In $d$ dimensions, the model for a massless $p$-form in curved space is known to be a reducible gauge theory for $p>1$, and therefore its covariant quantisation cannot be carried out using the standard Faddeev-Popov scheme. However, adding a mass term and also introducing a Stueckelberg reformulation of the resulting $p$-form model, one ends up with an irreducible gauge theory which can be quantised à la Faddeev and Popov. We derive a compact expression for the massive $p$-form effective action, $Γ^{(m)}_p$, in terms of the functional determinants of Hodge-de Rham operators. We then show that the effective actions $Γ^{(m)}_p$ and $Γ^{(m)}_{d-p-1}$ differ by a topological invariant. This is a generalisation of the known result in the massless case that the effective actions $Γ_p$ and $Γ_{d-p-2}$ coincide modulo a topological term. Finally, our analysis is extended to the case of massive super $p$-forms coupled to background ${\cal N}=1$ supergravity in four dimensions. Specifically, we study the quantum dynamics of the following massive super $p$-forms: (i) vector multiplet; (ii) tensor multiplet; and (iii) three-form multiplet. It is demonstrated that the effective actions of the massive vector and tensor multiplets coincide. The effective action of the massive three-form is shown to be a sum of those corresponding to two massive scalar multiplets, modulo a topological term.
Partially massless theory in three dimensions is revisited and its relationship with the self-dual massive gravity is considered. The only mode of the partially massless theory is shown explicitly through an action for a scalar field on (A)dS background. This fact can be generalized to higher dimensions. This degree of freedom is altered when a triadic Chern-Simons is introduced, giving rise to the self-dual massive gravity on (A)dS background. We present another physical system with partially massless symmetry and its connection with topologically massive gravity is discussed.
On the holographic complexity dual to the bulk action, we investigate the action growth for a shock wave geometry in a massive gravity theory within the Wheeler-De Witt (WDW) patch at the late time limit. For a global shock wave, the graviton mass does not affect the action growth in the bulk, i.e. the complexity on the boundary, showing that the action growth (complexity) is the same for both the Einstein gravity and the massive gravity. Nevertheless, for a local shock wave that depends on transverse coordinates, the action growth (complexity) is proportional to the butterfly velocity for the…
We study correlation functions of scalar operators on the boundary of the $AdS_3$ space deformed by moving massive particles in the context of the AdS/CFT duality. To calculate two-point correlation functions we use the geodesic approximation and the renormalized image method. We compare results of the renormalized image method with direct calculations using tracing of winding geodesics around the cone singularities, and show on examples that they are equivalent. We demonstrate that in the geodesic approximation the correlators exhibit a zone structure. This structure substantially depends on …
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.
In the holographic picture, the Brout-Englert-Higgs (BEH) mechanism in d-dimensional Yang-Mills theories is conjectured to provide a Higgs-like mechanism for gravity in d+1 dimensions, resulting in massive (or massless) gravitons in IR (or UV) completions. Accordingly, one could imagine dual (magnetic-type) fields of massive gravitons in the IR (low-energy) limit that are coupled to the curl of their own energy-momentum, as well as to the rotation of matter fields on large scales. This hypothesis, which might solve cosmological issues currently ascribed to dark matter and dark energy, needs to…
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.
我们研究了具有背景通量的弦论和M理论到六维的紧化。非零通量导致额外的质量参数。我们推导出相应的（大质量）超引力理论的S-和T-对偶规则。具体地说，我们研究了在K3上紧化的IIA型超弦理论和在K3上紧化的IIB型超弦理论之间的大量T-对偶。此外，我们将K3 x S^1上的M理论与T^4上的杂化弦之间的6D“弦-弦”S对偶性推广到大质量情形。而在有质量的T-对偶的情况下，质量参数是在U-对偶群O（4，20）的基本表示中，我们发现在有质量的S-对偶的情况下，它们是在3-指标反对称表示中。在后一种情况下，所涉及的质量参数扩展了Kaloper和Myers的参数。我们应用我们的对偶规则的质量膜解决方案，如域壁解决方案对应的质量参数，并找到新的质量膜解决方案。最后，我们讨论了高维解释的对偶和膜解决方案。
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 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.
In this paper we discuss correlation function computations in massive topological Landau-Ginzburg orbifolds, extending old results of Vafa. We then apply these computations to provide further tests of the nonabelian mirrors proposal and two-dimensional Hori-Seiberg dualities with $(S)O_{\pm}$ gauge groups and their mirrors.
In this work, we investigate the quasinormal modes for a massive scalar field with a nonminimal coupling with gravity in the spacetime of a loop quantum black hole, known as the Self-Dual Black Hole. In this way, we have calculated the characteristic frequencies using the 3rd order WKB approach, where we can verify a strong dependence with the mass of scalar field, the parameter of nonminimal coupling with gravity, and parameters of the Loop Quantum Gravity. From our results, we can check that the Self-Dual Black Hole is stable under the scalar perturbations when assuming small values for the …
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…
We calculate the Kaluza-Klein spectrum of spin-2 fluctuations around the ${\cal N}=3$ warped ${\rm AdS}_4\times M_6$ solution in massive IIA supergravity. This solution was conjectured to be dual to the $D=3$ ${\cal N}=3$ superconformal ${\rm SU}(N)$ Chern-Simons matter theory with level $k$ and 2 adjoint chiral multiplets. The ${\rm SO}(3)_R\times{\rm SO}(3)_D$ isometry of the ${\cal N}=3$ solution is identified with the ${\rm SU}(2)_F\times {\rm SU}(2)_{\cal R}$ global symmetry of the dual ${\cal N}=3$ SCFT. We show that the ${\rm SO}(3)_R\times{\rm SO}(3)_D$ quantum numbers and the ${\rm Ad…
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 mo…
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.
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 consider massive dual pairs of p-forms and (D-p-1)-forms described by non-linear Lagrangians, where non-linear curvature terms in one theory translate into non-linear mass-like terms in the dual theory. In particular, for D=2p and p even the two non-linear structures coincide when the non-linear massless theory is self-dual. This state of affairs finds a natural realization in the four-dimensional massive N=1 supersymmetric Born-Infeld action, which describes either a massive vector multiplet or a massive linear (tensor) multiplet with a Born-Infeld mass-like term. These systems should play…
We investigate the tendency in variations of the dual CFT$_2$ when a rotating AdS$_3$ black hole changes by fluxes transferred by the scattering of a massive scalar field according to the AdS/CFT correspondence. The conserved quantities of the black hole are definitely constrained by the extremal condition. Moreover, the laws of thermodynamics provide a direction for the changes in the conserved quantities, so the black hole cannot be extremal under the scattering. This is naturally preferred. By the relationship between the rotating AdS$_3$ black hole and dual CFT$_2$, we find that such chang…
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.
We describe a field theory for "massive dual gravity" in N spacetime dimensions. We obtain a Lagrangian that gives the lowest order coupling of the field to the N-dimensional curl of its own energy-momentum tensor. We then briefly discuss classical solutions. Finally, we show the theory is the exact dual of the Ogievetsky-Polubarinov model generalized to any N.
