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Pablo Rodríguez

Bio: Pablo Rodríguez is an academic researcher from Centro de Estudios Científicos. The author has contributed to research in topics: Tensor & Conformal symmetry. The author has co-authored 1 publications.

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TL;DR: The conformal symmetry algebra in 2D (Diff(S1)⊕Diff (S1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process.
Abstract: The conformal symmetry algebra in 2D (Diff(S1)⊕Diff(S1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT2, the BMS3 generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, T and $$ \overline{T} $$ , closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS3 becomes a bona fide symmetry once the CFT2 is marginally deformed by the addition of a $$ \sqrt{T\overline{T}} $$ term to the Hamiltonian. The generic deformed theory is manifestly invariant under diffeomorphisms and local scalings, but it is no longer a CFT2 because its energy and momentum densities fulfill the BMS3 algebra. The deformation can also be described through the original CFT2 on a curved metric whose Beltrami differentials are determined by the variation of the deformed Hamiltonian with respect to T and $$ \overline{T} $$ . BMS3 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 N free bosons, which coincides with ultra-relativistic limits only for N = 1. Furthermore, Cardy formula and the S-modular transformation of the torus become mapped to their corresponding BMS3 (or flat) versions.

17 citations


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TL;DR: In this paper , a free scalar theory in two dimensions exhibiting BMS symmetry was studied, which can also be interpreted as the ultrarelativistic limit of a flipped representation.
Abstract: The BMS (Bondi--van der Burg--Metzner--Sachs) symmetry arises as the asymptotic symmetry of flat spacetime at null infinity. In particular, the BMS algebra for three-dimensional flat spacetime (${\mathrm{BMS}}_{3}$) is generated by the super-rotation generators that form a Virasoro subalgebra with central charge ${c}_{L}$, together with mutually commuting super-translation generators. The super-rotation and supertranslation generators have nontrivial commutation relations with another central charge ${c}_{M}$. In this paper, we study a free scalar theory in two dimensions exhibiting ${\mathrm{BMS}}_{3}$ symmetry, which can also be understood as the ultrarelativistic limit of a free scalar ${\mathrm{CFT}}_{2}$ in the flipped representation. Upon canonical quantization on the highest weight vacuum, the central charges are found to be ${c}_{L}=2$ and ${c}_{M}=0$. Because of the vanishing central charge ${c}_{M}=0$, the theory features novel properties: there exist primary states which form a multiplet, and the Hilbert space can be organized by an enlarged version of BMS modules dubbed the staggered modules. We further calculate correlation functions and the torus partition function, the latter of which is also shown explicitly to be modular invariant. Is it interesting to note that our model has vanishing ${c}_{M}$, a feature also shared by the so-called flat space chiral gravity in Bagchi et al. [Flat-Space Chiral Gravity, Phys. Rev. Lett. 109, 151301 (2012)].

15 citations

Journal ArticleDOI
TL;DR: In this article , a recursive algorithm is proposed to compute the coefficients of the power series expansion of the solution to the metric flow equation, under some quite restrictive assumptions on the stress-energy tensor.
Abstract: We consider a one-parameter family of composite fields -- bi-linear in the components of the stress-energy tensor -- which generalise the $\mathrm{T}\bar{\mathrm{T}}$ operator to arbitrary space-time dimension $d\geq 2$. We show that they induce a deformation of the classical action which is equivalent -- at the level of the dynamics -- to a field-dependent modification of the background metric tensor according to a specific flow equation. Even though the starting point is the flat space, the deformed metric is generally curved for any $d>2$, thus implying that the corresponding deformation can not be interpreted as a coordinate transformation. The central part of the paper is devoted to the development of a recursive algorithm to compute the coefficients of the power series expansion of the solution to the metric flow equation. We show that, under some quite restrictive assumptions on the stress-energy tensor, the power series yields an exact solution. Finally, we consider a class of theories in $d=4$ whose stress-energy tensor fulfils the assumptions above mentioned, namely the family of abelian gauge theories in $d=4$. For such theories, we obtain the exact expression of the deformed metric and the vierbein. In particular, the latter result implies that ModMax theory in a specific curved space is dynamically equivalent to its Born-Infeld-like extension in flat space. We also discuss a dimensional reduction of the latter theories from $d=4$ to $d=2$ in which an interesting marginal deformation of $d=2$ field theories emerges.

12 citations

Journal ArticleDOI
TL;DR: In this article , it was shown that the classical symmetry algebra can be transferred from two copies of Virasoro to the BMS algebra by infinite boosts or degenerate linear transformations on coordinates.
Abstract: A bstract Bondi-Metzner-Sachs (BMS) symmetries, or equivalently Conformal Carroll symmetries, are intrinsically associated to null manifolds and in two dimensions can be obtained as an Inönü-Wigner contraction of the two-dimensional (2 d ) relativistic conformal algebra. Instead of performing contractions, we demonstrate in this paper how this transmutation of symmetries can be achieved by infinite boosts or degenerate linear transformations on coordinates. Taking explicit cues from the worldsheet theory of null strings, we show boosting the system is equivalent to adding a current-current deformation term to the Hamiltonian. As the strength of this deformation term reaches a critical value, the classical symmetry algebra “flows” from two copies of Virasoro to the BMS algebra. We further explore the situation where the CFT coordinates are asymmetrically transformed, and degenerate limits lead to chiral theories.

10 citations

Journal ArticleDOI
TL;DR: In this paper , the analysis of the asymptotic properties of gravity in higher spacetime dimensions D , with a particular emphasis on the case D = 5, is presented.
Abstract: A bstract We develop the analysis of the asymptotic properties of gravity in higher spacetime dimensions D , with a particular emphasis on the case D = 5. Our approach deals with spatial infinity and is Hamiltonian throughout. It is shown that the asymptotic symmetry algebra BMS 5 , which is realized non linearly, contains a four-fold family of angle- dependent supertranslations. The structure of this non-linear algebra is investigated and a presentation in which the Poincaré subalgebra is linearly realized is constructed. Invariance of the energy is studied. Concluding comments on higher dimensions D ≥ 6 are also given.

8 citations

Journal ArticleDOI
TL;DR: In this paper , asymptotic symmetries of electric and magnetic Carrollian gravitational theories with a negative cosmological constant $\Lambda$ are analyzed in 3+1 space-time dimensions.
Abstract: Asymptotic symmetries of electric and magnetic Carrollian gravitational theories with a negative cosmological constant $\Lambda$ are analyzed in 3+1 space-time dimensions. In the magnetic theory, the asymptotic symmetry algebra is given by the conformal Carroll algebra in three dimensions, which is infinite-dimensional and isomorphic to the BMS$_{4}$ algebra. These results are in full agreement with holographic expectations, providing a new framework for the study of "Carrollian holography." On the contrary, in the case of the electric theory, the presence of a negative $\Lambda$ turns out to be incompatible with a consistent set of asymptotic conditions, that can be traced back to the absence of a sensible ground state configuration. This can be improved if the Carrollian theory obtained from an electric contraction of Euclidean General Relativity is considered. In this case, asymptotic conditions can be constructed with an asymptotic symmetry algebra given by $so\left(1,4\right)$. However, it is shown that the space of spherically symmetric solutions of this theory is degenerate.

7 citations