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 with gauge variant variables defining a pure topological field theory. Combining results obtained within the Lagrangian and Hamiltonian formulations, a new completed structure for a gauge invariant dual factorisation of TMGT is thus achieved.
We analyze the De Donder-Weyl covariant field equations for the topologically massive Yang-Mills theory. These equations are obtained through the Poisson-Gerstenhaber bracket described within the polysymplectic framework. Even though the Lagrangian defining the system of our interest is singular, we show that by appropriately choosing the polymomenta one may obtain an equivalent regular Lagrangian, thus avoiding the standard analysis of constraints. Further, our simple treatment allows us to only consider the privileged $(n-1)$-forms in order to obtain the correct field equations, in oppositio…
We discuss the formulation of cosmological topologically massive (simple) supergravity theory in three-dimensional Riemann-Cartan space-times. We use the language of exterior differential forms and the properties of Majorana spinors on 3-dimensional space-times to explicitly demonstrate the local supersymmetry of the action density involved. Coupled field equations that are complete in both of their bosonic and fermionic sectors are derived by a first order variational principle subject to a torsion-constraint imposed by the method of Lagrange multipliers. We compare these field equations with…
Using the superconformal framework, we construct a new off-shell model for $\cal N=4$ topologically massive supergravity which is minimal in the sense that it makes use of a single compensating vector multiplet and involves no free parameter. As such, it provides a counterexample to the common lore that two compensating multiplets are required within the conformal approach to supergravity with eight supercharges in diverse dimensions. This theory is an off-shell $\cal N=4$ supersymmetric extension of chiral gravity. All of its solutions correspond to non-conformally flat superspaces. Its maxim…
We investigate the unfolded formulation of bosonic Lorentz tensor fields of arbitrary spin in $AdS_3$ containing a parity breaking mass parameter. They include deformations of the linearisations of the Prokushkin--Vasiliev higher spin theory around its critical points. They also provide unfolded formulations of linearized topologically massive higher spin fields including their critical versions. The gauge invariant degrees of freedom are captured by infinite towers of zero forms. We also introduce two inequivalent sets of gauge potentials given by trace constrained Fronsdal fields and trace u…
Within the framework of (2,0) anti-de Sitter (AdS) supersymmetry in three dimensions, we propose a multiplet of higher-spin currents. Making use of this supercurrent, we construct two off-shell gauge formulations for a massless multiplet of half-integer superspin $(s+\frac 12)$, for every integer $s>0$. In the $s=1$ case, one formulation describes the linearised action for (2,0) anti-de Sitter supergravity, while the other gives the type III minimal supergravity action in (2,0) AdS superspace, with both linearised supergravity actions originally derived in arXiv:1109.0496. The constructed mass…
We derive a geometric formulation of the 2d central charge $c_r$ from infinite families of 4d $\mathcal{N}=1$ superconformal field theories topologically twisted on constant curvature Riemann surfaces. They correspond to toric quiver gauge theories and are associated to D3 branes probing five dimensional Sasaki-Einstein geometries in the AdS/CFT correspondence. We show that $c_r$ can be expressed in terms of the areas of the toric diagram describing the moduli space of the 4d theory, both for toric geometries with smooth and singular horizons. We also study the relation between a-maximization …
Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (i) A systematic formulation of topological invariants of Floquet systems based on the cooperation of topology and symmetries. Topological invariants are constructed for the ten symmetry classes in all spatial dimensions, for both homogeneous Floquet systems (Floquet topological insulators and superconductors) and Floquet topological defects. Meanwhile, useful representative Dirac Hamiltonians for all the sy…
We revisit the problem of the bulk-boundary unitarity clash in 2 + 1 dimensional gravity theories, which has been an obstacle in providing a viable dual two-dimensional conformal field theory for bulk gravity in anti-de Sitter (AdS) spacetime. Chiral gravity, which is a particular limit of cosmological topologically massive gravity (TMG), suffers from pertur- bative log-modes with negative energies inducing a non-unitary logarithmic boundary field theory. We show here that any f(R) extension of TMG does not improve the situation. We also study the perturbative modes in the metric formulation o…
