Related papers: The Conformal Mode in 2D Simplicial Gravity
The metric of two-dimensional quantum gravity interacting with conformal matter is believed to collapse to a branched polymer metric when the central charge c>1. We show analytically that the spectral dimension of such a branched polymer…
We provide Vasiliev's four-dimensional bosonic higher-spin gravities with six families of exact solutions admitting two commuting Killing vectors. Each family contains a subset of generalized Petrov Type-D solutions in which one of the two…
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel,…
For scalar field theory, a new generalization of the Exact RG to curved space is proposed, in which the conformal anomaly is explicitly present. Vacuum terms require regularization beyond that present in the canonical formulation of the…
In this habilitation thesis we provide an introduction to gravitational models in two spacetime dimensions. Focus is put on exactly solvable models. We begin by introducing and motivating different possible gravitational actions, including…
We provide a new derivation of the Hawking mass and Willmore energy functionals for asymptotically AdS spacetimes, by embedding Einstein-AdS gravity in Conformal Gravity. By construction, the evaluation of the four-dimensional Conformal…
We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on right-movers. The local symmetries include one copy of the Virasoro algebra and a U(1) current algebra. This differs from the 2d…
We show that the Ashtekar-Magnon-Das (AMD) mass and other conserved quantities are equivalent to the Kounterterm charges in the asymptotically AdS spacetimes that satisfy the Einstein equations, if we assume the same asymptotic fall-off…
Recent advancements in 3D Gaussian Splatting (3DGS) have greatly influenced neural fields, as it enables high-fidelity rendering with impressive visual quality. However, 3DGS has difficulty accurately representing surfaces. In contrast,…
The BRST cohomology group in the space of local functionals of the fields for the two-dimensional conformally invariant gravity is calculated. All classical local actions (ghost number equal to zero) and all candidate anomalies are given…
We investigate several quantum phenomena related to quadratic gravity after rewriting the general fourth-order action in a more convenient form that is second-order in derivatives and produces only first-class constraints in phase space. We…
An infinite number of topological conformal algebras with varying central charges are explicitly shown to be present in $2d$ gravity (treated both in the conformal gauge and in the light-cone gauge) coupled to minimal matter. The central…
We present a "Chern-Simons-like" action for the "general massive gravity" model propagating two spin-2 modes with independent masses in three spacetime dimensions (3D), and we use it to find a simple Hamiltonian form of this model. The…
Theories with generalised conformal structure contain a dimensionful parameter, which appears as an overall multiplicative factor in the action. Examples of such theories are gauge theories coupled to massless scalars and fermions with…
We show that the spectral dimension d_s of two-dimensional quantum gravity coupled to Gaussian fields is two for all values of the central charge c <= 1. The same arguments provide a simple proof of the known result d_s= 4/3 for branched…
The determinant method in the conformal bootstrap is applied for the critical phenomena of a single polymer in arbitrary $D$ dimensions. The scale dimensions (critical exponents) of the polymer ($2< D \le 4$) and the branched polymer ($3 <…
Symmetries and anomalies of a $d$-dimensional quantum field theory are often encoded in a $(d+1)$-dimensional topological action, called symmetry topological field theory (TFT). We derive the symmetry TFT for the 2-form and 1-form…
We deduce the appearance of a polymeric phase in 4-dimensional simplicial quantum gravity by varying the values of the coupling constants and discuss the geometric structure of the phase in terms of ergodic moves. A similar result is true…
Let $M$ be a smooth projective variety and $\mathbf{D}$ an ample normal crossings divisor. From topological data associated to the pair $(M, \mathbf{D})$, we construct, under assumptions on Gromov-Witten invariants, a series of…
Stochastic partial differential equations can be used to model second order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and…