We show that minimal massive 3d gravity (MMG), as well as the topological massive gravity, are particular cases of a more general `minimal massive gravity' theory (with a single massive propagating mode) arising upon spontaneous breaking of a local symmetry in a Chern-Simons gravity based on a Hietarinta or Maxwell algebra. Similar to the MMG case, the requirements that the propagating massive mode is neither tachyon nor ghost and that the central charges of an asymptotic algebra associated with a boundary CFT are positive, impose restrictions on the range of the parameters of the theory.
In this talk I describe recent work (hep-th/9606029) in which I classified all conceivable 2+1 dimensional Chern-Simons (CS) theories with continuous compact abelian gauge group or finite abelian gauge group. The CS theories with finite abelian gauge group that can be obtained from the spontaneous breakdown of a CS theory with gauge group the direct product of various compact U(1) gauge groups were also identified. Those that can not be reached in this way are actually the most interesting since they lead to nonabelian phenomena such as nonabelian braid statistics, Alice fluxes and Cheshire ch…
In this paper we investigate the canonical quantization of a non-Abelian topologically massive Chern-Simons theory in which the gauge fields are minimally coupled to a multiplet of scalar fields in such a way that the gauge symmetry is spontaneously broken. Such a model produces the Chern-Simons-Higgs mechanism in which the gauge excitations acquire mass both from the Chern-Simons term and from the Higgs-Kibble effect. The symmetry breaking is chosen to be only partially broken, in such a way that in the broken vacuum there remains a residual non-Abelian symmetry. We develop the canonical oper…
A detailed analysis of Chern-Simons (CS) theories in which a compact abelian direct product gauge group U(1)^k is spontaneously broken down to a direct product H of (finite) cyclic groups is presented. The spectrum features global H charges, vortices carrying flux labeled by the elements of H and dyonic combinations. Due to the Aharonov-Bohm effect these particles exhibit toplogical interactions. The remnant of the U(1)^k CS term in the discrete H gauge theory describing the effective long distance physics of such a model is shown to be a 3-cocycle for H summarizing the nontrivial topological …
We present a second order gravity action which consists of ordinary Einstein action augmented by a first-order, vector like, Chern-Simons quasi topological term.This theory is ghost-free and propagates a pure spin-2 mode. It is diffeomorphism invariant, although its local Lorentz invariance has been spontaneously broken.
It is shown that topological massive gravity augmented by the triadic gravitational Chern-Simons first order term is a curved a pure spin-2 action. This model contains two massive spin-2 excitations. However, since its light-front energy is not semidefinite positive, this double CS-action does not have any physical relevance.In other words, topological massive gravity cannot be spontaneously broken down by the presence of the triadic CS term.
We consider a spontaneously broken nonabelian topologically massive gauge theory in a broken phase possessing a residual nonabelian symmetry. Recently there has been some question concerning the renormalization of the Chern-Simons coefficient in such a broken phase. We show that, in this broken vacuum, the renormalized ratio of the Chern-Simons coupling to the gauge coupling is shifted by $1/4π$ times an integer, preserving the usual integer quantization condition on the bare parameters.
We study the locality properties of the vortex operators in compact U(1) Maxwell-Chern-Simons and SU(N) Yang-Mills-Chern-Simons theories in 2+1 dimensions. We find that these theories do admit local vortex operators and thus in the UV regularized versions should contain stable magnetic vortices. In the continuum limit however the energy of these vortex excitations generically is logarithmically UV divergent. Nevertheless the classical analysis shows that at small values of CS coefficient $κ$ the vortices become light. It is conceivable that they in fact become massless and condense due to quan…
In this paper we study a $2+1$ dimensional system in which fermions are coupled to the self-dual topological vortex in $U(1) \times U(1)$ Chern-Simons theory, where both $U(1)$ gauge symmetries are spontaneously broken. We consider two Abelian Higgs scalars with visible and hidden sectors coupled to a fermionic field through three interaction Lagrangians, where one of them violates the fermion number. Using a fine tuning procedure, we could obtain the number of the fermionic zero modes which is equal to the absolute value of the sum of the vortex numbers in the visible and hidden sectors.
Massive QCD at $θ=π$ breaks CP spontaneously and admits domain walls whose dynamics and phases depend on the number of flavors and their masses. We discuss these issues within the Witten-Sakai-Sugimoto model of holographic QCD. Besides showing that this model reproduces all QCD expectations, we address two interesting claims in the literature. The first is about the possibility that the QCD domain-wall theory is fully captured by three-dimensional physics, only. The second regards the existence of quantum phases in certain Chern-Simons theories coupled to fundamental matter. Both claims are su…
We study one-loop correction to the Chern-Simons coefficient $κ=k/4π$ in $N=1,2,3$ supersymmetric Yang-Mills Chern-Simons systems. In the pure bosonic case, the shift of the parameter $k$ is known to be $k\rightarrow k + c_v$, where $c_v$ is the quadratic Casimir of the gauge group. In the $N=1$ case, the fermionic contribution cancels the bosonic contribution by half and the shift is $k \rightarrow k+ c_v/2$, making the theory anomalous if $c_v$ is odd. In the $N=2,3$ cases, the fermionic contribution cancels the bosonic contribution completely and there is no correction. We also calculate th…
Quantum corrections to Lorentz- and CPT-violating QED in flat spacetime produce unusual radiative corrections, which can be finite but of undetermined magnitude. The corresponding radiative corrections in a gravitational theory are even stranger, since the term in the fermion action involving a preferred axial vector $b^μ$ would give rise to a gravitational Chern-Simons term that is proportional $b^μ$, yet which actually does not break Lorentz invariance. Initially, the coefficient of this gravitational Chern-Simons term appears to have the same ambiguity as the coefficient for the analogous t…
By imposing self-duality conditions, we obtain the explicit form in which gauge theories spontaneously breakdown in the Bogomol'nyi limit. In this context, we reconsider the Abelian Higgs, Chern-Simons Higgs and Maxwell-Chern-Simons Higgs models. On the same footing, we find a topological Higgs potential for a Maxwell-Chern-Simons extended theory presenting both minimal and nonminimal coupling. Finally, we perform a numerical calculation in the asymmetric phase and show the solutions to the self-dual equations of motion of the topological theory. We argue about certain relations among the para…
We re-examine three-dimensional gauge theory with a Chern-Simons term in which the Lorentz invariance is spontaneously broken by dynamical generation of a magnetic field. A non-vanishing magnetic field leads, through the Nambu-Goldstone theorem, to the decrease of zero-point energies of photons, which accounts for a major part of the mechanism. The asymmetric spectral flow plays an important role. The instability in pure Chern-Simons theory is also noted.
We propose a random matrix theory for QCD in three dimensions with a Chern-Simons term at level $k$ which spontaneously breaks the flavor symmetry according to U($2N_{\rm f}$) $\to $ U($N_{\rm f}+k$)$\times$U($N_{\rm f}-k$). This random matrix model is obtained by adding a complex part to the action for the $k=0$ random matrix model. We derive the pattern of spontaneous symmetry breaking from the analytical solution of the model. Additionally, we obtain explicit analytical results for the spectral density and the spectral correlation functions for the Dirac operator at finite matrix dimension,…
In a wide class of three-dimensional Abelian gauge theories with a bare Chern-Simons term, the Lorentz invariance is spontaneously broken by dynamical generation of a non-vanishing magnetic field. A detailed computation of an energy density of the true vacuum is given. The originally massive photon becomes massless, fulfilling the role of a Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance.
We study parity-violating effects, particularly the generation of angular momentum density and its relation to the parity-odd and dissipationless transport coefficient Hall viscosity, in strongly-coupled quantum fluid systems in 2+1 dimensions using holographic method. We employ a class of 3+1-dimensional holographic models of Einstein-Maxwell system with gauge and gravitational Chern-Simons terms coupled to a dynamical scalar field. The scalar can condensate and break the parity spontaneously. We find that when the scalar condensates, a non-vanishing angular momentum density and an associated…
We consider the class of d=4 CFTs at finite temperature and chemical potential that are holographically described within D=5 Einstein-Maxwell theory with a Chern-Simons term. The high temperature phase, which is spatially homogeneous and isotropic, is dual to the AdS-Reissner-Nordstrom black brane solution. For sufficiently large Chern-Simons coupling, we construct new electrically charged AdS black hole solutions that are dual to the low temperature, spatially modulated phase. In this phase the current, associated with the abelian global symmetry, spontaneously acquires a helical order. The n…
We show in this paper that Abelian Chern-Simons term is induced in 2+1 and 3+1 dimensional rotating superfluid $^{3}$He-A and plays important roles in its dynamics. Because U(1) symmetry is spontaneously broken in $^{3}$He-A, Goldstone mode appears and contributes to induced Chern-Simons term. We found that the coefficient of Chern-Simons term, which is equivalent to Hall conductance, depends on an infra-red cut off of the Goldstone mode, and that the orbital angular momentum of $^{3}$He-A in a cylinder geometry is derived from Chern-Simons term.
In this thesis we investigate the effective actions for massive Kaluza-Klein states, focusing on the massive modes of spin-3/2 and spin-2 fields. To this end we determine the spontaneously broken gauge symmetries associated to these `higher spin' states and construct the unbroken phase of the Kaluza-Klein theory. We show that for the particular background AdS_3 x S*3 x S*3 a consistent coupling of the first massive spin-3/2 multiplet requires an enhancement of local supersymmetry, which in turn will be spontaneously broken in the Kaluza-Klein vacuum. The corresponding action is constructed as …
We study three-dimensional non-linear models of vector and vector-spinor Goldstone fields associated with the spontaneous breaking of certain higher-spin counterparts of supersymmetry whose Lagrangians are of a Volkov-Akulov type. Goldstone fields in these models transform non-linearly under the spontaneously broken rigid symmetries. We find that the leading term in the action of the vector Goldstone model is the Abelian Chern-Simons action whose gauge symmetry is broken by a quartic term. As a result, the model has a propagating degree of freedom which, in a decoupling limit, is a quartic Gal…
We present the scalar field effective potential for nonrelativistic self-interacting scalar and fermion fields coupled to an Abelian Chern-Simons gauge field. Fermions are non-minimally coupled to the gauge field via a Pauli interaction. Gauss's law linearly relates the magnetic field to the matter field densities; hence, we also include radiative effects from the background gauge field. However, the scalar field effective potential is transparent to the presence of the background gauge field to leading order in the perturbative expansion. We compute the scalar field effective potential in two…
We study the scalar perturbation on the background of a Kerr black hole in the dynamical Chern-Simons modified gravity with a quadratic coupling between the scalar field and Chern-Simons term. In particular, the late-time tails of scalar perturbations are investigated numerically in time domain by using the hyperboloidal foliation method. It is found that the Kerr black hole becomes unstable under linear perturbations in a certain region of the parameter space, which depends on the harmonic azimuthal index $m$ of the perturbation's mode. This may indicate that some Kerr black holes in this the…
We present two examples of parity-invariant $[U(1)]^{2}$ Chern-Simons-Higgs models with spontaneously broken symmetry. The models possess topological vortex excitations. It is argued that the smallest possible flux quanta are composites of one quantum of each type $(1,1)$. These hybrid anyons will dominate the statistical properties near the ground state. We analyse their statistical interactions and find out that unlike in the case of Jackiw-Pi solitons there is short range magnetic interaction which can lead to formation of bound states of hybrid anyons. In addition to mutual interactions th…
It is well known that a physical medium that sets a Lorentz frame generates a Lorentz-breaking gap for a graviton. We examine such generated "mass" terms in the presence of a fluid medium whose ground state spontaneously breaks spatial translation invariance in $d = D+1$ spacetime dimensions, and for a solid in $D = 2$ spatial dimensions. By requiring energy positivity and subluminal propagation, certain constraints are placed on the equation of state of the medium. In the case of $D = 2$ spatial dimensions, classical gravity can be recast as a Chern-Simons gauge theory and motivated by this w…
The Maxwell-Chern-Simons gauge theory with charged scalar fields is analyzed at two loop level. The effective potential for the scalar fields is derived in the closed form, and studied both analytically and numerically. It is shown that the U(1) symmetry is spontaneously broken in the massless scalar theory. Dimensional transmutation takes place in the Coleman-Weinberg limit in which the Maxwell term vanishes. We point out the subtlety in defining the pure Chern-Simons scalar electrodynamics and show that the Coleman-Weinberg limit must be taken after renormalization. Renormalization group ana…
In three dimensional Maxwell-Chern-Simons massless scalar electrodynamics with $ ϕ^6$ coupling, the $U(1)$ symmetry is spontaneously broken at two loop order regardless of the presence or absence of the Maxwell term. Dimensional transmutation takes place in pure Chern-Simons scalar electrodynamics. The beta function for the $ϕ^6$ coupling is independent of gauge couplings.
Planar Chern-Simons (CS) theories in which a compact abelian gauge group U(1) x U(1) is spontaneously broken to U(1) x Z_N are investigated. Among other things, it is noted that the theories just featuring the mixed CS term coupling the broken to the unbroken U(1) gauge fields in general exhibits an interesting form of confinement: only particles carrying certain multiples of the fundamental vortex flux unit and certain multiples of the fundamental charge of the unbroken U(1) gauge field can appear as free particles. Adding the usual CS term for the broken U(1) gauge fields does not change muc…
We study a spontaneously broken SU(2) Chern-Simons-Higgs model coupled though a Higgs portal to an uncharged triplet scalar with a vacuum state competing with the Higgs one. We find vortex-like solutions to the field equations in different parameter space regions. Depending on the scalar coupling constants we find a parameter region in which the competing order creates a halo about the Chern-Simons-Higgs vortex core, together with two other regions, one where no vortex solutions exist, the other where ordinary Chern-Simons-Higgs vortices can be found. We derive the low-energy theory for the mo…
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 ro…
Three dimensional, $U(N)$ symmetric, field theory with fermion matter coupled to a topological Chern--Simons term, in the large $N$ limit is analyzed in details. We determine the conditions for the existence of a massless conformal invariant ground state as well as the conditions for a massive phase. We analyze the phase structure and calculate gauge invariant corelators comparing them in several cases to existing results. In addition to the non-critical explicitly broken scale invariance massive case we consider also a massive ground state where the scale symmetry is spontaneously broken. We …
Within gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the…
We find a new type of topological vortex solution in the $U(1)_Z \times U(1)_A$ Chern Simons gauge theory in the presence of a $U(1)_A$ magnetic field background. In this theory $U(1)_Z$ is broken spontaneously by the $U(1)_A$ magnetic field. These vortices exhibit long range interactions as they are charged under the unbroken $U(1)_A$. They deplete the $U(1)_A$ magnetic field near their core and also break both $C$ and $P$ symmetries. Understanding the nature of these vortices sheds light on the ground state structure of the superconductivity studied in [1]. We also study the Berezinsky-Koste…
We present a unified analysis of the self-dual, second order, topologically massive and the recently introduced fourth order models of massive gravity in 3D. We show that there is a family of first order actions which interpolate between these different single excitation models. We show how the master actions are related by duality transformation. We construct by the same method the master action which relates the fourth order new massive model with two excitations and the usual second order model with Fierz-Pauli mass. We show that the more general model obtained by adding a Chern-Simons term…
We generalize the Giveon-Kutasov duality for the 3d $\mathcal{N}=3$ $U(N)_{k,k+nN}$ Chern-Simons matter gauge theory with $F$ fundamental hypermultiplets by introducing $SU(N)$ and $U(1)$ Chern-Simons levels differently. We study the supersymmetric partition functions and the superconformal indices of the duality, which supports the validity of the duality proposal. From the duality, we can map out the low-energy phases: For example, confinement appears for $F+k-N=-n=1$ or $N=2F=k=-n=2$. For $F+k-N<0$, supersymmetry is spontaneously broken, which is in accord with the fact that the partition f…
Gauge theories with no Maxwell term are investigated in various setups. The dynamical generation of the Maxwell term is correlated to the scale invariance properties of the system. This is discussed mainly in the cases where the gauge coupling carries dimensions. The term is generated when the theory contains a scale explicitly, when it is asymptotically free and in particular also when the scale invariance is spontaneously broken. The terms are not generated when the scale invariance is maintained. Examples studied include the large $N$ limit of the $CP^{N-1}$ model in $(2+ε)$ dimensions, a 3…
In this paper, we consider dynamical Chern-Simons gravity with the identification of the scalar field coupled though the Pontryagin density with the axion dark matter, and we discuss the effects of the parametric resonance on gravitational waves (GWs). When we consider GWs in a coherently oscillating axion cloud, we confirm that significant resonant amplification of GWs occurs in a narrow frequency band, and the amplification is restricted to the late epoch after the passage of the incident waves. We also identify the condition that an axion cloud spontaneously emits GWs. Once we take into acc…
We present a minimal bottom-up extension of the Chern-Simons bulk action for holographic translational symmetry breaking that naturally gives rise to pair density waves. We construct stationary inhomogeneous black hole solutions in which both the U(1) symmetry and spatially translational symmetry are spontaneously broken at finite temperature and charge density. This novel solution provides a dual description of a superconducting phase intertwined with charge, current and parity orders.
Gravitational theories with fixed background fields break local Lorentz and diffeomorphism invariance either explicitly or spontaneously. In the case of explicit breaking it is known that conflicts can arise between the dynamics and geometrical constraints, while spontaneous breaking evades this problem. It is for this reason that in the gravity sector of the Standard-Model Extension (SME) it is assumed that the background fields (SME coefficients) originate from spontaneous symmetry breaking. However, in other examples, such as Chern-Simons gravity and massive gravity, diffeomorphism invarian…
In this thesis, we studied the Topologically Massive Gravity (TMG) in two perspectives. Firstly, by using real scalar and abelian gauge fields, we built the Weyl-invariant extension of TMG which unifies cosmological TMG and Topologically Massive Electrodynamics (TME) with a Proca mass term. Here, we have demonstrated that the presence of (Anti)-de Sitter spaces as the background solution, spontaneously breaks the local Weyl symmetry, whereas the radiative corrections at two-loop level breaks the symmetry in flat vacuum. The breaking of Weyl symmetry fixes all the dimensionful parameters and pr…
