is still a lot of freedom to be explored for Chern-Simons type theories in three dimensions, possibly related to M-theory.

Holographic formulation of quantum supergravity

We show that ${\cal N}=1$ supergravity with a cosmological constant can be expressed as constrained topological field theory based on the supergroup $Osp(1|4)$. The theory is then extended to include timelike boundaries with finite spatial area. Consistent boundary conditions are found which induce a boundary theory based on a supersymmetric Chern-Simons theory. The boundary state space is constructed from states of the boundary supersymmetric Chern-Simons theory on the punctured two sphere and naturally satisfies the Bekenstein bound, where area is measured by the area operator of quantum supergravity.

Dynamics of Script N = 2 supersymmetric Chern-Simons theories

We discuss several aspects of three dimensional N=2 supersymmetric gauge theories coupled to chiral multiplets. The generation of Chern-Simons couplings at low-energies results in novel behaviour including compact Coulomb branches, non-abelian gauge symmetry enhancement and interesting patterns of dynamically generated potentials. We further show how, given any pair of mirror theories with N=4 supersymmetry, one may flow to a pair of mirror theories with N=2 supersymmetry by gauging a suitable combination of the R-symmetries. The resulting theories again have interesting properties due to Chern-Simons couplings.

Moduli space of vacua of supersymmetric Chern-Simons theories and type IIB branes

We study the correspondence between the moduli space of vacua of three-dimensional supersymmetric Yang-Mills (Maxwell) Chern-Simons theories and brane configurations with (p,q)5-brane. For Coulomb branches, the number of the massless adjoint scalar fields in various supersymmetric theories exactly coincides with the number of the freely moving directions of D3-branes stretched between two 5-branes. When we include a matter superfield into the supersymmetric Chern-Simons theory two distinct symmetric and asymmetric phase appear. The symmetric phase is peculiar to this Chern-Simons Higgs system. We find the corresponding brane configuration for these phases. We also identify the stringy counterpart of the topological vortex state in the asymmetric phase.

ℵ 0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO( N) symmetry. We call these ℵ 0 (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ℵ 0 supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ℵ 0 globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ℵ 0 supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.

Supersymmetric KP equation embedded in supersymmetric self-dual Yang-Mills theory

We show that the N = 1 supersymmetric Kadomtsev-Petviashvili (SKP) equation of Manin and Radul can be embedded into recently formulated N = 1 self-dual supersymmetric Yang-Mills theories after appropriate dimensional reduction and truncation, which yield three-dimensional supersymmetric Chern-Simons theories. Based on this result, we also give a conjectural N = 2 SKP equation. Subsequently some exact solutions of these systems including fermionic fields are given.

Remarks on N=2 supersymmetric Chern-Simons theories

We discuss the complete superspace formulation of general non-abelian N=2 supersymmetric Chern-Simons theories. It is shown that the component level spin-0 self-interactions in such models are not completely determined by the superpotential. We compute the anomalous dimensions and beta-functions of the N=2 supersymmetric non-abelian Chern-Simons theory, when the self-interactions of scalar multiplets are absent. A simple classification of the “soft-breaking terms” of N=2 supersymmetry is also performed.

Thermal and quantum fluctuations in supersymmetric Chern-Simons theory

We study radiative corrections to the Abelian self-dual Chern-Simons theory at zero and finite temperatures. The analysis is performed with the help of functional methods. We consider the supersymmetric extension of scalar matter fields minimally coupled to a gauge field whose dynamics is governed solely by the Chern-Simons term. The scalar field potential is a self-dual sixth-order polynomial with U(1)-symmetry-breaking and symmetry-preserving minima which are degenerate. We find that the zero-temperature one-loop radiative corrections do not remove this degeneracy and both minima remain supersymmetric. We calculate the leading-order finite-temperature contributions to the effective potential in the high-temperature limit and we find that the U(1)-symmetry is restored. In contrast to four-dimensional field theories that restore the U(1)-symmetry at high temperatures, the restoration of the U(1)-symmetry in the abelian self-dual Chern-Simons theory occurs at the two-loop level. The Chern-Simons system without supersymmetry is discussed, as well as the scalar field model without Chern-Simons gauge fields. The same finite temperature result emerges in these cases.