Topological Mass Term Research Articles

Implications of the topological Chern-Simons mass in the gap equation

In this paper, we solve the gap equation of the Yang-Mills-Gribov-Zwanziger-Chern-Simon theory by considering the first order in the Chern-Simon topological mass term, $M$. As a result, we find three possible solutions to the gap equation, i.e. three different Gribov parameters. In addition, we analyze the regime of the theory for each of these Gribov parameters and we obtain a different result from the literature.

Discrete and higher-form symmetries in SCFTs from wrapped M5-branes

We analyze topological mass terms of BF type arising in supersymmetric M-theory compactifications to AdS5. These describe spontaneously broken higher-form gauge symmetries in the bulk. Different choices of boundary conditions for the BF terms yield dual field theories with distinct global discrete symmetries. We discuss in detail these symmetries and their ’t Hooft anomalies for 4d mathcal{N} = 1 SCFTs arising from M5-branes wrapped on a Riemann surface without punctures, including theories from M5-branes at a ℤ2 orbifold singularity. The anomaly polynomial is computed via inflow and contains background fields for discrete global 0-, 1-, and 2-form symmetries and continuous 0-form symmetries, as well as axionic background fields. The latter are properly interpreted in the context of anomalies in the space of coupling constants.

Topological mass generation and 2-forms

In this work we revisit the topological mass generation of 2-forms and establish a connection to the unique derivative coupling arising in the quartic Lagrangian of the systematic construction of massive $2-$form interactions, relating in this way BF theories to Galileon-like theories of 2-forms. In terms of a massless $1-$form $A$ and a massless $2-$form $B$, the topological term manifests itself as the interaction $B\wedge F$, where $F = {\rm d} A$ is the field strength of the $1-$form. Such an interaction leads to a mechanism of generation of mass, usually referred to as "topological generation of mass" in which the single degree of freedom propagated by the $2-$form is absorbed by the $1-$form, generating a massive mode for the $1-$form. Using the systematical construction in terms of the Levi-Civita tensor, it was shown that, apart from the quadratic and quartic Lagrangians, Galileon-like derivative self-interactions for the massive 2-form do not exist. A unique quartic Lagrangian $\epsilon^{\mu\nu\rho\sigma}\epsilon^{\alpha\beta\gamma}_{\;\;\;\;\;\;\sigma}\partial_{\mu}B_{\alpha\rho}\partial_{\nu}B_{\beta\gamma}$ arises in this construction in a way that it corresponds to a total derivative on its own but ceases to be so once an overall general function is introduced. We show that it exactly corresponds to the same interaction of topological mass generation. Based on the decoupling limit analysis of the interactions, we bring out supporting arguments for the uniqueness of such a topological mass term and absence of the Galileon-like interactions. Finally, we discuss some preliminary applications in cosmology.

Dynamical generation of topological masses in Dirac fermions

We report discovery of a topological Mott insulator in strongly-correlated Dirac semimetals. Such an interaction-driven topological state has been theoretically proposed but not yet observed with unbiased large scale numerical simulations. In our model, interactions between electrons are mediated by Ising spins in a transverse field. The results indicate that the topological mass term is dynamically generated and the resulting quantum phase transition belongs to the (2+1)D $N=8$ chiral Ising universality class. These conclusions stem from large scale sign free quantum Monte Carlo simulations.

Spin Gauge Interactions as a Topological Mechanism of Superconductivity

We talk about a low energy, effective, topological theory of superconductivity in which a topological mass term is radiatively induced in one loop effective action. In this field theoretic model, an antisymmetric tensor field couples with the vorticity current of charged Dirac fermions in the Lagrangian. The fermion loop generates a coupling between the gauge field and the antisymmetric tensor field below an ultraviolet cut-off. The spin interactions mediated by the antisymmetric tensor field induces a mass for the photon field indicating Meissner effect. The dual antisymmetric tensor field produces a current which satisfies the relativistic version of the London equations of superconductivity. In the non-relativistic limit, the static effective potential shows a linear, always attractive term between two electrons. Thus, the theory can be considered as an alternative, low energy, effective field theory of superconductivity without spontaneous symmetry breaking.

A 3-form gauge potential in 5D in connection with a possible dark sector of 4D-electrodynamics

We here propose a 5-dimensional {\bf Abelian gauge} model based on the mixing between a $U(1)$ potential and an Abelian 3-form field by means of a topological mass term. An extended covariant derivative is introduced to minimally couple a Dirac field to the $U(1)$ potential, while this same covariant derivative non-minimally couples the 3-form field to the charged fermion. A number of properties are discussed in 5D; in particular, the appearance of a topological fermionic current. A 4-dimensional reduced version of the model is investigated and, { \bf in addition to the $U(1)$ electric- and magnetic-sort of fields,} there emerges an extra set of electric- and magnetic-like fields which contribute a negative pressure and may be identified as a possible fraction of dark energy. The role of the topological fermionic current is also contemplated upon dimensional reduction from 5D to 4D. Other issues we present in 4 space-time dimensions are the emergence {\bf of a pseudo-scalar massive particle,} an extra massive neutral gauge boson,{\bf which we interpret as a kind of paraphoton}, and the calculation of spin- and velocity-dependent interparticle potentials associated to the exchange of the intermediate bosonic fields of the model.

RG flows from (1,0) 6D SCFTs to N = 1 SCFTs in four and three dimensions

We study $AdS_5\times \Sigma_2$ and $AdS_4\times \Sigma_3$ solutions of $N=2$, $SO(4)$ gauged supergravity in seven dimensions with $\Sigma_{2,3}$ being $S^{2,3}$ or $H^{2,3}$. The $SO(4)$ gauged supergravity is obtained from coupling three vector multiplets to the pure $N=2$, $SU(2)$ gauged supergravity. With a topological mass term for the 3-form field, the $SO(4)\sim SU(2)\times SU(2)$ gauged supergravity admits two supersymmetric $AdS_7$ critical points, with $SO(4)$ and $SO(3)$ symmetries, provided that the two $SU(2)$ gauge couplings are different. These vacua correspond to $N=(1,0)$ superconformal field theories (SCFTs) in six dimensions. In the case of $\Sigma_2$, we find a class of $AdS_5\times S^2$ and $AdS_5\times H^2$ solutions preserving eight supercharges and $SO(2)\times SO(2)$ symmetry, but only $AdS_5\times H^2$ solutions exist for $SO(2)$ symmetry. These should correspond to some $N=1$ four-dimensional SCFTs. We also give RG flow solutions from the $N=(1,0)$ SCFTs in six dimensions to these four-dimensional fixed points including a two-step flow from the $SO(4)$ $N=(1,0)$ SCFT to the $SO(3)$ $N=(1,0)$ SCFT that eventually flows to the $N=1$ SCFT in four dimensions. For $AdS_4\times\Sigma_3$, we find a class of $AdS_4\times S^3$ and $AdS_4\times H^3$ solutions with four supercharges, corresponding to $N=1$ SCFTs in three dimensions. When the two $SU(2)$ gauge couplings are equal, only $AdS_4\times H^3$ are possible. The uplifted solutions for equal $SU(2)$ gauge couplings to eleven dimensions are also given.

Yang-Mills as Massive Chern-Simons Theory: A Third Way to Three-Dimensional Gauge Theories

The Yang-Mills (YM) equation in three spacetime dimensions (3D) can be modified to include a novel parity-preserving interaction term, with an inverse mass parameter, in addition to a possible topological mass term. The novelty is that the modified YM equation is not the Euler-Lagrange equation of any gauge-invariant local action for the YM gauge potential alone. Instead, consistency is achieved in the "third way" exploited by 3D minimal massive gravity. We relate our results to the "novel Higgs mechanism" for Chern-Simons gauge theories.

Noncompact gauging of N=2 7D supergravity and AdS/CFT holography

Half-maximal gauged supergravity in seven dimensions coupled to $n$ vector multiplets contains $n+3$ vectors and $3n+1$ scalars parametrized by $\mathbb{R}^+\times SO(3,n)/SO(3)\times SO(n)$ coset manifold. The two-form field in the gravity multiplet can be dualized to a three-form field which admits a topological mass term. Possible non-compact gauge groups take the form of $G_0\times H\subset SO(3,n)$ with a compact group $H$. $G_0$ is one of the five possibilities; $SO(3,1)$, $SL(3,\mathbb{R})$, $SO(2,2)$, $SO(2,1)$ and $SO(2,2)\times SO(2,1)$. We investigate all of these possible non-compact gauge groups and classify their vacua. Unlike the gauged supergravity without a topological mass term, there are new supersymmetric $AdS_7$ vacua in the $SO(3,1)$ and $SL(3,\mathbb{R})$ gaugings. These correspond to new $N=(1,0)$ superconformal field theories (SCFT) in six dimensions. Additionally, we find a class of $AdS_5\times S^2$ and $AdS_5\times H^2$ backgrounds with $SO(2)$ and $SO(2)\times SO(2)$ symmetries. These should correspond to $N=1$ SCFTs in four dimensions obtained from twisted compactifications of six-dimensional field theories on $S^2$ or $H^2$. We also study RG flows from six-dimensional $N=(1,0)$ SCFT to $N=1$ SCFT in four dimensions and RG flows from a four-dimensional $N=1$ SCFT to a six-dimensional SYM in the IR. The former are driven by a vacuum expectation value of a dimension-four operator dual to the supergravity dilaton while the latter are driven by vacuum expectation values of marginal operators.

Alternative Derivation of the Mean-Field Equations for Composite Fermions

The Hamiltonian describing a composite fermion system is usually presented in a phenomenological way. By using a classical nonrelativistic U(1) × U(1) gauge field model for the electromagnetic interaction of electrons, we show how to obtain the mean-field Hamiltonian describing composite fermions in 2 + 1 dimensions. In order to achieve this goal, the Dirac Hamiltonian formalism for constrained systems is used. Furthermore, we compare these results with the ones corresponding to the inclusion of a topological mass term for the electromagnetic field in the Lagrangian.

N =2 SO(4) 7D gauged supergravity with topological mass term from 11 dimensions

We construct a consistent reduction ansatz of eleven-dimensional supergravity to $N=2$ $SO(4)$ seven-dimensional gauged supergravity with topological mass term for the three-form field. The ansatz is obtained from a truncation of the $S^4$ reduction giving rise to the maximal $N=4$ $SO(5)$ gauged supergravity. Therefore, the consistency is guaranteed by the consistency of the $S^4$ reduction. Unlike the gauged supergravity without topological mass having a half-supersymmetric domain wall vacuum, the resulting 7D gauged supergravity theory admits a maximally supersymmetric $AdS_7$ critical point. This corresponds to $N=(1,0)$ superconformal field theory in six dimensions. We also study RG flows from this $N=(1,0)$ SCFT to non-conformal $N=(1,0)$ Super Yang-Mills theories in the seven-dimensional framework and use the reduction ansatz to uplift this RG flow to eleven dimensions.

More on asymptotically anti-de Sitter spaces in topologically massive gravity

Recently, the asymptotic behaviour of three-dimensional anti-de Sitter gravity with a topological mass term was investigated. Boundary conditions were given that were asymptotically invariant under the two-dimensional conformal group and that included a fall-off of the metric sufficiently slow to consistently allow pp-wave type of solutions. Now, pp-waves can have two different chiralities. Above the chiral point and at the chiral point, however, only one chirality can be considered, namely the chirality that has the milder behaviour at infinity. The other chirality blows up faster than AdS and does not define an asymptotically AdS spacetime. By contrast, both chiralities are subdominant with respect to the asymptotic behaviour of AdS spacetime below the chiral point. Nevertheless, the boundary conditions given in the earlier treatment only included one of the two chiralities (which could be either one) at a time. We investigate in this paper whether one can generalize these boundary conditions in order to consider simultaneously both chiralities below the chiral point. We show that this is not possible if one wants to keep the two-dimensional conformal group as asymptotic symmetry group. Hence, the boundary conditions given in the earlier treatment appear to be the best possible ones compatible with conformal symmetry. In the course of our investigations, we provide general formulas controlling the asymptotic charges for all values of the topological mass (not just below the chiral point).

Weak localization properties of the dopedZ2topological insulator

Localization properties of the doped ${Z}_{2}$ topological insulator are studied by weak localization theory. The disordered Kane-Mele model for graphene is taken as a prototype and analyzed with attention to effects of the topological mass term, intervalley scattering, and the Rashba spin-orbit interaction. The known tendency of graphene to antilocalize in the absence of intervalley scattering between $K$ and ${K}^{\ensuremath{'}}$ points is naturally placed as the massless limit of the Kane-Mele model. The latter is shown to have a unitary behavior even in the absence of magnetic field due to the topological mass term. When intervalley scattering is introduced, the topological mass term leaves the system in the unitary class, whereas the ordinary mass term, which appears if A and B sublattices are inequivalent, turns the system to weak localization. The Rashba spin-orbit interaction in the presence of $K\text{\ensuremath{-}}{K}^{\ensuremath{'}}$ scattering drives the system to weak antilocalization in sharp contrast to the ideal graphene case.

Nonlinear electrodynamics in 3D gravity with torsion

We study exact solutions of nonlinear electrodynamics coupled to three-dimensional gravity with torsion. We show that in any static and spherically symmetric configuration, at least one component of the electromagnetic field has to vanish. In the electric sector of the theory, we construct an exact solution, characterized by the azimuthal electric field. When the electromagnetic action is modified by a topological mass term, we find two types of the self-dual solutions.

Self-dual Maxwell field in 3D gravity with torsion

We study the system of a self-dual Maxwell field coupled to 3D gravity with torsion, with the Maxwell field modified by a topological mass term. General structure of the field equations reveals a new, dynamical role of the classical central charges, and gives a simple correspondence between self-dual solutions with torsion and their Riemannian counterparts. We construct two exact self-dual solutions, corresponding to the sectors with a massless and massive Maxwell field, and calculate their conserved charges.

Gauge-invariant factorization and canonical quantization of topologically massive gauge theories in any dimension

Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for a bosonic p-tensor field in any spacetime dimension. These theories include the (2+1)-dimensional Maxwell–Chern–Simons and (3+1)-dimensional Cremmer–Scherk actions as particular cases. Within the Hamiltonian formulation, the embedded topological field theory (TFT) sector related to the topological mass term is not manifest in the original phase space. However, through an appropriate canonical transformation, a gauge-invariant factorization of phase space into two orthogonal sectors is feasible. The first of these sectors includes canonically conjugate gauge-invariant variables with free massive excitations. The second sector, which decouples from the total Hamiltonian, is equivalent to the phase-space description of the associated non-dynamical pure TFT. Within canonical quantization, a likewise factorization of quantum states thus arises for the full spectrum of TMGT in any dimension. This new factorization scheme also enables a definition of the usual projection from TMGT onto topological quantum field theories in a most natural and transparent way. None of these results rely on any gauge-fixing procedure whatsoever.

Noncompact gaugings, chiral reduction and dual sigma models in supergravity

We show that the half-maximal SU(2) gauged supergravity with a topological mass term admits coupling of an arbitrary number of n vector multiplets. The chiral circle reduction of the ungauged theory in the dual 2-form formulation gives N = (1, 0) supergravity in 6D coupled to 3p scalars that parametrize the coset SO(p, 3)/SO(p) × SO(3), a dilaton and (p + 3) axions with p ⩽ n. Demanding that R-symmetry gauging survive in 6D is shown to put severe restrictions on the 7D model, in particular requiring noncompact gaugings. We find that the SO(2, 2) and SO(3, 1) gauged 7D supergravities give a U(1)R, and the SO(2, 1) gauged 7D supergravity gives an Sp(1)R gauged chiral 6D supergravity coupled to certain matter multiplets. In the 6D models obtained, with or without gauging, we show that the scalar fields of the matter sector parametrize the coset SO(p + 1, 4)/SO(p + 1) × SO(4), with the (p + 3) axions corresponding to its Abelian isometries. In the ungauged 6D models, upon dualizing the axions to 4-form potentials, we obtain coupling of p linear multiplets and one special linear multiplet to chiral 6D supergravity.

Topological mass term in effective Brane-World scenario with torsion

In this work we investigate a braneworld scenario where a Kalb-Ramond field propagates, together with gravity, in a five dimensional AdS slice. The rank-2 Kalb-Ramond field is associated with torsion. We study the compactification of the Kalb-Ramond field to four dimensional space-time without gauge fixing, focusing on the effects of torsion. On the brane the Kalb-Ramond field interacts with A?-gauge and scalar matter fields. We analyze the propagators of this theory and as an application investigate the consistency of such a model in the presence of a cosmic string configuration. One interesting feature of this model is the presence of topological charge coming from a topological mass term that couples the gauge field A? with Kalb-Ramond modes.

Gauged locally supersymmetric D=3 nonlinear sigma models

We construct supersymmetric deformations of general, locally supersymmetric, nonlinear sigma models in three spacetime dimensions, by extending the pure supergravity theory with a Chern–Simons term and gauging a subgroup of the sigma model isometries, possibly augmented with R-symmetry transformations. This class of models is shown to include theories with standard Yang–Mills Lagrangians, with optional moment interactions and topological mass terms. The results constitute a general classification of three-dimensional gauged supergravities.

Propagators forp-forms inAdS2p+1and correlation functions in theAdS7/(2,0)CFT correspondence

In ${\mathrm{AdS}}_{2p+1}$ we construct propagators for p-forms whose Lagrangians contain terms of the form $A\ensuremath{\wedge}\mathrm{dA}.$ In particular we explore the case of forms satisfying self-duality in odd dimensions, and the case of forms with a topological mass term. We point out that the ``complete'' set of maximally symmetric bitensors previously used in all the other propagator papers is incomplete---there exists another bitensor which can and does appear in the formulas for the propagators in this particular case. Nevertheless, its presence does not affect the other propagators computed so far. On the ${\mathrm{AdS}}_{7}$ side of the ${\mathrm{AdS}}_{7}/(2,0)$ conformal field theory correspondence we compute the 2 and 3 point functions involving the self-dual tensor of the maximal 7D gauged supergravity (SUGRA), ${S}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}.$ Since the 7 dimensional antisymmetric self-dual tensor obeys first order field equations $(S+*dS=0),$ to get a nonvanishing 2 point function we add a boundary term (to satisfy the variational principle on a manifold with boundary) to the 7D action. The 3 point functions we compute are of the type $\mathrm{SSB}$ and $SBB,$ describing vertex interactions with the gauge fields ${B}_{\ensuremath{\mu}}.$