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 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 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.

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 DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

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 PROBING THE FROISSART BOUND FOR MODELS WITH CHARGED VECTOR FIELDS IN D=3

1994 ◽  
Vol 09 (18) ◽  
pp. 1695-1700 ◽  
Author(s):  
O.M. DEL CIMA
Keyword(s):  
Asymptotic Behavior ◽  
Scattering Amplitudes ◽  
Gauge Field ◽  
Vector Fields ◽  
Three Dimensional ◽  
Tree Level ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Maxwell Fields ◽  
Chern Simons

One discusses the tree-level unitarity and presents asymptotic behavior of scattering amplitudes for three-dimensional gauge-invariant models where complex Chern- Simons-Maxwell fields (with and without a Proca-like mass) are coupled to an Abelian gauge field.

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.

scholarly journals ARE THERE ANY NEW VACUA OF GAUGED ${\mathcal N}=8$ SUPERGRAVITY IN FOUR DIMENSIONS?

2010 ◽  
Vol 25 (09) ◽  
pp. 1819-1851 ◽  
Author(s):  
CHANGHYUN AHN ◽  
KYUNGSUNG WOO
Keyword(s):  
Domain Wall ◽  
Cosmological Constant ◽  
Critical Point ◽  
Scalar Potential ◽  
Three Dimensional ◽  
Scalar Fields ◽  
Four Dimensions ◽  
Matter Theory ◽  
Chern Simons ◽  
Constraint Surface

We consider the most general SU(3) singlet space of gauged [Formula: see text] supergravity in four dimensions. The SU(3)-invariant six scalar fields in the theory can be viewed in terms of six real four-forms. By exponentiating these four-forms, we eventually obtain the new scalar potential. For the two extreme limits, we reproduce the previous results found by Warner in 1983. In particular, for the [Formula: see text] critical point, we find the constraint surface parametrized by three scalar fields on which the cosmological constant has the same value. We obtain the BPS domain-wall solutions for restricted scalar submanifold. We also describe the three-dimensional mass-deformed superconformal Chern–Simons matter theory dual to the above supersymmetric flows in four dimensions.

CANONICAL QUANTIZATION OF BIANCHI CLASS A MODELS IN N=2 SUPERGRAVITY

1996 ◽  
Vol 11 (03) ◽  
pp. 227-245 ◽  
Author(s):  
A.D.Y. CHENG ◽  
P.V. MONIZ
Keyword(s):  
Cosmological Constant ◽  
Canonical Quantization ◽  
Constant Term ◽  
Scalar Fields ◽  
Internal Symmetry ◽  
Point Of View ◽  
Supergravity Theory ◽  
Class A ◽  
Physical Validity ◽  
Chern Simons

The theory of N=2 supergravity is applied to Bianchi class A models. Their canonical formulation is addressed for two cases: when the O(2) internal symmetry is (a) global or (b) local. A cosmological constant and mass-like term for the gravitinos are required in the latter but are absent in the former. For the case of global O(2) symmetry, it is shown that the presence of a Maxwell field in the supersymmetry constraints is sufficient to imply a non-conservation of the fermionic number. This effect corresponds to a mixing between different Lorentz invariant fermionic sectors in the wave function of the universe. It is similar to what a cosmological constant term would have caused but considerably different from what occurs in FRW and Bianchi models in N=1 supergravity with scalar fields and fermionic partners. The nonconservation effect is interpreted from the point of view of N=2 supergravity theory. For case (b), we obtain the more general solution of the gauge constraint. Possible quantum physical states are then discussed regarding previous works where Ashtekar variables have been used. These states can be obtained from an N=2 supersymmetric Chern-Simons functional. Some comments concerning the physical validity of the Chern-Simons solution and its transformation into metric representation variables are included.

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