arXiv subjects

Hernán A. González

Publications and source records attributed to Hernán A. González.

18 recordsLinked to original sources

arXiv2026

Scalar subleading soft theorems from an infinite tower of charges

We investigate conservation laws in the absence of gauge invariance by analyzing interacting scalar theories with a massless scalar field. We construct an infinite tower of charges that arise from the subleading equations of motion at null infinity and are built from specific combinations of asymptotic field coefficients. Interestingly, these expressions are finite from the outset, requiring no holographic renormalization. By carefully analyzing the dynamics at spatial infinity, we show that this tower of surface integrals commutes with the S-matrix of the interacting model at tree level. As an application, we demonstrate that the conservation of these charges leads to an infinite set of subleading soft relations, valid at tree level in a cubic interaction with massive scalar fields.

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arXiv2025

Matching conditions at null infinity in the presence of logarithms: the role of advanced and retarded radiation

We provide a new perspective on the general matching conditions between the future of past null infinity and the past of future null infinity, emphasizing the impact of dominant logarithmic terms in the asymptotic expansion of the fields near null infinity. We explicitly consider the cases of a massless scalar field and of electromagnetism. Key in our derivation is the identification of the physical origin of these logarithms, which are associated with advanced and retarded radiation saturating the finite energy flux condition at null infinity (in a space of functions which is made precise). The matching conditions arise then from the requirement of Coulombic (i.e., $1/r$) behaviour at spatial infinity.

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arXiv2025

Energy Detectors and Asymptotic Symmetries

We study detector operators measuring energy to a power $Δ-2$ at null infinity in four-dimensional gauge theories and gravity. These operators transform as conformal primaries on the celestial sphere and provide a natural basis for describing energy-flux observables in scattering processes. Using the collinear factorization of scattering amplitudes, we derive the universal leading structure of the operator product expansion. A key consequence of our analysis is the precise identification of the $Δ=2$ detector, the number operator. Exploiting the fact that soft charges generate symmetries of the S-matrix, we demonstrate that the number of particles is entirely determined by the product of two soft currents: in gravity, the operator is the square of the supertranslation generator, while in Yang-Mills yields a product of $SU(N)$ Kac-Moody soft currents. This work establishes thus a direct link between detector observables and the soft sector of celestial holography.

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arXiv2024

Asymptotic structure of scalar-Maxwell theory at the null boundary

We apply the Hamiltonian formalism to investigate the massless sector of scalar field theory coupled with Maxwell electrodynamics through the Pontryagin term. Specifically, we analyze asymptotic symmetries at the null infinity of this theory, conserved charges, and their algebra. We find that the theory possesses asymptotic shift symmetries of the fields not present in the bulk manifold coming from the zero modes of the symplectic matrix of constraints. Consequently, we conclude that the real scalar field also contains asymptotic symmetries previously found in the literature by a different approach. We show that these symmetries are the origin of the electric-magnetic duality in electromagnetism with the topological Pontryagin term, and obtain non-trivial central extension between the electric and magnetic conserved charges. Finally, we examine the full interacting theory and find that, due to the interaction, the symmetry generators are more difficult to identify among the constraints, such that we obtain them in the weak-coupling limit. We find that the asymptotic structure of the theory simplifies due to a fast fall-off of the scalar field, leading to decoupled scalar and Maxwell asymptotic sectors, and losing the electric-magnetic duality.

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arXiv2024

Chiral shift symmetries as an infinite tower of subleading super-shift symmetries

Chiral shift symmetries of the massless free bosons in two dimensions are global symmetries that are somewhat similar to asymptotic symmetries. They are most transparent in double-null coordinates where they are parametrized by two functions of one variable. In BMS-type coordinates, half of them appear as an infinite tower of sub-leading super-shift symmetries.

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arXiv2024

New boundary conditions in Einstein-scalar gravity in three dimensions

We analyze the backreaction of a class of scalar field self-interactions with the possibility of evolving from an AdS vacuum to a fixed point where the scalar field potential vanishes. Exact solutions which interpolate between these regions, ranging from stationary black hole to dynamical spacetimes are constructed. Their surface charges are finite but non-integrable. We study the properties of these charges on the solutions. In particular, we show that the integrable part of the charges provides a realization of the conformal algebra by means of a modification of the Dirac bracket proposed by Barnich and Troessaert. The latter construction allows for a field dependent central extension, whose value tends to the Brown-Henneaux central charge at late times.

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arXiv2023

Kac-Moody symmetry in the light front of gauge theories

We discuss the emergence of a new symmetry generator in a Hamiltonian realisation of four-dimensional gauge theories in the flat space foliated by retarded (advanced) time. It generates an asymptotic symmetry that acts on the asymptotic fields in a way different from the usual large gauge transformations. The improved canonical generators, corresponding to gauge and asymptotic symmetries, form a classical Kac-Moody charge algebra with a non-trivial central extension. In particular, we describe the case of electromagnetism, where the charge algebra is the $\mathrm{U}(1)$ current algebra with a level proportional to the coupling constant of the theory, $κ=4π^2/e^2$. We construct bilinear generators yielding Virasoro algebras on the null boundary. We also provide a non-Abelian generalization of the previous symmetries by analysing the evolution of Yang-Mills theory in Bondi coordinates.

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arXiv2022

DC conductance and memory in 3D gravity

Transport properties are investigated in the two-dimensional dual dynamics of AdS$_{3}$ gravity. By providing boundary conditions that deform the ADM lapse and shift functions, we construct a lower dimensional model comprising two copies of chiral boson excitations with anisotropic scaling symmetry. Using bosonization, an electric current is identified. By means of the Kubo formula, we find a DC conductance depending on the level of the theory and the dynamical exponents. The bulk realization of the linear response is related to a type of gravitational memory emerging in the context of near-horizon boundary conditions. The process is adiabatic and represents a permanent spacetime deformation parametrized by anisotropic chiral bosons through a large gauge transformation.

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arXiv2021

The structure of IR divergences in celestial gluon amplitudes

The all-loop resummation of SU$(N)$ gauge theory amplitudes is known to factorize into an IR-divergent (soft and collinear) factor and a finite (hard) piece. The divergent factor is universal, whereas the hard function is a process-dependent quantity. We prove that this factorization persists for the corresponding celestial amplitudes. Moreover, the soft/collinear factor becomes a scalar correlator of the product of renormalized Wilson lines defined in terms of celestial data. Their effect on the hard amplitude is a shift in the scaling dimensions by an infinite amount, proportional to the cusp anomalous dimension. This leads us to conclude that the celestial-IR-safe gluon amplitude corresponds to a expectation value of operators dressed with Wilson line primaries. These results hold for finite $N$. In the large $N$ limit, we show that the soft/collinear correlator can be described in terms of vertex operators in a Coulomb gas of colored scalar primaries with nearest neighbor interactions. In the particular cases of four and five gluons in planar $\mathcal{N}=4$ SYM theory, where the hard factor is known to exponentiate, we establish that the Mellin transform converges in the UV thanks to the fact that the cusp anomalous dimension is a positive quantity. In other words, the very existence of the full celestial amplitude is owed to the positivity of the cusp anomalous dimension.

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arXiv2019

The anisotropic chiral boson

We construct the theory of a chiral boson with anisotropic scaling, characterized by a dynamical exponent $z$, whose action reduces to that of Floreanini and Jackiw in the isotropic case ($z=1$). The standard free boson with Lifshitz scaling is recovered when both chiralities are nonlocally combined. Its canonical structure and symmetries are also analyzed. As in the isotropic case, the theory is also endowed with a current algebra. Noteworthy, the standard conformal symmetry is shown to be still present, but realized in a nonlocal way. The exact form of the partition function at finite temperature is obtained from the path integral, as well as from the trace over $\hat{u}(1)$ descendants. It is essentially given by the generating function of the number of partitions of an integer into $z$-th powers, being a well-known object in number theory. Thus, the asymptotic growth of the number of states at fixed energy, including subleading corrections, can be obtained from the appropriate extension of the renowned result of Hardy and Ramanujan.

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arXiv2019

Extended Symmetries at the Black Hole Horizon

We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Virasoro algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability conditions get modified, we find that the computation of the zero-modes correctly reproduces the black hole entropy. Furthermore, we analyze the case of three spacetime dimensions, in which the integrability conditions notably simplify and the field equations can be solved analytically to produce a family of exact solutions that realize the boundary conditions explicitly. We examine other features, such as the form of the algebra in the extremal limit and the relation to other works in the literature.

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arXiv2018

Boundary theories for dilaton supergravity in 2D

The $\mathfrak{osp}(2,N)$-BF formulation of dilaton supergravity in two dimensions is considered. We introduce a consistent class of asymptotic conditions preserved by the extended superreparametrization group of the thermal circle at infinity. In the $N=1$ and $N=2$ cases the phase space foliation in terms of orbits of the super-Virasoro group allows to formulate suitable integrability conditions for the boundary terms that render the variational principle well-defined. Once regularity conditions are imposed, requiring trivial holonomy around the contractible cycle the asymptotic symmetries are broken to some subsets of exact isometries. Different coadjoint orbits of the asymptotic symmetry group yield different types of boundary dynamics; we find that the action principle can be reduced to either the extended super-Schwarzian theory, consistent with the dynamics of a non-vanishing Casimir function, or to superparticle models, compatible with bulk configurations whose Casimir is zero. These results are generalized to $\mathcal{N} \geq 3$ by making use of boundary conditions consistent with the loop group of OSp$(2,N)$. Appropriate integrability conditions permit to reduce the dynamics of dilaton supergravity to a particle moving on the OSp$(2,N)$ group manifold. Generalizations of the boundary dynamics for $\mathcal{N}>2$ are obtained once bulk geometries are supplemented with super-AdS$_2$ asymptotics.

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arXiv2018

Revisiting the asymptotic dynamics of General Relativity on AdS$_3$

The dual dynamics of Einstein gravity on AdS$_3$ supplemented with boundary conditions of KdV-type is identified. It corresponds to a two-dimensional field theory at the boundary, described by a novel action principle whose field equations are given by two copies of the "potential modified KdV equation". The asymptotic symmetries then transmute into the global Noether symmetries of the dual action, giving rise to an infinite set of commuting conserved charges, implying the integrability of the system. Noteworthy, the theory at the boundary is non-relativistic and possesses anisotropic scaling of Lifshitz type.

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arXiv2018

Towards a bulk description of higher spin SYK

We consider on the bulk side extensions of the Sachdev--Ye--Kitaev (SYK) model to Yang--Mills and higher spins. To this end we study generalizations of the Jackiw--Teitelboim (JT) model in the BF formulation. Our main goal is to obtain generalizations of the Schwarzian action, which we achieve in two ways: by considering the on-shell action supplemented by suitable boundary terms compatible with all symmetries, and by applying the Lee--Wald--Zoupas formalism to analyze the symplectic structure of dilaton gravity. We conclude with a discussion of the entropy (including log-corrections from higher spins) and a holographic dictionary for the generalized SYK/JT correspondence.

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arXiv2015

Nonlinearly charged Lifshitz black holes for any exponent $z>1$

Charged Lifshitz black holes for the Einstein-Proca-Maxwell system with a negative cosmological constant in arbitrary dimension $D$ are known only if the dynamical critical exponent is fixed as $z=2(D-2)$. In the present work, we show that these configurations can be extended to much more general charged black holes which in addition exist for any value of the dynamical exponent $z>1$ by considering a nonlinear electrodynamics instead of the Maxwell theory. More precisely, we introduce a two-parametric nonlinear electrodynamics defined in the more general, but less known, so-called $(\mathcal{H},P)$-formalism and obtain a family of charged black hole solutions depending on two parameters. We also remark that the value of the dynamical exponent $z=D-2$ turns out to be critical in the sense that it yields asymptotically Lifshitz black holes with logarithmic decay supported by a particular logarithmic electrodynamics. All these configurations include extremal Lifshitz black holes. Charged topological Lifshitz black holes are also shown to emerge by slightly generalizing the proposed electrodynamics.

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arXiv2013

Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory

In the gravitational context, Liouville theory is the two-dimensional conformal field theory that controls the boundary dynamics of asymptotically AdS_3 spacetimes at the classical level. By taking a suitable limit of the coupling constants of the Hamiltonian formulation of Liouville, we construct and analyze a BMS_3 invariant two-dimensional field theory that is likely to control the boundary dynamics at null infinity of three dimensional asymptotically flat gravity.

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arXiv2013

A 2D field theory equivalent to 3D gravity with no cosmological constant

In (2+1) space-time dimensions the Einstein theory of gravity has no local degrees of freedom. In fact, in the presence of a negative cosmological term, it is described by a (1+1) dimensional theory living on its boundary: Liouville theory. It is invariant under the action of the two-dimensional conformal group, which, in the gravitational context, corresponds to the asymptotic symmetries of asymptotically AdS geometries. In the flat case, when the cosmological term is turned off, a theory describing gravity at the boundary is absent. In this note we show that, in the Hamiltonian setup, such a theory may be constructed. The theory is BMS3 invariant, as it should, corresponding to the asymptotic symmetry group of an asymptotically flat spacetime.

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arXiv2012

The flat limit of three dimensional asymptotically anti-de Sitter spacetimes

In order to get a better understanding of holographic properties of gravitational theories with a vanishing cosmological constant, we analyze in detail the relation between asymptotically anti-de Sitter and asymptotically flat spacetimes in three dimensions. This relation is somewhat subtle because the limit of vanishing cosmological constant cannot be naively taken in standard Fefferman-Graham coordinates. After reformulating the standard anti-de Sitter results in Robinson-Trautman coordinates, a suitably modified Penrose limit is shown to connect both asymptotic regimes.

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