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We study the cosmology of a quadratic metric-compatible torsionful gravity theory in the presence of a perfect hyperfluid. The gravitational action is an extension of the Einstein-Cartan theory given by the usual Einstein-Hilbert…
The Cumulative Drag Index defined recently by Prasanna has been generalised to include the centrifugal acceleration. We have studied the behaviour of the drag index for the Kerr metric and the Neugebauer-Meinel metric representing a…
The recent developments towards the possible non-perturbative formulation of string/M theory using supersymmetric Yang-Mills matrix models (SYMs) are discussed. In the first part, we give a critical review on the status of our present…
We present a new set of boundary conditions for General Relativity on AdS$_3$, where the dynamics of the boundary degrees of freedom are described by two independent left and right members of the Gardner hierarchy of integrable equations,…
We consider integrable systems that are connected with orthogonal separation of variables in complex Riemannian spaces of constant curvature. An isomorphism with the hyperbolic Gaudin magnet, previously pointed out by one of us, extends to…
The gravitational Gauss law requires any addition of energy to be accompanied by the addition of gravitational flux. The possible configurations of this flux for a given source may be called gravitational hair, and several recent works…
We analyse weighted Motzkin paths with step multiplicities that vary linearly with height. In the balanced case the associated exponential generating function satisfies a Pearson-type PDE, and solving by characteristics yields closed…
We study the geodesic equation for the Dirichlet (gradient) metric in the space of Kaehler potentials. We first solve the initial value problem for the geodesic equation of the combination metric, including the gradient metric. We then…
Starting from the framework defined by Matveev and Shevchishin we derive the local and the global structure for the four types of super-integrable Koenigs metrics. These dynamical systems are always defined on non-compact manifolds, namely…
We invoke probe brane arguments to classify the asymptotic behavior of general five-dimensional supergravity theories with eight supercharges near infinite distance boundaries of the vector multiplet moduli space. Imposing consistency of…
The path integral for higher-derivative quantum gravity with torsion is considered. Applying the methods of two-dimensional quantum gravity, this path integral is analyzed in the limit of conformally self-dual metrics. A scaling law for…
In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the…
We conjecture that $W$ gravity can be interpreted as the gauge theory of $\phi$ diffeomorphisms in the space of dimensionally-reduced $D=2+2$ $SU^*(\infty)$ Yang-Mills instantons. These $\phi$ diffeomorphisms preserve a volume-three form…
We introduce a new set of boundary conditions for three-dimensional higher spin gravity with gauge group $SL(3,\mathbb{R})\times SL(3,\mathbb{R})$, where its dynamics at the boundary is described by the members of the modified Boussinesq…
We study boundary conditions for 3-dimensional higher spin gravity that admit asymptotic symmetry algebras expected of 2-dimensional induced higher spin theories in the light cone gauge. For the higher spin theory based on sl(3, R) plus…
It is shown that the large $N$ limit of SU(N) YM in $curved$ $m$-dim backgrounds can be subsumed by a higher $m+n$ dimensional gravitational theory which can be identified to an $m$-dim generally invariant gauge theory of diffs $N$, where…
We examine some properties of the filled Wilson loop observables in the Kazakov-Migdal model of induced QCD. We show that they have a natural interpretation in a modification of the original model in which the $Z_N$ gauge symmetry is broken…
There exists a widely spread notion that gravitational effects can strongly violate global symmetries. It may lead to many important consequences. We will argue, in particular, that nonperturbative gravitational effects in the axion theory…
In this note we construct asymptotically Lifshitz spacetimes in the Chern-Simons formulation of three dimensional higher spin gravity and relate the resulting theories to integrable systems which are elements of the KdV hierarchy.
When a globally supersymmetric theory is scale invariant, it must possess a Virial supercurrent supermultiplet. The multiplet structure is analogous to the R-current supermultiplet in globally R-symmetric theories but we put extra "$i$"s in…