arXiv subjects

Ricardo Troncoso

Publications and source records attributed to Ricardo Troncoso.

At least 19 recordsLinked to original sources

arXiv2026

Holographic warped CFTs from General Relativity on AdS$_3$

We introduce a new set of boundary conditions for three-dimensional Einstein gravity with negative cosmological constant. The canonical generators plainly realize the semidirect sum of Virasoro and $u(1)$ Kac-Moody algebras in its standard form, without the need of additional redefinitions of the global charges. We show that requiring Euclidean BTZ and thermal AdS$_3$ to be diffeomorphic precisely induces the warped modular $S$-transformation of the chemical potentials. The corresponding warped Cardy formula then exactly reproduces the Bekenstein-Hawking entropy, where the ground state is identified as Euclidean AdS$_3$. An explicit comparison with the boundary conditions of Brown-Henneaux and Compere-Song-Strominger is also addressed.

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arXiv2026

Carroll black holes

Despite the absence of a lightcone structure, some solutions of Carroll gravity show black hole-like behaviour. We define Carroll black holes as solutions of Carroll gravity that exhibit Carroll thermal properties and have a Carroll extremal surface, notions introduced in our work. The latter is a Carroll analogue of a Lorentzian extremal surface. As examples, we discuss the Carroll versions of Schwarzschild, Reissner-Nordstroem, and BTZ black holes and black hole solutions of generic 1+1 dimensional Carroll dilaton gravity, including Carroll JT and Carroll Witten black holes.

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arXiv2025

Enhanced Conformal $BMS_3$ Symmetries

An enhanced version of the conformal BMS$_{3}$ algebra is presented. It is shown to emerge from the asymptotic structure of an extension of conformal gravity in 3D by Pope and Townsend that consistently accommodates an additional spin-2 field, once it is endowed with a suitable set of boundary conditions. The canonical generators of the asymptotic symmetries then span a precise nonlinear W$_{(2,2,2,2,1,1,1)}$ algebra, whose central extensions and coefficients of the nonlinear terms are completely determined by the central charge of the Virasoro subalgebra. The wedge algebra corresponds to the conformal group in four dimensions $SO(4,2)$ and therefore, enhanced conformal BMS$_{3}$ can also be regarded as an infinite-dimensional nonlinear extension of the AdS$_{5}$ algebra with nontrivial central extensions. It is worth mentioning that our boundary conditions might be considered as a starting point in order to consistently incorporate either a finite or an infinite number of conformal higher spin fields.

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arXiv2023

$p$-form electrodynamics as edge modes of a topological field theory

$p$-form electrodynamics in $d\geq 2$ dimensions is shown to emerge as the edge modes of a topological field theory with a precise set of boundary conditions, through the Hamiltonian reduction of its action. Electric and magnetic charges correspond to Noether ones in the topological field theory. For chiral $p$-forms, the topological action can be consistently truncated, so that the Henneaux-Teitelboim action is recovered from a pure Chern-Simons theory, with a manifestly covariant stress-energy tensor at the boundary. Topologically massive $p$-form electrodynamics as well as axion couplings are also shown to be described through this mechanism by considering suitable (self-)interaction terms in the topological theory.

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arXiv2023

BMS$_{3}$ (Carrollian) field theories from a bound in the coupling of current-current deformations of CFT$_{2}$

Two types of Carrollian field theories are shown to emerge from finite current-current deformations of toroidal CFT$_{2}$'s when the deformation coupling is precisely fixed, up to a sign. In both cases the energy and momentum densities fulfill the BMS$_{3}$ algebra. Applying these results to the bosonic string, one finds that the electric-like deformation (positive coupling) reduces to the standard tensionless string. The magnetic-like deformation (negative coupling) yields to a new theory, still being relativistic, devoid of tension and endowed with an "inner Carrollian structure". Classical solutions describe a sort of "self-interacting null particle" moving along generic null curves of the original background metric, not necessarily geodesics. This magnetic-like theory is also shown to be recovered from inequivalent limits in the tension of the bosonic string. Electric- and magnetic-like deformations of toroidal CFT$_{2}$'s can be seen to correspond to limiting cases of continuous exactly marginal (trivial) deformations spanned by an SO(1,1) automorphism of the current algebra. Thus, the absolute value of the current-current deformation coupling is shown to be bounded. When the bound saturates, the deformation ceases to be exactly marginal, but still retains the full conformal symmetry in two alternative ultrarelativistic regimes.

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arXiv2022

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

Einstein gravity minimally coupled to a scalar field with a two-parameter Higgs-like self-interaction in three spacetime dimensions is recast in terms of a Chern-Simons form for the algebra $g^{+}\oplus g^{-}$ where, depending on the sign of the self-interaction couplings, $g^{\pm}$ 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 for pure gravity, but with 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.

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arXiv2022

Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations

The conformal algebra in 2D (Diff($S^{1}$)$\oplus$Diff($S^{1}$)) 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 can then also be seen to 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.

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arXiv2021

Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations

The conformal symmetry algebra in 2D (Diff($S^{1}$)$\oplus$Diff($S^{1}$)) is shown to be related to its ultra/non-relativistic version (BMS$_{3}$$\approx$GCA$_{2}$) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT$_{2}$, the BMS$_{3}$ generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, $T$ and $\bar{T}$, closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS$_{3}$ becomes a bona fide symmetry once the CFT$_{2}$ is marginally deformed by the addition of a $\sqrt{T\bar{T}}$ term to the Hamiltonian. The generic deformed theory is manifestly invariant under diffeomorphisms and local scalings, but it is no longer a CFT$_{2}$ because its energy and momentum densities fulfill the BMS$_{3}$ algebra. The deformation can also be described through the original CFT$_{2}$ on a curved metric whose Beltrami differentials are determined by the variation of the deformed Hamiltonian with respect to $T$ and $\bar{T}$. BMS$_{3}$ symmetries then arise from deformed conformal Killing equations, corresponding to diffeomorphisms that preserve the deformed metric and stress-energy tensor up to local scalings. As an example, we briefly address the deformation of $\mathrm{N}$ free bosons, which coincides with ultra-relativistic limits only for $\mathrm{N}=1$. Furthermore, Cardy formula and the S-modular transformation of the torus become mapped to their corresponding BMS$_{3}$ (or flat) versions.

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arXiv2020

The (super)conformal BMS$_3$ algebra

The conformal extension of the BMS$_{3}$ algebra is constructed. Apart from an infinite number of 'superdilatations,' in order to incorporate 'superspecial conformal transformations,' the commutator of the latter with supertranslations strictly requires the presence of nonlinear terms in the remaining generators. The algebra appears to be very rigid, in the sense that its central extensions as well as the nonlinear terms coefficients become determined by the central charge of the Virasoro subalgebra. The wedge algebra corresponds to the conformal group in three spacetime dimensions $SO(3,2)$, so that the full algebra can also be interpreted as an infinite-dimensional nonlinear extension of the AdS$_{4}$ algebra with nontrivial central charges. Moreover, since the Lorentz subalgebra ($sl(2,R)$) is non-principally embedded within the conformal (wedge) algebra, according to the conformal weight of the generators, the conformal extension of BMS$_{3}$ can be further regarded as a $W_{(2,2,2,1)}$ algebra. An explicit canonical realization of the conformal extension of BMS$_{3}$ is then shown to emerge from the asymptotic structure of conformal gravity in 3D, endowed with a new set of boundary conditions. The supersymmetric extension is also briefly addressed.

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arXiv2020

Gravitational dual of averaged free CFT's over the Narain lattice

It has been recently argued that the averaging of free CFT's over the Narain lattice can be holographically described through a Chern-Simons theory for $U\left(1\right)^{D}\times U\left(1\right)^{D}$ with a precise prescription to sum over three-dimensional handlebodies. We show that a gravitational dual of these averaged CFT's would be provided by Einstein gravity on AdS$_{3}$ with $U\left(1\right)^{D-1}\times U\left(1\right)^{D-1}$ gauge fields, endowed with a precise set of boundary conditions closely related to the "soft hairy" ones. Gravitational excitations then go along diagonal $SL\left(2,\mathbb{R}\right)$ generators, so that the asymptotic symmetries are spanned by $U\left(1\right)^{D}\times U\left(1\right)^{D}$ currents. The stress-energy tensor can then be geometrically seen as composite of these currents through a twisted Sugawara construction. Our boundary conditions are such that for the reduced phase space, there is a one-to-one map between the configurations in the gravitational and the purely abelian theories. The partition function in the bulk could then also be performed either from a non-abelian Chern-Simons theory for two copies of $SL\left(2,\mathbb{R}\right)\times U\left(1\right)^{D-1}$ generators, or formally through a path integral along the family of allowed configurations for the metric. The new boundary conditions naturally accommodate BTZ black holes, and the microscopic number of states then appears to be manifestly positive and suitably accounted for from the partition function in the bulk. The inclusion of higher spin currents through an extended twisted Sugawara construction in the context of higher spin gravity is also briefly addressed.

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arXiv2019

Hypergravity in five dimensions

We show that a spin-$5/2$ field can be consistently coupled to gravitation without cosmological constant in five-dimensional spacetimes. The fermionic gauge "hypersymmetry" requires the presence of a finite number of additional fields, including a couple of $U(1)$ fields, a spinorial two-form, the dual of the graviton (of mixed $(2,1)$ Young symmetry) and a spin-$3$ field. The gravitational sector of the action is described by the purely quadratic Gauss-Bonnet term, so that the field equations for the metric are of second order. The local gauge symmetries of the full action principle close without the need of auxiliary fields. The field content corresponds to the components of a connection for an extension of the "hyper-Poincaré" algebra, which apart from the Poincaré and spin-$3/2$ generators, includes a generator of spin $2$ and a $U(1)$ central extension. It is also shown that this algebra admits an invariant trilinear form, which allows to formulate hypergravity as a gauge theory described by a Chern-Simons action in five dimensions.

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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

Spacetime structure near generic horizons and soft hair

We explore the spacetime structure near non-extremal horizons in any spacetime dimension greater than two and discover a wealth of novel results: 1. Different boundary conditions are specified by a functional of the dynamical variables, describing inequivalent interactions at the horizon with a thermal bath. 2. The near horizon algebra of a set of boundary conditions, labeled by a parameter $s$, is given by the semi-direct sum of diffeomorphisms at the horizon with "spin-$s$ supertranslations". For $s=1$ we obtain the first explicit near horizon realization of the Bondi-Metzner-Sachs algebra. 3. For another choice, we find a non-linear extension of the Heisenberg algebra, generalizing recent results in three spacetime dimensions. This algebra allows to recover the aforementioned (linear) ones as composites. 4. These examples allow to equip not only black holes, but also cosmological horizons with soft hair. We also discuss implications of soft hair for black hole thermodynamics and entropy.

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arXiv2019

Lifshitz Scaling, Microstate Counting from Number Theory and Black Hole Entropy

Non-relativistic field theories with anisotropic scale invariance in (1+1)-d are typically characterized by a dispersion relation $E\sim k^{z}$ and dynamical exponent $z>1$. The asymptotic growth of the number of states of these theories can be described by an extension of Cardy formula that depends on $z$. We show that this result can be recovered by counting the partitions of an integer into $z$-th powers, as proposed by Hardy and Ramanujan a century ago. This gives a novel relationship between the characteristic energy of the dispersion relation with the cylinder radius and the ground state energy. For free bosons with Lifshitz scaling, this relationship is shown to be identically fulfilled by virtue of the reflection property of the Riemann $ζ$-function. The quantum Benjamin-Ono$_{2}$ (BO$_{2}$) integrable system, relevant in the AGT correspondence, is also analyzed. As a holographic realization, we provide a special set of boundary conditions for which the reduced phase space of Einstein gravity with a couple of $U(1)$ fields on AdS$_3$ is described by the BO$_{2}$ equations. This suggests that the phase space can be quantized in terms of quantum BO$_{2}$ states. Indeed, in the semiclassical limit, the ground state energy of BO$_{2}$ coincides with the energy of global AdS$_{3}$, and the Bekenstein-Hawking entropy for BTZ black holes is recovered from the anisotropic extension of Cardy formula.

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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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arXiv2017

Integrable systems with BMS$_{3}$ Poisson structure and the dynamics of locally flat spacetimes

We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS$_{3}$ algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis is performed in terms of two-dimensional gauge fields for $isl(2,R)$. Although the algebra is not semisimple, the formulation can be carried out à la Drinfeld-Sokolov because it admits a nondegenerate invariant bilinear metric. The hierarchy turns out to be bi-Hamiltonian, labeled by a nonnegative integer $k$, and defined through a suitable generalization of the Gelfand-Dikii polynomials. The symmetries of the hierarchy are explicitly found. For $k\geq 1$, the corresponding conserved charges span an infinite-dimensional Abelian algebra without central extensions, and they are in involution; while in the case of $k=0$, they generate the BMS$_{3}$ algebra. In the special case of $k=1$, by virtue of a suitable field redefinition and time scaling, the field equations are shown to be equivalent to a specific type of the Hirota-Satsuma coupled KdV systems. For $k\geq 1$, the hierarchy also includes the so-called perturbed KdV equations as a particular case. A wide class of analytic solutions is also explicitly constructed for a generic value of $k$. Remarkably, the dynamics can be fully geometrized so as to describe the evolution of spacelike surfaces embedded in locally flat spacetimes. Indeed, General Relativity in 3D can be endowed with a suitable set of boundary conditions, so that the Einstein equations precisely reduce to the ones of the hierarchy aforementioned. The symmetries of the integrable systems then arise as diffeomorphisms that preserve the asymptotic form of the spacetime metric, and therefore, they become Noetherian. The infinite set of conserved charges is recovered from the corresponding surface integrals in the canonical approach.

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arXiv2017

Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS$_3$ and nonlinear energy bounds

The asymptotically flat structure of $\mathcal{N}=(2,0)$ supergravity in three spacetime dimensions is explored. The asymptotic symmetries are spanned by an extension of the super-BMS$_3$ algebra, with two independent $\hat{u}(1)$ currents of electric and magnetic type. These currents are associated to $U(1)$ fields being even and odd under parity, respectively. Remarkably, although the $U(1)$ fields do not generate a backreaction on the metric, they provide nontrivial Sugawara-like contributions to the BMS$_3$ generators, and hence to the energy and the angular momentum. The entropy of flat cosmological spacetimes with $U(1)$ fields then acquires a nontrivial dependence on the $\hat{u}(1)$ charges. If the spin structure is odd, the ground state corresponds to Minkowski spacetime, and although the anticommutator of the canonical supercharges is linear in the energy and in the electric-like $\hat{u}(1)$ charge, the energy becomes bounded from below by the energy of the ground state shifted by the square of the electric-like $\hat{u}(1)$ charge. If the spin structure is even, the same bound for the energy generically holds, unless the absolute value of the electric-like charge is less than minus the mass of Minkowski spacetime in vacuum, so that the energy has to be nonnegative. The explicit form of the Killing spinors is found for a wide class of configurations that fulfills our boundary conditions, and they exist precisely when the corresponding bounds are saturated. It is also shown that the spectra with periodic or antiperiodic boundary conditions for the fermionic fields are related by spectral flow, in a similar way as it occurs for the $\mathcal{N}=2$ super-Virasoro algebra. Indeed, our super-BMS$_3$ algebra can be recovered from the flat limit of the superconformal algebra with $\mathcal{N}=(2,2)$, truncating the fermionic generators of the right copy.

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arXiv2017

Log corrections to entropy of three dimensional black holes with soft hair

We calculate log corrections to the entropy of three-dimensional black holes with "soft hairy" boundary conditions. Their thermodynamics possesses some special features that preclude a naive direct evaluation of these corrections, so we follow two different approaches. The first one exploits that the BTZ black hole belongs to the spectrum of Brown-Henneaux as well as soft hairy boundary conditions, so that the respective log corrections are related through a suitable change of the thermodynamic ensemble. In the second approach the analogue of modular invariance is considered for dual theories with anisotropic scaling of Lifshitz type with dynamical exponent z at the boundary. On the gravity side such scalings arise for KdV-type boundary conditions, which provide a specific 1-parameter family of multi-trace deformations of the usual AdS3/CFT2 setup, with Brown-Henneaux corresponding to z=1 and soft hairy boundary conditions to the limiting case z=0. Both approaches agree in the case of BTZ black holes for any non-negative z. Finally, for soft hairy boundary conditions we show that not only the leading term, but also the log corrections to the entropy of black flowers endowed with affine u(1) soft hair charges exclusively depend on the zero modes and hence coincide with the ones for BTZ black holes.

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