Day 3

Marc Henneaux

The logarithmic BMS_{4} algebra

Abstract:

The BMS_{4} algebra is extended by adding logarithmic

supertranslations. This enables one to redefine the generators of the BMS_{4} algebra in such a way that the pure supertranslations and the logarithmic supertranslations commute with all the Poincaré generators, and, in particular, transform in the trivial representation of the Lorentz group. This provides a supertranslation-invariant definition of the Lorentz charges. The same construction applies to the Maxwell theory and yields Poincaré-invariant angle-dependent U(1) gauge transformations.

Hernán González

Hamiltonian description of gauge theories in the light front

Abstract:

We discuss the emergence of a new kind of a symmetry generator in the Hamiltonian realization of four-dimensional gauge theories in the flat space foliated by retarded or advanced time. It generates an asymptotic symmetry that acts on the asymptotic fields in a way different from the standard large gauge transformations. The improved canonical generators, corresponding to both gauge generators and the new asymptotic ones, form a Kac-Moody algebra with a non-trivial central extension. We work out in detail the cases of electromagnetism and Yang-Mills theory.

Alfredo Pérez

Magnetic Carrollian gravity from the Carroll algebra

Abstract:

In this talk, I explicitly establish the equivalence between the magnetic Carrollian limit of Einstein gravity defined through the Hamiltonian formalism and the Carrollian theory of gravity defined through a gauging of the Carroll algebra along the lines of standard Poincaré (or (A)dS) gaugings.

Marc Geiller

The partial Bondi gauge

Abstract:

I will review the recent construction of an extended solution space for gravity, based on a so-called partial Bondi gauge fixing. This aims at investigating the possible relaxations of the boundary conditions, in order to include for example a cosmological constant, a polyhomogeneous expansion, and an arbitrary time-dependent boundary metric. I will also explain how to properly map these results to the Newman-Penrose formalism. Finally, I will discuss the application to three-dimensional gravity, where a new asymptotic symmetry can be revealed after working out all the subtleties of the covariant phase space formalism.

Marcela Cárdenas

Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields

Abstract:

Einstein gravity minimally coupled to a scalar field with a two-parameter Higgs-like self-interaction in 3D is recast in terms of a Chern-Simons form for the algebra g+ ⊕ g− where, depending on the sign of the self-interaction couplings, g± can be so(2,2), so(3,1) or iso(2,1). The field equations can then be expressed through the field strength of non- flat composite gauge fields, and conserved charges are readily obtained from boundary terms in the action that agree with those of standard Chern-Simons theory, but for pure gravity (non-flat) connections. Regularity of the fields then amounts to requiring the holonomy of the connections along contractible cycles to be trivial. These conditions are automatically fulfilled for the scalar soliton and allow to recover the Hawking temperature and chemical potential in the case of the rotating hairy black holes presented here, whose entropy can also be obtained by the same formula that holds in the case of a pure Chern-Simons theory. In the conformal (Jordan) frame the theory is described by General Relativity with cosmological constant conformally coupled to a self-interacting scalar field, and its formulation in terms of a Chern-Simons form for suitably composite gauge fields is also briefly addressed.

Eloy Ayón-Beato

On the electrodynamics of the first nonlinearly charged spinning black hole

Abstract:

After many years of efforts, the first nonlinearly charged rotating black hole has been finally reported by Garcia. This is an important result that was pending in General Relativity, since nonlinear generalizations of the Kerr-Newman solution were not yet known. Unfortunately, the Lagrangian supporting this configuration cannot be expressible in terms of the standard invariants using elementary functions. In the present talk we show how to circumvent this problem by using the formulations of nonlinear electrodynamics in terms of mixed electromagnetic eigenvalues, introduced by Salazar, Garcia and Plebanski almost four decades ago. In doing so, we prove that the underlying theory becomes fully determined, and hence the new found nonlinearly charged stationary axisymmetric spacetimes correspond to exact solutions of a well-defined self-gravitating nonlinear electrodynamics whose fundamental structural functions are explicitly provided.

Alberto Faraggi

Interpolating Boundary Conditions on $AdS_2$ and Supersymmetric Wilson Loops

Abstract:

We consider two instances of boundary conditions for massless scalars on $AdS_2$ that interpolate between the Dirichlet and Neumann cases while preserving scale invariance. Assessing invariance under the full $SL(2;\mathds{R})$ conformal group is not immediate given their non-local nature. To further clarify this issue, we compute holographically 2- and 4-point correlation functions using the aforementioned boundary conditions and study their transformation properties. Concretely, motivated by the dual description of some multi-parametric families of Wilson loops in ABJM theory, we look at the excitations of an open string around an $AdS_2\subset AdS_4\times\mathbb{CP}^3$ worldsheet, thus obtaining correlators of operators inserted along a $1$-dimensional defect in ${\cal N}=6$ super Chern-Simons-matter theory at strong coupling. Of the two types of boundary conditions analyzed, only one leads to the expected functional structure for conformal primaries; the other exhibits covariance under translations and rescalings but not under special conformal transformations.

Danilo Díaz

Casimir/Cardy regimes for GJMS operators on the torus: role of the multiplicative anomaly

Abstract:

We compute the multiplicative anomaly for higher-derivatives operators (GJMS) on the torus and explore the consequence for the low/high temperature regimes. In particular, we recover the "ubiquitous" central charge "c". We then comment on extensions to higher dimensions (four) and the possible role of the multiplicative anomaly in the resolutions of some notorious discrepancies in computations of entanglement entropy and Casimir energies.

Beer&Pizza Poster Session

F. Tello, O. Labrín, A. Chakraborti, A. Varas Zamora, N. Cáceres, F. Sulantay, M. Busnego, C. Vera, M. Oyarzo, M. Yañez, F. Colipi, G. Barriga, P. Cabrera, C. Ramirez

*Location: Human Sciences Faculty, 2nd floor.