Related papers: From Principal Chiral Model to Self-dual Gravity
We show that the Einstein equations in the vacuum are invariant under an $SO(2)$ duality symmetry which rotates the curvature 2-form into its tangent space Hodge dual. Akin to electric-magnetic duality in gauge theory, the duality operation…
The metric-affine variational principle is applied to generate teleparallel and symmetric teleparallel theories of gravity. From the latter is discovered an exceptional class which is consistent with a vanishing affine connection. Based on…
In this paper we discuss the interplay among (~super-~)coordinate, Weyl and \l\ anomaly both in chiral and non-chiral super-gravity represented by $(1,0)$ and $(1,1)$ two-dimensional models. It is shown that for this purpose two…
The gravitational part of the holographic dual to the SYK model has been conjectured to be Jackiw-Teitelboim (JT) gravity. In this paper we construct an AdS2 background in N = (2,2) JT gravity and show that the gravitational dynamics are -…
Following a recent proposal for integrable theories in higher dimensions based on zero curvature, new Lorentz invariant submodels of the principal chiral model in 2+1 dimensions are found. They have infinite local conserved currents, which…
Chiral p-forms are, in fact, present in many supersymmetric and supergravity models in two, six and ten dimensions. In this work, the dual projection procedure, which is essentially equivalent to a canonical transformation, is used to…
We discuss a new interaction for chiral models in four-dimensional ${\cal N}=1$ supergavity. It contains a new arbitrary function in addition to the K\"ahler potential and superpotential. Its features include linearly realized off-shell…
We derive a manifestly duality-symmetric formulation of the action principle for conformal gravity linearized around Minkowski space-time. The analysis is performed in the Hamiltonian formulation, the fourth-order character of the equations…
We build a matrix model of a chiral [SU(N)]^K gauge theory (5D SQCD deconstructed down to 4D) using random unitary matrices to model chiral bifundamental fields (N,N-bar) (without (N-bar,N)). We verify the duality by matching the loop…
We construct a new covariant action for "flat" self-dual gravity in four spacetime dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon…
A model of two--dimensional gravity with an action depending only on a linear connection is considered. This model is a topological one, in the sense that the classical action does not contain a metric or zweibein at all. A metric and an…
For a Hamiltonian $H \in C^2(\mathbb{R}^{N \times n})$ and a map $u:\Omega \subseteq \mathbb{R}^n /!\longrightarrow \mathbb{R}^N$, we consider the supremal functional \[ \label{1} \tag{1} E_\infty (u,\Omega) \ :=\…
Recently the new interest arised (hep-ph/0403139) to the chiral coefficients $L_{11}, L_{12}, L_{13}$ in the low-energy ChPT lagrangian describing the pseudoscalar meson coupling to gravity and/or light singlet dilatons. In 90ties we…
A hodograph transformation for a wide family of multidimensional nonlinear partial differential equations is presented. It is used to derive solutions of the heavenly equation (dispersionless Toda equation) as well as a family of explicit…
In a previous work [arXiv:2009.03428] we proposed a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent $SU(\infty)$…
Starting from a manifestly Lorentz- and diffeomorphism-invariant classical action we perform a perturbative derivation of the gravitational anomalies for chiral bosons in 4n+2 dimensions. The manifest classical invariance is achieved using…
We study the vacuum structures of four-dimensional $\mathcal{N} = 1$ old minimal supergravity with higher derivative corrections. We find that $\mathcal{N} = 1$ supergravity with Riemann curvature square corrections and higher derivative…
A chiral alternative to the vierbein field in general relativity was considered by 't Hooft in an attempt to facilitate the construction of a quantum theory of gravity. These objects $ f^a{}_{\mu\nu}$ behave like the "cube root" of the…
In $D=2+1$ dimensions there are two dual descriptions of parity singlets of helicity $\pm 1$, namely the self-dual model of first-order (in derivatives) and the Maxwell-Chern-Simons theory of second-order. Correspondingly, for helicity $\pm…
We investigate the integrability of the SO(N) principal chiral model on a half-line, and find that mixed Dirichlet/Neumann boundary conditions (as well as pure Dirichlet or Neumann) lead to infinitely many conserved charges classically in…