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I describe the conceptual and mathematical basis of an approach which describes gravity as an emergent phenomenon. Combining principle of equivalence and principle of general covariance with known properties of local Rindler horizons,…
We derive the black hole solutions with horizons of non-trivial topology and investigate their properties in the framework of an approach to quantum gravity being an extension of Bohm's formulation of quantum mechanics. The solutions we…
We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in arxiv:1806.03690. The gravitational functional integral…
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…
In the last years higher dimensional physics has won importance. Despite the Superstrings, higher dimensional effects, in measurable scales of energy (some TeV), became only possible with Randall-Sundrum's models (RS). In particular, recent…
We investigate the Becchi-Rouet-Stora-Tyutin (BRST) formalism for gauge theories on spherically symmetric black hole spacetimes, with or without a cosmological constant ($\Lambda\geq0$). This is illustrated through the example of scalar…
Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.
Possible geometric frameworks for a unified theory of gravity and electromagnetism are investigated: General relativity is enlarged by allowing for an arbitrary complex linear connection and by constructing an extended spinor derivative…
In the first part of this paper we investigate the operator aspect of higher-rank supersymmetric model which is introduced as a Lie theoretic extension of the $N=2$ minimal model with the simplest case $su(2)$ corresponding to the $N=2$…
At the classical level, two-dimensional dilaton gravity coupled to an abelian gauge field has charged black hole solutions, which have much in common with four-dimensional Reissner-Nordstrom black holes, including multiple asymptotic…
Starting from the covariant action for $W_3$ gravity, we discuss the BRST quantization of $W_3$ gravity. Taking the chiral gauge the BRST charge has a natural interpretation in terms of the quantum Drinfeld--Sokolov reduction for…
We study the quantization of two versions of unimodular gravity, namely, fully diffeomorphism-invariant unimodular gravity and unimodular gravity with fixed metric determinant utilizing standard path integral approach. We derive the BRST…
In this short review of Doubly Special Relativity I describe first the relations between DSR and (quantum) gravity. Then I show how, in the case of a field theory with curved momentum space, the Hopf algebra of symmetries naturally emerges.…
Semi-classical gravity is an approximation to quantum gravity where gravity is treated classically and matter quantum mechanically. Matter is described by quantum field theory on curved space-time, whereas gravity is described by a…
For the the quintic quasitopological action which has no well-defined variational principle, we introduced a surface term that for a spacetime with flat boundaries make the action well-defined. Moreover, we investigated the numerical…
We present a worldline description of topological non-abelian BF theory in arbitrary space-time dimensions. It is shown that starting with a trivial classical action defined on the worldline, the BRST cohomology has a natural representation…
We survay our recent results on fractional gravity theory. It is also provided the Main Theorem on encoding of geometric data (metrics and connections in gravity and geometric mechanics) into solitonic hierarchies. Our approach is based on…
In an odd-dimensional spacetime, gravity can be formulated as a proper gauge theory based on the Chern-Simons action for a suitable gauge group. Performing dimensional reduction, one obtains, as an effective theory, Chamseddine's…
In topological 1D gravity, the genus zero one-point function combined with the gradient of the action function leads to a spectral curve and its special deformation. After quantization, the partition function is identified as an element in…
We study linearizability and stable linearizability of actions of finite groups on the Segre cubic and Burkhardt quartic, using techniques from group cohomology, birational rigidity, and the Burnside formalism.