Ghost fields in quantum field theory have been a long-standing problem. Specifically, theories with higher derivatives involve ghosts that appear in the Hamiltonian in the form of linear momenta term, which is commonly known as the Ostrogradski ghost. Higher derivative theories may involve both types of constraints i.e. first class and second class. Interestingly, these higher derivative theories may have non-Hermitian Hamiltonian respecting $\mathcal{PT}-$symmetries. In this paper, we have considered the $\mathcal{PT}-$symmetric nature of the extended Maxwell-Chern-Simon's theory and employed the second class constraints to remove the linear momenta terms causing the instabilities. We found that the removal is not complete rather conditions arise among the coefficients of the operator ${Q}$.
We explore Chern-Simons theories coupled to fundamental ghost-like matter in the large $N$ limit at 't Hooft coupling $λ$. These theories have been conjectured to be holographically dual to parity-violating, asymptotically dS$_4$ universes with a tower of light higher-spin fields. On $\mathbb{R}^3$, to all orders in large-$N$ perturbation theory, we show that Chern-Simons-ghost theories are related to ordinary Chern-Simons-matter theories by mapping $N \rightarrow - N$ and keeping $λ$ fixed. Consequently, the bosonization duality of ordinary Chern-Simons-matter theories extends to a bosonizati…
In the pure spinor formalism for the superstring, the b-ghost is a composite operator satisfying {Q,b}=T where Q is the pure spinor BRST operator and T is the holomorphic stress tensor. The b-ghost is holomorphic in a flat target-space background, but it is not holomorphic in a generic curved target-space background and instead satisfies $\bar\partial b$ = [Q, Ω] for some Ω. In this paper, Ω is explicitly constructed for the case of an open superstring in a super-Maxwell background.
We quantize the Maxwell Chern Simons theory in a geometric representation that generalizes the Abelian Loop Representation of Maxwell theory. We find that in the physical sector, the model can be seen as the theory of a massles scalar field with a topological interaction that enforces the wave functional to be multivalued. This feature allows to relate the Maxwell Chern Simons theory with the quantum mechanics of particles interacting through a Chern Simons field
We construct parity and time reversal invariant Maxwell-Chern-Simons gauge theory coupled to fermions with adding the parity partner to the matter and the gauge fields, which can give nontopological vortex solutions depending on the sign of the Chern-Simons coupling constant.
The large-mass behaviour of loop variables in Maxwell-Chern-Simons theory is analysed by means of a gauge-field transformation which allows to reset the Maxwell-Chern-Simons action to pure Chern-Simons.
We study the possibility of establishing the dual equivalence between the noncommutative Maxwell-Chern-Simons theory and the noncommutative self-dual theory. It turns to be that whereas in the commutative case the Maxwell-Chern-Simons theory can be mapped into the sum of the self-dual theory and the Chern-Simons theory, in the noncommutative case such a mapping is possible only for the theory with the modified Maxwell term.
We study interactions between like charges in the noncommutative Maxwell-Chern-Simons electrodynamics {\it{minimally}} coupled to spinors or scalars. We demonstrate that the non-relativistic potential profiles, for only spatial noncommutativity, are nearly identical to the ones generated by a {\it{non-minimal}} Pauli magnetic coupling, originally introduced by Stern \cite{js}. Although the Pauli term has crucial roles in the context of physically relevant objects such as anyons and like-charge bound states (or "Cooper pairs"), its inception \cite{js} (see also \cite{others}) was ad-hoc and phe…
Applying a master action technique we obtain the dual of the noncommutative Maxwell-Chern-Simons theory. The equivalence between the Maxwell-Chern-Simons theory and the self-dual model in commutative space-time does not survive in the non-commutative setting. We also point out an ambiguity in the Seiberg-Witten map.
We explain how static multi-vortex solutions arise in non-linear field theories, by taking the non-linear Schrödinger equation coupled to Chern-Simons field (Jackiw-Pi model) and a fermion Chern-Simons theory as simple examples. We then construct a fermion Maxwell-Chern-Simons theory which has consistent static field equations, and show that it has the same vortex solutions as the Jackiw-Pi model, but gives rise to quite different vortex dynamics.
Following systematically the generalized Hamiltonian approach of Batalin and Fradkin, we demonstrate the equivalence of a self-dual model with the Maxwell-Chern-Simons theory by embedding the former second-class theory into a first-class theory.
We present a three-dimensional Chern-Simons gravity based on a deformation of the Maxwell algebra. This symmetry allows introduction of a non-vanishing torsion to the Maxwell Chern-Simons theory, whose action recovers the Mielke-Baelker model for particular values of the coupling constants. By considering suitable boundary conditions, we show that the asymptotic symmetry is given by the $\widehat{\mathfrak{bms}}_3\oplus\mathfrak{vir}$ algebra with three independent central charges.
The equivalence between a higher derivative extension of Maxwell-Chern-Simons Proca model and some gauge invariant theories from the point of view of the Hamiltonian path integral quantization in the framework of gauge-unfixing approach is investigated. The Hamiltonian path integrals of the first-class systems take manifestly Lorentz-covariant forms.
We consider a non-relativistic (NR) limit of $(2+1)$-dimensional Maxwell Chern-Simons (CS) gravity with gauge algebra [Maxwell] $\oplus \ u(1)\oplus u(1)$. We obtain a finite NR CS gravity with a degenerate invariant bilinear form. We find two ways out of this difficulty: To consider i) [Maxwell] $\oplus\ u(1)$, which does not contain Extended Bargmann gravity (EBG); or, ii) the NR limit of [Maxwell] $\oplus\ u(1)\oplus u(1)\oplus u(1)$, which is a Maxwellian generalization of the EBG.
Noncommutative Maxwell-Chern-Simons theory in 3-dimensions is defined in terms of star product and noncommutative fields. Seiberg-Witten map is employed to write it in terms of ordinary fields. A parent action is introduced and the dual action is derived. For spatial noncommutativity it is studied up to second order in the noncommutativity parameter θ. A new noncommutative Chern-Simons action is defined in terms of ordinary fields, inspired by the dual action. Moreover, a transformation between noncommuting and ordinary fields is proposed.
Within the superfield approach, we prove the absence of UV/IR mixing in the three-dimensional noncommutative supersymmetric Maxwell-Chern-Simons theory at any loop order and demonstrate its finiteness in one, three and higher loop orders.
We have constructed nonrelativistic fermion and scalar field theories coupled to a Maxwell-Chern-Simons gauge field which admit static multi-vortex solutions. This is achieved by introducing a magnetic coupling term in addition to the usual minimal coupling.
The Symplectic Projector Method is applied to derive the local physical degrees of freedom and the physical Hamiltonian of the Maxwell-Chern-Simons theory in $d=1+2$. The results agree with the ones obtained in the literature through different approaches.
In this paper, we use gauge embedding procedure and master action approach to establish the equivalence between the self-dual and Maxwell-Chern-Simons models with Lorentz symmetry breaking. As a result, new kinds of Lorentz-breaking terms arise.
The 3D Maxwell-Chern-Simons theory with planar, single-edged, boundary is considered. It is shown that its holographic reduction on a flat euclidean 2D spacetime is a scalar field theory describing a conserved chiral current, which corresponds to the electric continuity equation. Differently from the theory with planar, double-edged boundary, in this holographic bulk-boundary approach physical quantities like the chiral velocity of the edge excitations depend also on the non-topological Maxwell term.
We take advantage of the superspace formalism and explicitly find the N=2 supersymmetric extension of the Maxwell Chern-Simons model. In our construction a special form of a potential term and indispensability of an additional neutral scalar field arise naturally. By considering the algebra of supersymmetric charges we find Bogomol'nyi equations for the investigated model.
We examine the energetics of $Q$-balls in Maxwell-Chern-Simons theory in two space dimensions. Whereas gauged $Q$-balls are unallowed in this dimension in the absence of a Chern-Simons term due to a divergent electromagnetic energy, the addition of a Chern-Simons term introduces a gauge field mass and renders finite the otherwise-divergent electromagnetic energy of the $Q$-ball. Similar to the case of gauged $Q$-balls, Maxwell-Chern-Simons $Q$-balls have a maximal charge. The properties of these solitons are studied as a function of the parameters of the model considered, using a numerical tec…
We find soliton solutions in the 2+1 dimensional non-commutative Maxwell Chern-Simons Higgs theories. In the limit of the Chern-Simons coefficient going to zero, these solutions go over to the previously found solutions in the non-commutative Maxwell Higgs theories. The new solutions may have relevance in the theory of the fractional quantum Hall effect and possibly in string vacua corresponding to open strings terminating on D2 branes in the presence of D0 branes.
We investigate probe limit vortex solutions of a charged scalar field in Einstein-Maxwell theory in 3+1 dimensions, for an asymptotically AdS Schwarzschild black hole metric with the addition of an axionic coupling to the Maxwell field. We show that the inclusion of such a term, together with a suitable potential for the axion field, can induce an effective Chern-Simons term on the 2+1 dimensional boundary. We obtain numerical solutions of the equations of motion and find Maxwell-Chern-Simons like magnetic vortex configurations, where the magnetic field profile varies with the size of the effe…
We investigate the effective potential for Abelian Maxwell--Chern--Simons systems. The calculations follow an alternate approach, recently proposed as a gauge invariant formulation of the effective potential, constructed in terms of a gauge invariant order parameter. We compare the results with another investigation, obtained within a standard route of calculating the effective potential.
Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory
Massachusetts Institute of Technology（麻省理工学院）；University of Perugia（佩鲁贾大学）；University of Bonn（波恩大学）；The Cyprus Institute（塞浦路斯研究所）；Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射中心）；Harvard University（哈佛大学）
We examine the energetics of Q-balls in Maxwell-Chern-Simons theory in two space dimensions. Whereas gauged Q-balls are unallowed in this dimension in the absence of a Chern-Simons term due to a divergent electromagnetic energy, the addition of a Chern-Simons term introduces a gauge field mass and renders finite the otherwise-divergent electromagnetic energy of the Q-ball. Similar to the case of gauged Q-balls, Maxwell-Chern-Simons Q-balls have a maximal charge. The properties of these solitons are studied as a function of the parameters of the model considered, using a numerical technique kno…
Using a group-invariant version of the Faddeev-Popov method we explicitly obtain the partition functions of the Self-Dual Model and Maxwell-Chern-Simons theory. We show that their ratio coincides with the partition function of abelian Chern-Simons theory to within a phase factor depending on the geometrical properties of the manifold.
The large distance behavior of the Maxwell- Chern-Simons (MCS) equations is analyzed, and it is found that the pure Chern-Simons limit, (when the Maxwell term is dropped from the equations), does not describe the large distance limit of the MCS model. This necessitates the solution of the original problem. The MCS gauge theory coupled to a nonrelativistic matter field, (governed by the gauged non-linear Schrödinger equation), is studied. It turns out, that there are no regular self-dual solutions as in the pure Chern-Simons case, but the model admits interesting, though singular self-dual solu…
We consider the Maxwell-Chern-Simons theory in noncommutative three dimensional space-time. We show that the Seiberg-Witten map is ambiguous due to the dimensional coupling constant. To get the dual theory we start from a master action obtained by promoting the global shift invariance to a local one. We also obtain the mapping between the observables of the two equivalent theories. We show that the equivalence between the Maxwell-Chern-Simons theory and the self-dual model in commutative space-time does not survive in the non-commutative setting.
The low-energy electron-electron scattering potential is derived and discussed for the Maxwell-Chern-Simons model coupled to QED_3 with spontaneous symmetry breaking. One shows that the Higgs mechanism might favour electron-electron bound states.
A non-relativistic version of the 2+1 dimensional gauged Chern-Simons O(3) sigma model, augmented by a Maxwell term, is presented and shown to support topologically stable static self-dual vortices. Exactly like their counterparts of the ungauged model, these vortices are shown to exhibit Hall behaviour in their dynamics.
We show that N=2 supersymmetric Maxwell-Chern-Simons-Higgs systems in three dimension can be realized as gauge theories on a D2-brane in D8-branes background with a non-zero B-field. We reproduce a potential of Coulomb branch of the Chern-Simons theory as a potential of a D2-brane in a classical D8-brane solution and show that each Coulomb vacuum is realized by a D2-brane stabilized in the bulk at a certain distance from D8-branes.
We study various three-dimensional supersymmetric Maxwell Chern-Simons solitons by using type IIB brane configurations. We give a systematic classification of soliton spectra such as topological BPS vortices and nontopological vortices in $\mathcal{N}=2,3$ supersymmetric Maxwell Chern-Simons system via the branes of type IIB string theory. We identify the brane configurations with the soliton spectra of the field theory and obtain a nice agreement with field theory aspects. We also discuss possible brane constructions for BPS domain wall solutions.
5-dimensional Einstein-Maxwell-Chern-Simons theory with Chern-Simons coefficient $λ=1$ has supersymmetric black holes with vanishing horizon angular velocity, but finite angular momentum. Here supersymmetry is associated with a borderline between stability and instability, since for $λ>1$ a rotational instability arises, where counterrotating black holes appear, whose horizon rotates in the opposite sense to the angular momentum. For $λ>2$ black holes are no longer uniquely characterized by their global charges, and rotating black holes with vanishing angular momentum appear.
The Maxwell-Chern-Simons (MCS) theory with planar boundary is considered. The boundary is introduced according to Symanzik's basic principles of locality and separability. A method of investigation is proposed, which, avoiding the straight computation of correlators, is appealing for situations where the computation of propagators, modified by the boundary, becomes quite complex. For MCS theory, the outcome is that a unique solution exists, in the form of chiral conserved currents, satisfying a Kac-Moody algebra, whose central charge does not depend on the Maxwell term.
The boundary effects in the screening of an applied magnetic field in a finite temperature 2+1 dimensional model of charged fermions minimally coupled to Maxwell and Chern-Simons fields are investigated. It is found that in a sample with only one boundary -a half-plane- a total Meissner effect takes place, while in a sample with two boundaries -an infinite strip- the external magnetic field partially penetrates the material.
We study the exact equivalence between the self-dual model minimally coupled with a Dirac field and the Maxwell-Chern-Simons model with non-minimal magnetic coupling to fermions. We show that the fermion sectors of the models are equivalent only if a Thirring like interaction is included. Using functional methods we verify that, up to renormalizations, the equivalence persists at the quantum level.
We study the equivalence between the self-dual and the Maxwell-Chern-Simons (MCS) models coupled to dynamical, U(1) charged matter, both fermionic and bosonic. This is done through an iterative procedure of gauge embedding that produces the dual mapping of the self-dual vector field theory into a Maxwell-Chern-Simons version. In both cases, to establish this equivalence a current-current interaction term is needed to render the matter sector unchanged. Moreover, the minimal coupling of the original self-dual model is replaced by a non-minimal magnetic like coupling in the MCS side. Unlike the …
We find the static vortex solutions of the model of Maxwell-Chern-Simons gauge field coupled to a (2+1)-dimensional four-fermion theory. Especially, we introduce two matter currents coupled to the gauge field minimally: the electromagnetic current and a topological current associated with the electromagnetic current. Unlike other Chern-Simons solitons the N-soliton solution of this theory has binding energy and the stability of the solutions is maintained by the charge conservation laws.
The loop representation formulation of non-relativistic particles coupled with abelian gauge fields is studied. Both Maxwell and Chern-Simons interactions are separately considered. It is found that the loop-space formulations of these models share significant similarities, although in the Chern-Simons case there exists an unitary transformation that allows to remove the degrees of freedom associated with the paths. The existence of this transformation, which allows to make contact with the anyonic interpretation of the model, is subjected to the fact that the charge of the particles be quanti…
Focusing on gauge degrees of freedom specified by a 1+3 dimensions model hosting a Maxwell term plus a Lorentz and CPT non-invariant Chern-Simons-like contribution, we obtain a minimal extension of such a system to a supersymmetric environment. We comment on resulting peculiar self-couplings for the gauge sector, as well as on background contribution for gaugino masses. Furthermore, a non-polynomial generalization is presented.
The Maxwell--Chern--Simons model with scaler matter in the adjoint representation is analyzed from an alternative approach which is regular in the $θ\to 0$ limit. This method is complementary to the usual operator formalism applied to explore the nonperturbative solutions which gives singular results in the $θ\to 0$ limit. The absence of any regular non-trivial lumpy solutions satisfying B--P--S bound has been conclusively demonstrated.
The non-relativistic Maxwell-Chern-Simons model recently introduced by Manton is shown to admit self-dual vortex solutions with non-zero electric field. The interrelated ``geometric'' and ``hidden'' symmetries are explained. The theory is also extended to (non-relativistic) spinors. A relativistic, self-dual model, whose non-relativistic limit is the Manton model is also presented. The relation to previous work is discussed.
We find self-dual vortex solutions in a Maxwell-Chern-Simons model with anomalous magnetic moment. From a recently developed N=2-supersymmetric extension, we obtain the proper Bogomol'nyi equations together with a Higgs potential allowing both topological and non-topological phases in the theory.
We construct an action for holomorphic Chern-Simons theory that couples the gauge field to off-shell gravitational backgrounds, comprising the complex structure and the (3,0)-form of the target space. Gauge invariance of the off-shell action is achieved by enlarging the field space to include an appropriate system of Lagrange multipliers, ghost and ghost-for-ghost fields. Both the BRST transformations and the BV action are compactly and neatly written in terms of superfields which include fields, backgrounds and their antifields. We show that the anti-holomorphic target space derivative can be…
Differential regularization is used to investigate the one-loop quantum corrections to Chern-Simons-Maxwell spinor and scalar electrodynamics. We illustrate the techniques to write the loop amplitudes in coordinate space. The short-distance expansion method is developed to perform the Fourier transformation of the amplitudes into momentum space and the possible renormalization ambiguity in Chern-Simons type gauge theories in terms of differential regularization is discussed. We also stress that the surface terms appearing in the differential regularization should be kept along for finite theor…
Self-dual abelian Higgs system, involving both the Maxwell and Chern-Simons terms are obtained from Carroll-Field-Jackiw theory by dimensional reduction. Bogomol'nyi-type equations are studied from theoretical and numerical point of view. In particular we show that the solutions of these equations are Nielsen-Olesen vortices with electric charge.
In this paper, we study the three-dimensional noncommutative Maxwell-Chern-Simons theory. In the present analysis, a complete account for the gauge field two-point function renormalizability is presented and physical significant quantities are carefully established. The respective form factor expressions from the gauge field self-energy are computed at one-loop order. More importantly, an analysis of the gauge field dispersion relation, in search of possible noncommutative anomalies and infrared finiteness, is performed for three special cases, with particular interest in the highly noncommuta…
We find soliton solutions of the noncommutative Maxwell-Chern-Simons theory confined to a finite quantum Hall droplet. The solitons are exactly as hypothesized in \cite{Manu}. We also find new variations on these solitons. We compute their flux and their energies. The model we consider is directly related to the model proposed by Polychronakos\cite{Poly} and studied by Hellerman and Van Raamsdonk\cite{HvR} where it was shown that it is equivalent to the quantum Hall effect.
