Here we start from a dual version of Vasiliev's first order action for massless spin-2 particles (linearized first order Einstein-Hilbert) and derive, via Kaluza-Klein dimensional reduction from $D+1$ to $D$ dimensions, a set of dual massive spin-2 models. This set includes the massive "BR" model, a spin-2 analogue of the spin-1 Cremmer-Scherk model. In our approach the linearized Riemann curvature emerges from a solution of a functional constraint. In $D=2+1$ the BR model can be written as a linearized version of a new bimetric model for massive gravitons. We also have a new massive spin-2 model, in arbitrary dimensions, invariant under linearized diffeomorphisms. It is given in terms of a non symmetric rank-2 tensor and a mixed symmetry tensor.
Using the superfield formalism and the master action approach, we prove, both at the classical and quantum levels, the dual equivalence between four-dimensional supersymmetric self-dual and topologically massive models coupled to dynamical matter.
Massive dual spin zero fields are reconsidered in four spacetime dimensions. A closed-form Lagrangian is presented that describes a field coupled to the gradient of its own energy-momentum tensor.
We present a first order formulation for the fourth order action of the new massive dual gravity in four dimensions. This proposal is easily generalized to arbitrary dimension. Also, we obtain the dual actions for massless and massive Curtright fields in D dimensions.
In this work, we show that duality symmetry can be implemented for massive theories at the level of the action, whenever we can formulate appropriates gauge invariant actions. For a massive vectorial field, we use a known gauge invariant description, while for a massive graviton, we introduce a novel gauge invariant action in order to show duality invariance.
We study compactifications of string theory and M-theory to six dimensions with background fluxes. The nonzero fluxes lead to additional mass parameters. We derive the S- and T-duality rules for the corresponding (massive) supergravity theories. Specifically, we investigate the massive T-duality between Type IIA superstring theory compactified on K3 with background fluxes and Type IIB superstring theory compactified on K3. Furthermore, we generalise to the massive case the 6D 'string-string' S-duality between M-theory on K3 x S^1 and the Heterotic String on T^4. Whereas in the case of massive …
We show that, with the help of a general BRST symmetry, different theories in 3 dimensions can be connected through a fundamental topological field theory related to the classical limit of the Chern-Simons model.
Gauge field configuration for a magnetic monopole and its dual configuration are studied in SU(2) gauge theory. We present a relation between the monopole field and its dual field. Since these fields can become massive, their massive Lagrangians are derived. In the dual case, an additional term appears. We show this term is necessary to produce a linear potential between a monopole charge and an antimonopole charge.
We show that dualization of Stueckelberg-like massive gauge theories and $B\wedge F$ models, follows form a general p-dualization of interacting theories in d spacetime dimensions. This is achieved by a particular choice of the external current.
We reconsider a massive dual spin 2 field theory in four spacetime dimensions. We obtain the Lagrangian that describes the lowest order coupling of the field to the four-dimensional curl of its own energy-momentum tensor. We then find some static solutions for the dual field produced by other energy-momentum sources and we compare these to similar static solutions for non-dual "finite range" gravity. Finally, through use of a nonlinear field redefinition, we show the theory is the exact dual of the Ogievetsky-Polubarinov model for a massive spin 2 field.
There exists a well-known duality between the Maxwell-Chern-Simons theory and the self-dual massive model in 2+1 dimensions. This dual description has been extended to topologically massive gauge theories (TMGT) in any dimension. This Letter introduces an unconventional approach to the construction of this type of duality through a reparametrisation of the master theory action. The dual action thereby obtained preserves the same gauge symmetry structure as the original theory. Furthermore, the dual action is factorised into a propagating sector of massive gauge invariant variables and a sector…
We extend the duality between massive and topologically massive antisymmetric tensor gauge theories in arbitrary space-time dimensions to include topological defects. We show explicitly that the condensation of these defects leads, in 4 dimensions, to confinement of electric strings in the two dual models. The dual phase, in which magnetic strings are confined is absent. The presence of the confinement phase explicitly found in the 4-dimensional case, is generalized, using duality arguments, to arbitrary space-time dimensions.
A massive version of T-duality in six dimensions is given, that maps the K3 compactification of Romans' theory onto the K3 compactification of Type IIB theory. This is done by performing a (standard) Kaluza-Klein reduction on six-dimensional massive Type IIA and a Scherk-Schwarz reduction on Type IIB, mapping both theories onto the same five-dimensional theory. We also comment shortly on the difficulties arising if one intends to construct a massive generalisation of the six-dimensional string-string duality.
In this paper we investigate dual formulations for massive tensor fields. Usual procedure for construction of such dual formulations based on the use of first order parent Lagrangians in many cases turns out to be ambiguous. We propose to solve such ambiguity by using gauge invariant description of massive fields which works both in Minkowski space as well as (Anti) de Sitter spaces. We illustrate our method by two concrete examples: spin-2 "tetrad" field h_{μa}, the dual field being "Lorentz connection" ω_{μ,ab} and "Riemann" tensor R_{μν,ab} with the dual Σ_{μν,abc}.
In this report we study the dual equivalence between the generalized self-dual (SD) and topologically massive (TM) models. To this end we linearize the model using an auxiliary field and apply a gauge embedding procedure to construct a gauge equivalent model. We clearly show that, under the above conditions, a nonlinear SD model always has a duality equivalent TM action.The general result obtained is then particularized for a number of examples, including the Born-Infeld-Chern-Simons (BICS) model recently discussed in the literature.
We present evidence for the target space duality symmetry associated with massive excited states of closed bosonic string. The evolution of string is considered in ${\hat D}$ spacetime dimensions; out of which d spacial dimensions are compactified on torus. The phase space Hamiltonian formulation is adopted to unveil the T-duality symmetry from the worldsheet perspective. The existence of this symmetry is verified for a few massive levels. A systematic procedure is presented to study T-duality symmetry of vertex operators for all massive levels of closed bosonic string. It is argued that all v…
We have developed dualization of ordinary and ``Stueckelberg compensated'' massive phase for the Kalb-Ramond theory. The compensated phase allows to study the interplay between spin jumping and duality. We show that spin jumping is caused by mass, while gauge symmetry is not necessary for this effect to take place.
We describe brane configurations that interpolate between the N=6 AdS4xCP3 background of Type IIA supergravity and the N=0 AdS4xCP3 background of massive Type IIA supergravity. Using the T-dual Type IIB configurations we prove that this leads to unequal Chern-Simons levels in the dual gauge theory, and find the precise relation between the parameters of the gauge theory and the RR fluxes of the background. This provides further evidence for the conjecture of Gaiotto and Tomasiello about the CFT dual of the massive Type IIA background.
We reduce the Type IIA supergravity theory with a generalized Scherk-Schwarz ansatz that exploits the scaling symmetry of the dilaton, the metric and the NS 2-form field. The resulting theory is a new massive, gauged supergravity theory in four dimensions with a massive 2-form field and a massive 1-form field. We show that this theory is S-dual to a theory with a massive vector field and a massive 2-form field, which are dual to the massive 2-form and 1-form fields in the original theory, respectively. The S-dual theory is shown to arise from a Scherk-Schwarz reduction of the heterotic theory.…
Bosonization of the gauged, massive Thirring model in 2+1-dimensions produces a Maxwell-Chern-Simons gauge theory, coupled to a dynamical, massive vector field. Exploiting the Master Lagrangian formalism, two dual theories are constructed, one of them being a gauge theory. The full two-point functions of both the interacting fields are computed in the path integral quantization scheme. Furthermore, some new dual models, derived from the original master lagrangian and valid for different regimes of coupling parameters, are constructed and analysed in details.
A generalization of duality transformations for arbitrary Lorentz tensors is presented, and a systematic scheme for constructing the dual descriptions is developed. The method, a purely Lagrangian approach, is based on a first order parent Lagrangian, from which the dual partners are generated. In particular, a family of theories which are dual to the massive spin two Fierz-Pauli field, both free and coupled to an external source, is constructed in terms of a third rank tensor which is taken as the basic configuration variable.
A non-abelian ``self-dual'' massive gauge theory describing a massive spin one physical mode is presented. The action is expressed in terms of two independent connections on a principle bundle over $2+1$ space-time. The kinetic terms are respectively a Chern-Simons and a $BF$ lagrangians, while the gauge invariant interaction is expressed in terms of the difference of the two connections. At the linearized level the theory is equivalent to the Topological Massive gauge theory. The covariant, $BRST$ invariant, effective action of the non-abelian sefl dual gauge theory is constructed.
A procedure to obtain higher-derivative free massive actions is proposed. It consists in dimensional reduction of conventional two-derivative massless actions, where solutions to constraints bring in higher derivatives. We apply this procedure to derive the arbitrary dimensional generalizations of (linearized) New Massive Gravity and New Topologically Massive Gravity.
The equations of motion that must be satisfied by fields that constitute realizations of the Poincare group algebra, for integral spin, and mass m, are obtained. For the case of massive spin 2 these equations are satisfied by the selfdual, intermediate and the linear topologically massive models, whose actions are connected by duality transformations. These duality transformations incorporate the gauge invariances that distinguish one action from the other. The relation between their partition functions is briefly discussed.
We study the equivalence between the $B\wedge F$ self-dual ($SD_{B\wedge F}$) and the $B\wedge F$ topologically massive ($TM_{B\wedge F}$) models including the coupling to dynamical, U(1) charged fermionic matter. This is done through an iterative procedure of gauge embedding that produces the dual mapping. In the interactive cases, the minimal coupling adopted for both vector and tensor fields in the self-dual representation is transformed into a non minimal magnetic like coupling in the topologically massive representation but with the currents swapped. It is known that to establish this equ…
We provide a unified treatment of electric-magnetic duality, at the action level and with manifest Lorentz invariance, for massive, massless as well as partially-massless gravitons propagating in maximally symmetric spacetimes of any dimension n>3. For massive and massless fields, we complete previous analyses that use parent-action techniques by giving dual descriptions that enable direct counting of physical degrees of freedom in the flat and massless limit. The same treatment is extended to the partially-massless case, where the duality has been previously discussed in covariant form only a…
Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators analogous to the Wilson Loop and the 't Hooft disorder operators. Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables.
We work out the effective gravitational action for 2D massive Euclidean fermions in a small mass expansion. Besides the leading Liouville action, the order $m^2$ gravitational action contains a piece characteristic of the Mabuchi action, much as for 2D massive scalars, but also several non-local terms involving the Green's functions and Green's functions at coinciding points on the manifold.
Using the manifestly spacetime-supersymmetric version of open superstring field theory, we construct the free action for the first massive states of the open superstring compactified to four dimensions. This action is in N=1 D=4 superspace and describes a massive spin-2 multiplet coupled to two massive scalar multiplets.
Two different massive gauge invariant spin-one theories in $3+1$ dimensions, one Stuckelberg formulation and the other `$B^{\wedge}F$' theory, with Kalb-Ramond field are shown to be related by duality. This is demonstrated by gauging the global symmetry in the model and constraining the corresponding dual field strength to be zero by a Lagrange multiplier, which becomes a field in the dual theory. Implication of this equivalence to the $5$ dimensional theories from which these theories can be obtained is discussed. The self-dual Deser-Jackiw model in $2+1$ dimensions, is also shown to result b…
We study the dual equivalence between the nonlinear generalization of the self-dual ($NSD_{B\wedge F}$) and the topologically massive $B\wedge F$ models with particular emphasis on the nonlinear electrodynamics proposed by Born and Infeld. This is done through a dynamical gauge embedding of the nonlinear self-dual model yielding to a gauge invariant and dynamically equivalent theory. We clearly show that nonpolinomial $NSD_{B\wedge F}$ models can be mapped, through a properly defined duality transformation, into $TM_{B\wedge F}$ actions. The general result obtained is then particularized for a…
We study the construction of covariant nonlinear duality-symmetric actions in dual formulation. Essentially, the construction is the PST-covariantisation and nonlinearisation of Zwanziger action. The covariantisation made use of three auxiliary scalar fields. Apart from these, the construction proceed in a similar way to that of the standard formulation. For example, the theories can be extended to include interactions with external fields, and that the theories possess two local PST symmetries. We then explicitly demonstrate the construction of covariant nonlinear duality-symmetric actions in…
In this work we study various aspects of six-dimensional ${\cal N}=(1,0)$ SCFTs. We consider the construction of their string duals in Massive IIA and discuss some observables in given examples. We study the dynamics of string solitons wrapping and rotating on the Massive IIA background and show that the associated Hamiltonian system is both non-integrable and chaotic, implying the non-integrability of the dual CFT. Our procedure is analytic, using well developed mathematical techniques, and numerical, by the explicit calculation of power spectra, Lyapunov coefficients and Poincaré sections.
We present here a relationship among massive self-dual models for spin-3 particles in $D=2+1$ via the Noether Gauge Embedment $(NGE)$ procedure. Starting with a first order model (in derivatives) $S_{SD(1)}$ we have obtained a sequence of four self-dual models $S_{SD(i)}$ where $i=1,2,3,4$. We demonstrate that the $NGE$ procedure generate the correct action for the auxiliary fields automatically. We obtain the whole action for the $4th$ order self-dual model including all the needed auxiliary fields to get rid of the ghosts of the theory.
We study the duality symmetry in p-form models containing a generalized $B_q\wedge F_{p+1}$ term in spacetime manifolds of arbitrary dimensions. The equivalence between the $B_q\wedge F_{p+1}$ self-dual ($SD_{B\wedge F}$) and the $B_q\wedge F_{p+1}$ topologically massive ($TM_{B\wedge F}$) models is established using a gauge embedding procedure, including the minimal coupling to conserved charged matter current. The minimal coupling adopted for both tensor fields in the self-dual representation is transformed into a non minimal magnetic like coupling in the topologically massive representation…
Using examples of a D=2 chiral scalar and a duality-symmetric formulation of D=4 Maxwell theory we study duality properties of actions for describing chiral bosons. In particular, in the D=4 case, upon performing a duality transform of an auxiliary scalar field, which ensures Lorentz covariance of the action, we arrive at a new covariant duality-symmetric Maxwell action, which contains a two-form potential as an auxiliary field. When the two-form field is gauge fixed this action reduces to a duality-symmetric action for Maxwell theory constructed by Zwanziger. We consider properties of this ne…
SU(2) gauge theory in the nonlinear gauge of the Curci-Ferrari type is studied in low-energy region. We give a classical solution that connects color electric charges. Its dual solution, which has a configuration of monopole, is also presented. Due to the gluon condensation subsequent to the ghost condensation, these classical fields become massive. The massive Lagrangian with the classical solution and that with the dual solution are derived. We show that these Lagrangians produce a linear potential between a quark and an antiquark. This is the mechanism of quark confinement that is different…
In this work, we revisit the duality between a self-dual non-gauge invariant theory and a topological massive theory in $3+1$ dimensions. The self-dual Lagrangian is composed by a vector field and an antisymmetric field tensor whereas the topological massive Lagrangian is build using a $B \wedge F$ term. Though the Lagrangians are quite different, they yield to equations of motion that are connected by a simple dual mapping among the fields. We discuss this duality by analyzing the degrees of freedom in both theories and comparing their propagating modes at the classical level. Moreover, we em…
We quantize the self-dual massive theory by using the Batalin-Tyutin Hamiltonian method, which systematically embeds second class constraint system into first class one in the extended phase space by introducing the new fields. Through this analysis we obtain simultaneously the Stückelberg scalar term related to the explicit gauge-breaking effect and the new type of Wess-Zumino action related to the Chern-Simons term.
We find explicit AdS4 solutions of massive type IIA with N=2 supersymmetry obtained deforming with a Roman mass the type IIA supersymmetric reduction of the M theory background AdS4 times M111. The family of solutions have SU(3) times SU(3) structure and isometry SU(3) times U(1)^2. They are conjectured to be dual to three-dimensional N=2 Chern-Simons theories with generic Chern-Simons couplings and gauge group ranks.
We give N=1 supersymmetric extension of D=4 dual gravity non-linear action proposed in arXiv:0806.2775. The dual supergravity action and symmetries of the model, but supersymmetry, are realized in a local way.
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…
Unfolded equations of motion for symmetric massive bosonic fields of any spin in Minkowski and (A)dS spaces are presented. Manifestly gauge invariant action for a spin $s \ge 2$ massive field in any dimension is constructed in terms of gauge invariant curvatures.
In continuation of our earlier proposal for evaluating thermal effective actions, we determine the exact fermion propagator in 1+1 dimensional massive QED. This propagator is used to derive the finite temperature effective action of the theory which generates systematically all the one loop Feynman amplitudes calculated in thermal perturbation theory. Various aspects of the effective action including its imaginary part are discussed.
It has been argued by some authors that the parent action approach cannot be used in order to establish the duality between the 2+1 Abelian and non-Abelian Self-Dual (SD) and Yang-Mills-Chern-Simons (YMCS) models for all the coupling regimes. We propose here an alternative (perturbative) point of view, and show that this equivalence can be achieved with the parent action approach.
In this paper we discuss an infinite family of new solutions in massive Type IIA supergravity with AdS$_3\times$S$^2$ factors, preserving ${\cal N}=(0,4)$ SUSY. After studying geometrical aspects of the backgrounds we propose a duality with a precise family of quivers that flow to (0,4) fixed points at low energies. These quivers consist on two families of (4,4) linear quivers coupled by matter fields. We present various tests of our proposal.
The T-duality symmetries of a family of two-dimensional massive integrable field theories defined in terms of asymmetric gauged Wess-Zumino-Novikov-Witten actions modified by a potential are investigated. These theories are examples of massive non-linear sigma models and, in general, T-duality relates two different dual sigma models perturbed by the same potential. When the unperturbed theory is self-dual, the duality transformation relates two perturbations of the same sigma model involving different potentials. Examples of this type are provided by the Homogeneous sine-Gordon theories, assoc…
The duality symmetries of various chiral boson actions are investigated using D=2 and D=6 space-time dimensions as examples. These actions involve the Siegel, Floreanini-Jackiw, Srivastava and Pasti-Sorokin-Tonin formulations. We discover that the Siegel, Floreanini-Jackiw and Pasti-Sorokin-Tonin actions have self-duality with respect to a common anti-dualization of chiral boson fields in D=2 and D=6 dimensions, respectively, while the Srivastava action is self-dual with respect to a generalized dualization of chiral boson fields. Moreover, the action of the Floreanini-Jackiw chiral bosons int…
The question of graviton cloning in the context of the bulk/boundary correspondence is considered. It is shown that multi-graviton theories can be obtained from products of large-N CFTs. No more than one interacting massless graviton is possible. There can be however, many interacting massive gravitons. This is achieved by coupling CFTs via multi-trace marginal or relevant perturbations. The geometrical structure of the gravitational duals of such theories is that of product manifolds with their boundaries identified. The calculational formalism is described and the interpretation of such theo…
The Maldacena Nastase solution is generalised to include massive fundamental matter through the addition of a flavour profile. This gives a holographic dual to N=1 SYM-CS with massive fundamental matter with a singularity free IR. We study this solution in some detail confirming confinement and asymptotic freedom. A recently proposed solution generating technique is then applied which results in a new type-IIA supergravity solution. In a certain limit the geometry of this solution is asymptotically AdS_4X Y, where Y is the metric at the base of the Bryant-Salamon G_2 cone, which has topology S…
We show that non-chiral $N=2$ supergravity in ten-dimensions admits a family of dual actions where the one-form, two-form or three-form is replaced by the seven-form, six-form or five-form respectively. The dual actions and supersymmetry transformations are given.
We focus on the massive Thirring model in 1+1 dimensions at finite temperature and non-zero chemical potential, and comment on some parallels between this model and QCD. In QCD, calculations of physical quantities such as transport coefficients are extremely difficult. In the massive Thirring model, similar calculations are greatly simplified by exploiting the duality which exists with the sine-Gordon model and its relation, at high temperature, to the exactly solvable classical Coulomb gas on the line.
We consider a broad class of massive four dimensional effective theories describing an infinite tower of charged massive spin 1 states, interacting with massless spin 1 and spin 0. The spectrum is chosen to be the same as that appears in the Kaluza-Klein theory reduction of 5d Yang-Mills to ensure the absence of any spurious poles in a possible double copy formulation. The effective theories are characterized by multiple different couplings between different fields which are unconstrained by symmetries and low energy criteria. Remarkably, by demanding that the scattering amplitudes preserve co…
Different aspects of the self-dual (anti-self-dual) action of the Ashtekar canonical formalism are discussed. In particular, we study the equivalences and differences between the various versions of such an action. Our analysis may be useful for the development of an Ashtekar formalism in eight dimensions.
Using the parent Lagrangian method together with a dimensional reduction from $D$ to $(D-1)$ dimensions we construct dual theories for massive spin two fields in arbitrary dimensions in terms of a mixed symmetry tensor $T_{A[A_{1}A_{2}... A_{D-2}]}$. Our starting point is the well studied massless parent action in dimension $D$. The resulting massive Stueckelberg-like parent actions in $(D-1)$ dimensions inherits all the gauge symmetries of the original massless action and can be gauge fixed in two alternative ways, yielding the possibility of having either a parent action with a symmetric or …
We provide a simple derivation of the extremal values of the superpotential in massive vacua of N=1* SYM, making use of the required modular weight for the central charge of BPS walls interpolating between these vacua. This modular weight descends from the action of S-duality on the N=4 superalgebra which in turn is inherited from its classical action on the dyon spectrum. We show that this kinematic information, combined with minimal knowledge of the weak coupling asymptotics, is sufficient to determine the exact vacuum superpotentials in terms of Eisenstein series.
We study issues of duality and dual equivalence in non-commutative manifolds. In particular the question of dual equivalence for the actions of the non-commutative extensions of the self-dual model (NC-SD) in 3D space-time and the Maxwell-Chern-Simons model (MCS-SD) is investigate. We show that former model {\it is not} dual equivalent the non-commutative extension of the Maxwell-Chern-Simons model, as widely believed, but a to deformed version of it that is disclosed here. Our results are not restrict to any finite order in the Seiberg-Witten expansion involving the non-commutative parameter …
We construct a dual formulation, with respect to the conventional PST formalism, of the M5-brane action propagating in a generic 11d supergravity background. Constraint analysis is performed to further justify that our theory has the correct number of degrees of freedom. Comparison of this action with the existing M5-brane actions is carried out. We also show that a conventional D4-brane action is obtained upon double dimensional reduction.
