Day 5
January 20th
Full day: Aula Magna
Chairman: Morning Session (Cristóbal Corral), Afternoon Session (Omar Valdivia)
9:00 - 10:00
Alberto Güijosa
Holographic Rememorization of the Eternal Black Hole and the Membrane Paradigm
Abstract:
In the context of holography, the reduced density matrix associated with a subregion of the boundary theory is believed to be dual to a definite subregion of the bulk, known as the entanglement wedge. A potential objection is that, whereas the reduced density matrix suffices to compute any correlator in the given subregion, the corresponding bulk computation requires information that lies beyond the entanglement wedge. The objection is resolved by noting that the reduced state is only completely determined when the entanglement wedge is supplemented with a specific infrared boundary action, obtained through a variant of Wilsonian renormalization known as holographic rememorization. When applied to an eternal black hole, this method encodes the region behind the stretched horizon in a nonlocal boundary action. At low frequencies this setup makes contact with the standard membrane paradigm.
10:00 - 11:00
Vladimir Juricic
Projected topological branes and lattice defects
Abstract:
Topological states of quantum matter, featuring exotic robust, topologically and symmetry-protected boundary states, are at the forefront of research in the modern condensed matter physics. In the last decade, it has been understood that the crystalline symmetries play a fundamental role in the emergence and the protection of the topological phases, yielding a landscape of topological crystalline materials, with the topological lattice defects, e.g. dislocations, playing an important role in their probing. However, crystals are bound to live in three spatial dimensions, which thereby provides a natural constraint on the possible topological crystalline phases. Motivated by this, I will consider projected topological branes, which are holographic images of higher-dimension topological crystals on lower-dimensional branes, thereby providing the window into the landscape of the topological phase in spaces of dimensionality higher than three. I will discuss some of their general features, such as bulk-boundary correspondence, their probing through the lattice dislocations, and their manifestations in the transport, e.g. of the chiral anomaly. Finally, some of the possible experimental realizations and future directions in the study of projected topological branes will be highlighted.
11:00 - 11:30
Coffee break
11:30 - 12:10
Fernando Izaurieta
Gravitational Waves: A falsification Tool for Riemann-Cartan Gravity Theories?
Abstract:
We develop general mathematical tools to study the propagation of waves on Riemann-Cartan backgrounds in a way as model-independent as possible. Using this, we prove that torsional backgrounds can induce anomalous propagation of amplitude and polarization and assess whether it could allow using gravitational waves as a probe to detect torsion.
12:10 - 12:50
Adolfo Cisterna
The many faces of black holes with conformal hair
Abstract:
In this talk I will start revisiting some of the iconic solutions of Einstein gravity with conformally coupled scalar fields in three and four dimensions. With this scaffolding at hand I will introduce three novel works in which these type of geometries are essential: i) Three dimensional accelerating black holes with conformal hair, ii) Exact four dimensional hairy rotating wormholes and iii) Hawking and Page three dimensional phase transitions in theories with conformal coupling.
12:50 - 13:20
Kristiansen Lara
Geometrization of the Camassa-Holm hierarchy on AdS$_3$ General Relativity
Abstract:
The Camassa-Holm system is an integrable hierarchy that appears in different physical contexts. A usual approach to reveal the latter above is to show that its infinite conserved quantities Poisson commute with each other, namely, they are in involution. In this talk, we will show that this integrable hierarchy is equivalent to the 3D first-order Einstein equation with negative cosmological constant such that the involution of its infinite conserved charges translates to the infinite-dimensional abelian asymptotic symmetries of gravitational charges devoid of central extensions. Moreover, we will show that black hole configurations are attainable.
13:20-15:20
Lunch
15:20 - 16:20
Ricardo Troncoso
Nonlinear automorphism of the conformal algebra in 2D and $\sqrt{T\bar{T}}$ deformations
Abstract:
The conformal algebra in 2D is shown to be preserved under a nonlinear map that mixes both chiral (holomorphic) generators $T$ and $\bar{T}$. It depends on a single real parameter and it can be regarded as a ``nonlinear $SO(1,1)$ automorphism.'' The map preserves the form of the momentum density and naturally induces a flow on the energy density by a marginal $\sqrt{T\bar{T}}$ deformation. In turn, the general solution of the corresponding flow equation of the deformed action can be analytically solved in closed form, recovering the nonlinear automorphism. The deformed CFT_{2} can also be described through the original theory on a field-dependent curved metric whose lapse and shift functions are given by the variation of the deformed Hamiltonian with respect to the energy and momentum densities, respectively. The conformal symmetries of the deformed theories then also arise from diffeomorphisms that fulfill suitably deformed conformal Killing equations. Besides, Cardy formula is shown to map to itseft under the nonlinear automorphism. As a simple example, the deformation of N free bosons is briefly addressed, making contact with recent related results and the dimensional reduction of the ModMax theory. Furthermore, the nonlinear map between the conformal algebra in 2D and its ultra/non-relativistic versions (BMS_{3}\approx≈CCA_{2}\approx≈GCA_{2}), including the corresponding finite $\sqrt{T\bar{T}}$ deformation, are recovered from a limiting case of the nonlinear automorphism. The extension to a three-parameter nonlinear &ISO(1,1)& automorphism of the conformal algebra, and a discrete nonlinear automorphism of BMS_{3} are also briefly discussed.
16:20 - 17:00
Jordan Francois
Bundle geometry on field space for theories with diffeomorphisms symmetry: Applications to gravitational Dirac variables & the covariant presymplectic structure of gravity
Abstract:
We emphasize the elementary bundle geometry of the space of fields, F, supporting the action of diffeomorphisms. We first stress that the Lagrangian of a theory with Diff(M) symmetry is a section of a line bundle, associated to F, of a peculiar type: it is a "twisted bundle" generalising the standard notion of associated vector bundle. Then, we sketch how the so-called "dressing field method" allows to build basic forms on F, which then descend as forms on the orbit space F/Diff(M). Finally, we show that it is a unifying framework for gravitational dressings à la Giddings, relational variables à la Rovelli, and gravitational edge modes à la Donnelly-Freidel-Speranza (& others). In the latter case, it allows to systematically built the "extended" covariant phase space of a Diff(M)-theory. We stress the limits of the approach.
17:00 - 17:30
Mauricio Valenzuela
Constrained Hamiltonian analysis of fermion gauge systems
Abstract:
In this talk we review the canonical analysis of two fermion gauge systems and illustrate how they differ from boson systems in some essential aspects that affect the counting of degrees of freedom. The cases to be considered are: the pseudoclassical system arXiv:2212.02414, and the massless Rarita-Schwinger system (arXiv:2207.03009). Both cases enjoy fermion gauge symmetries, and the first case also enjoys time-reparametrization invariance. We shall see that there the “gauge does not strike twice” owing the failure of the Dirac conjecture—that all first class constraints are gauge generators—and hence some degrees of freedom, which would be typically removed under the assumption of the Dirac-conjecture, survive and therefore propagate. We shall discuss the consequences for supergravity and the so called Unconventional SUSY.