Evelyn Rodríguez

Bio: Evelyn Rodríguez is an academic researcher from University of the Bío Bío. The author has contributed to research in topics: Supersymmetry & Supergravity. The author has an hindex of 4, co-authored 12 publications receiving 102 citations. Previous affiliations of Evelyn Rodríguez include University of Talca & University of Concepción.

Generalizing the $$\mathfrak {bms}_{3}$$ and 2D-conformal algebras by expanding the Virasoro algebra

Abstract: By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the $$\mathfrak {bms}_{3}$$ algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called $$\mathfrak {B}_{k}$$ , $$\mathfrak {C}_{k}$$ and $$\mathfrak {D}_{k}$$ algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kac–Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.

Observations on BI from $\mathcal{N}=2$ Supergravity and the General Ward Identity

Abstract: The multi-vector generalization of a rigid, partially-broken $$ \mathcal{N}=2 $$ supersymmetric theory is presented as a rigid limit of a suitable gauged $$ \mathcal{N}=2 $$ supergravity with electric, magnetic charges and antisymmetric tensor fields. This on the one hand generalizes a known result by Ferrara, Girardello and Porrati while on the other hand allows to recover the multi-vector BI models of [4] from $$ \mathcal{N}=2 $$ supergravity as the end-point of a hierarchical limit in which the Planck mass first and then the supersymmetry breaking scale are sent to infinity. We define, in the parent supergravity model, a new symplectic frame in which, in the rigid limit, manifest symplectic invariance is preserved and the electric and magnetic Fayet-Iliopoulos terms are fully originated from the dyonic components of the embedding tensor. The supergravity origin of several features of the resulting rigid supersymmetric theory are then elucidated, such as the presence of a traceless SU(2)- Lie algebra term in the Ward identity and the existence of a central charge in the supersymmetry algebra which manifests itself as a harmless gauge transformation on the gauge vectors of the rigid theory; we show that this effect can be interpreted as a kind of “superspace non-locality” which does not affect the rigid theory on space-time. To set the stage of our analysis we take the opportunity in this paper to provide and prove the relevant identities of the most general dyonic gauging of Special-Kaehler and Quaternionic-Kaehler isometries in a generic $$ \mathcal{N}=2 $$ model, which include the supersymmetry Ward identity, in a fully symplectic-covariant formalism.

Extended asymptotic symmetries of three-dimensional gravity in flat space

Abstract: We study three-dimensional asymptotically flat spacetimes whose boundary dynamics is described by an enlargement and deformation of the $\mathfrak{bms}_3$ algebra with three independent central charges. This symmetry arises from a gravity action invariant under the local Maxwell group and is characterized by presence of Abelian generators which modify the commutation relations of the super-translations in the standard $\mathfrak{bms}_3$ algebra. Our analysis is based on the charge algebra of the theory in the BMS gauge, which includes the known solutions of standard asymptotically flat case. We also study the stationary solutions of the theory in ADM form and we show that the vacuum energy and the vacuum angular momentum of the stationary configuration are influenced by the presence of the gravitational Maxwell field.

Observations on BI from $\mathcal{N}=2$ Supergravity and the General Ward Identity

Abstract: The multi-vector generalization of a rigid, partially-broken $\mathcal{N}=2$ supersymmetric theory is presented as a rigid limit of a suitable gauged $\mathcal{N}=2$ supergravity with electric, magnetic charges and antisymmetric tensor fields. This on the one hand generalizes a known result by Ferrara, Girardello and Porrati while on the other hand allows to recover the multi-vector BI models from $\mathcal{N}=2$ supergravity as the end-point of a hierarchical limit in which the Planck mass first and then the supersymmetry breaking scale are sent to infinity. We define, in the parent supergravity model, a new symplectic frame in which, in the rigid limit, manifest symplectic invariance is preserved and the electric and magnetic Fayet-Iliopoulos terms are fully originated from the dyonic components of the embedding tensor. The supergravity origin of several features of the resulting rigid supersymmetric theory will be elucidated, such as the presence of a traceless ${\rm SU}(2)$- Lie algebra term in the Ward identity and the existence of a central charge in the supersymmetry algebra which manifests itself as a harmless gauge transformation on the gauge vectors of the rigid theory; we show that this effect can be interpreted as a kind of "superspace non-locality" which does not affect the rigid theory on space-time. To set the stage of our analysis we take the opportunity in this paper to provide and prove the relevant identities of the most general dyonic gauging of Special-Kaehler and Quaternionic-Kaehler isometries in a generic $\mathcal{N}=2$ model, which include the supersymmetry Ward identity, in a fully symplectic-covariant formalism.

Three-dimensional exotic Newtonian supergravity theory with cosmological constant

Abstract: We present a supersymmetric extension of the exotic Newtonian Chern–Simons gravity theory in three spacetime dimensions. The underlying new non-relativistic superalgebra is obtained by expanding the $${\mathcal {N}}=2$$ AdS superalgebra and can be written as two copies of the enhanced Nappi–Witten algebra, one of which is augmented by supersymmetry. We show that the exotic Newtonian superalgebra allows to introduce a cosmological constant to the extended Newtonian supergravity. Interestingly, the obtained supergravity action contains the extended Newton–Hooke supergravity as a sub-case.

Gauged Supergravities.

Abstract: We give a general review of extended supergravities and their gauging using the duality-covariant embedding tensor formalism. Although the focus is on four-dimensional theories, an overview of the gauging procedure and the related tensor hierarchy in the higher-dimensional models is given. The relation of gauged supergravities to flux compactifications is discussed and examples are worked out in detail.

Carroll contractions of Lorentz-invariant theories

Abstract: We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one “electric” and the other “magnetic”. Each can be obtained from the corresponding Lorentz-invariant theory written in Hamiltonian form through the same “contraction” procedure of taking the ultrarelativistic limit c → 0 where c is the speed of light, but with two different consistent rescalings of the canonical variables. This procedure can be applied to general Lorentz-invariant theories (p-form gauge fields, higher spin free theories etc) and has the advantage of providing explicitly an action principle from which the electrically-contracted or magnetically-contracted dynamics follow (and not just the equations of motion). Even though not manifestly so, this Hamiltonian action principle is shown to be Carroll invariant. In the case of p-forms, we construct explicitly an equivalent manifestly Carroll-invariant action principle for each Carroll contraction. While the manifestly covariant variational description of the electric contraction is rather direct, the one for the magnetic contraction is more subtle and involves an additional pure gauge field, whose elimination modifies the Carroll transformations of the fields. We also treat gravity, which constitutes one of the main motivations of our study, and for which we provide the two different contractions in Hamiltonian form.

Non-relativistic gravity theory based on an enlargement of the extended Bargmann algebra

Abstract: In this work we study a non-relativistic three dimensional Chern-Simons gravity theory based on an enlargement of the Extended Bargmann algebra. A finite nonrelativistic Chern-Simons gravity action is obtained through the non-relativistic contraction of a particular U(1) enlargement of the so-called AdS-Lorentz algebra. We show that the non-relativistic gravity theory introduced here reproduces the Maxwellian Exotic Bargmann gravity theory when a flat limit l → ∞ is applied. We also present an alternative procedure to obtain the non-relativistic versions of the AdS-Lorentz and Maxwell algebras through the semigroup expansion method.

Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra

Abstract: We study a three-dimensional Chern-Simons gravity theory based on the Maxwell algebra. We find that the boundary dynamics is described by an enlargement and deformation of the bms3 algebra with three independent central charges. This symmetry arises from a gravity action invariant under the local Maxwell group and is characterized by presence of Abelian generators which modify the commutation relations of the super-translations in the standard bms3 algebra. Our analysis is based on the charge algebra of the theory in the BMS gauge, which includes the known solutions of standard asymptotically flat case. The field content of the theory is different than the one of General Relativity, but it includes all its geometries as particular solutions. In this line, we also study the stationary solutions of the theory in ADM form and we show that the vacuum energy and the vacuum angular momentum of the stationary configuration are influenced by the presence of the gravitational Maxwell field.