scholarly journals Non-relativistic three-dimensional supergravity theories and semigroup expansion method

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Patrick Concha ◽  
Marcelo Ipinza ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez
Keyword(s):  
Supergravity Models ◽  
Lie Algebra ◽  
Three Dimensional ◽  
Expansion Method ◽  
Supersymmetric Extension ◽  
Supergravity Theory ◽  
Invariant Tensor ◽  
Contraction Process ◽  
Chern Simons ◽  
Supergravity Action

Abstract In this work we present an alternative method to construct diverse non-relativistic Chern-Simons supergravity theories in three spacetime dimensions. To this end, we apply the Lie algebra expansion method based on semigroups to a supersymmetric extension of the Nappi-Witten algebra. Two different families of non-relativistic superalgebras are obtained, corresponding to generalizations of the extended Bargmann superalgebra and extended Newton-Hooke superalgebra, respectively. The expansion method considered here allows to obtain known and new non-relativistic supergravity models in a systematic way. In particular, it immediately provides an invariant tensor for the expanded superalgebra, which is essential to construct the corresponding Chern-Simons supergravity action. We show that the extended Bargmann supergravity and its Maxwellian generalization appear as particular subcases of a generalized extended Bargmann supergravity theory. In addition, we demonstrate that the generalized extended Bargmann and generalized extended Newton-Hooke supergravity families are related through a contraction process.

scholarly journals Three-dimensional exotic Newtonian supergravity theory with cosmological constant

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Gravity Theory ◽  
Supersymmetric Extension ◽  
Supergravity Theory ◽  
Chern Simons ◽  
Supergravity Action

AbstractWe 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 $${\mathcal {N}}=2$$ 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.

scholarly journals Three-dimensional teleparallel Chern-Simons supergravity theory

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Ricardo Caroca ◽  
Patrick Concha ◽  
Diego Peñafiel ◽  
Evelyn Rodríguez
Keyword(s):  
Cosmological Constant ◽  
Riemannian Geometry ◽  
Three Dimensional ◽  
Supersymmetric Extension ◽  
Supergravity Theory ◽  
Gauge Invariant ◽  
Poincaré Algebra ◽  
Chern Simons

AbstractIn this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincaré algebra. At the bosonic level the theory describes a non-Riemannian geometry with a non-vanishing torsion. In presence of supersymmetry, the teleparallel supergravity theory is characterized by a non-vanishing super-torsion in which the cosmological constant can be seen as a source for the torsion. We show that the teleparallel supergravity theory presented here reproduces the Poincaré supergravity in the vanishing cosmological limit. The extension of our results to $${\mathcal {N}}=p+q$$ N = p + q supersymmetries is also explored.

scholarly journals Three-dimensional non-relativistic extended supergravity with cosmological constant

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Supersymmetric Extension ◽  
Supergravity Theory ◽  
Chern Simons

AbstractIn this paper, we present two novel non-relativistic superalgebras which correspond to supersymmetric extensions of the enlarged extended Bargmann algebra. The three-dimensional non-relativistic Chern–Simons supergravity actions invariant under the aforementioned superalgebras are constructed. The new non-relativistic superalgebras allow to accommodate a cosmological constant in a non-relativistic supergravity theory. Interestingly, we show that one of the non-relativistic supergravity theories presented here leads to the recently introduced Maxwellian exotic Bargmann supergravity when the flat limit $$\ell \rightarrow \infty $$ ℓ → ∞ is considered. Besides, we show that both descriptions can be written in terms of a supersymmetric extension of the Nappi–Witten algebra or the extended Newton–Hooke superalgebra.

scholarly journals Three-dimensional Maxwellian extended Newtonian gravity and flat limit

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez ◽  
Gustavo Rubio
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Expansion Method ◽  
Gravity Models ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
Relativistic Limit ◽  
Expansion Procedure ◽  
Three Space ◽  
Chern Simons

Abstract In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

scholarly journals Higher-derivative supergravity, AdS4 holography, and black holes

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Nikolay Bobev ◽  
Anthony M. Charles ◽  
Kiril Hristov ◽  
Valentin Reys
Keyword(s):  
Black Holes ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Conformal Supergravity ◽  
Supergravity Theory ◽  
Higher Derivative ◽  
All Solutions ◽  
M Theory ◽  
Supergravity Action

Abstract We use conformal supergravity techniques to study four-derivative corrections in four-dimensional gauged supergravity. We show that the four-derivative Lagrangian for the propagating degrees of freedom of the $$ \mathcal{N} $$ N = 2 gravity multiplet is determined by two real dimensionless constants. We demonstrate that all solutions of the two-derivative equations of motion in the supergravity theory also solve the four-derivative equations of motion. These results are then applied to explicitly calculate the regularized on-shell action for any asymptotically locally AdS4 solution of the two-derivative equations of motion. The four-derivative terms in the supergravity Lagrangian modify the entropy and other thermodynamic observables for the black hole solutions of the theory. We calculate these corrections explicitly and demonstrate that the quantum statistical relation holds for general stationary black holes in the presence of the four-derivative corrections. Employing an embedding of this supergravity model in M-theory we show how to use supersymmetric localization results in the holographically dual three-dimensional SCFT to determine the unknown coefficients in the four-derivative supergravity action. This in turn leads to new detailed results for the first subleading $$ {N}^{\frac{1}{2}} $$ N 1 2 correction to the large N partition function of a class of three-dimensional SCFTs on compact Euclidean manifolds. In addition, we calculate explicitly the first subleading correction to the Bekenstein-Hawking entropy of asymptotically AdS4 black holes in M-theory. We also discuss how to add matter multiplets to the supergravity theory in the presence of four-derivative terms and to generalize some of these results to six- and higher-derivative supergravity.

GRADED LIE ALGEBRA AND GENERALIZED CHERN-SIMONS ACTIONS IN ARBITRARY DIMENSIONS

1992 ◽  
Vol 07 (13) ◽  
pp. 1137-1147 ◽  
Author(s):  
NOBORU KAWAMOTO ◽  
YOSHIYUKI WATABIKI
Keyword(s):  
Lie Algebra ◽  
Essential Role ◽  
Three Dimensional ◽  
Gauge Invariant ◽  
Supersymmetric Version ◽  
Graded Lie Algebra ◽  
New Type ◽  
Arbitrary Dimensions ◽  
Chern Simons ◽  
Odd Dimensions

We obtain generalized Chern-Simons actions in arbitrary dimensions. A graded Lie algebra plays an essential role in extending into odd dimensions in contrast with the even-dimensional generalized Chern-Simons action which we have obtained previously. As a particular example we obtain three-dimensional generalized Chern-Simons action which includes the standard Chern-Simons action together with additional terms which are responsible for a new type of gauge symmetry as well as supersymmetry. As a particular supersymmetric version, we obtain an action whose partition function is Casson invariant. We also find series of gauge invariant physical observables.

DE SITTER GRAVITY AND SUPERGRAVITY IN THREE DIMENSIONS AS CHERN-SIMONS THEORIES

1990 ◽  
Vol 05 (12) ◽  
pp. 935-941 ◽  
Author(s):  
K. KOEHLER ◽  
F. MANSOURI ◽  
CENALO VAZ ◽  
L. WITTEN
Keyword(s):  
Gauge Theory ◽  
Cosmological Constant ◽  
Classical Theory ◽  
Three Dimensional ◽  
Three Dimensions ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Supergravity Theory ◽  
Gauge Transformations ◽  
Chern Simons

We construct a de Sitter supergravity theory in 2 + 1 dimensions as the Chern-Simons gauge theory of the supergroup OSp (1|2; C). The resulting action is a consistent classical supergravity theory with a positive cosmological constant. As in other three dimensional Chern-Simons theories, diffeomorphisms are shown to be equivalent to gauge transformations of OSp (1|2; C) on shell. Consistency of the corresponding classical theory is briefly discussed.

scholarly journals Fermi gas approach to general rank theories and quantum curves

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Naotaka Kubo
Keyword(s):  
Matrix Models ◽  
Critical Role ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Partition Functions ◽  
Density Matrices ◽  
General Rank ◽  
Chern Simons ◽  
The Ideal

Abstract It is known that matrix models computing the partition functions of three-dimensional $$ \mathcal{N} $$ N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.

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