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.

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 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.

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 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 Hidden conformal symmetry of smooth braneworld scenarios

2019 ◽  
Vol 35 (08) ◽  
pp. 2050039
Author(s):  
G. Alencar ◽  
M. Gogberashvili
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Conformal Symmetry ◽  
Scalar Fields ◽  
Internal Symmetry ◽  
Gauge Condition ◽  
Minimal Coupling ◽  
Field Action ◽  
Hyperbolic Potential ◽  
Natural Way

In this paper, we generalize our previous model ( arXiv:1705.09331 ), on a hidden conformal symmetry of smooth braneworld scenarios, to the case with two real scalar fields non-minimally coupled to gravity. The gauge condition reduces the action of the system to the action where gravity minimally couples to one of the scalar fields, plus a cosmological constant. We show that, depending on the internal symmetry of the scalar fields, the two possibilities, SO(2) or SO(1, 1), emerge. In the SO(2) case, we get a ghost-like scalar field action, which can describe two models — Standing Wave and Sine-Gordon smooth braneworlds. For the SO(1, 1) case we get the standard sign for the kinetic part of the scalar field. By breaking the SO(1, 1) symmetry (but keeping the conformal one) we are able to get two Randall–Sundrum models, with a non-minimal coupling and with a scalar field having hyperbolic potential. We conclude that this method can be seen as a solution-generating technique and a natural way to introduce nontrivial scalar fields that can provide smooth braneworld models.

scholarly journals New AdS4 vacua in dyonic ISO(7) gauged supergravity

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Nikolay Bobev ◽  
Thomas Fischbacher ◽  
Fridrik Freyr Gautason ◽  
Krzysztof Pilch
Keyword(s):  
Scalar Fields ◽  
Global Symmetry ◽  
Supergravity Theory

Abstract We identify 219 AdS4 solutions in four-dimensional dyonically gauged ISO(7) $$ \mathcal{N} $$ N = 8 supergravity and present some of their properties. One of the new solutions preserves $$ \mathcal{N} $$ N = 1 supersymmetry and provides a rare explicit example of an AdS4 vacuum dual to a 3d SCFT with no continuous global symmetry. There are also two new non-supersymmetric solutions for which all 70 scalar fields in the supergravity theory have masses above the BF bound. All of these AdS4 solutions can be uplifted to massive type IIA supergravity. Motivated by this we present the low lying operator spectra of the dual 3d CFTs for all known supersymmetric AdS4 solutions in the theory and organize them into superconformal multiplets.

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 ON CANONICAL QUANTIZATION OF THE GAUGED WZW MODEL WITH PERMUTATION BRANES

2011 ◽  
Vol 26 (26) ◽  
pp. 4647-4660
Author(s):  
GOR SARKISSIAN
Keyword(s):  
Riemann Surface ◽  
Phase Space ◽  
Boundary Conditions ◽  
Canonical Quantization ◽  
Simons Theory ◽  
Gauge Fields ◽  
Time Line ◽  
Chern Simons ◽  
Special Case ◽  
Chern Simons Theory

In this paper we perform canonical quantization of the product of the gauged WZW models on a strip with boundary conditions specified by permutation branes. We show that the phase space of the N-fold product of the gauged WZW model G/H on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of the double Chern–Simons theory on a sphere with N holes times the time-line with G and H gauge fields both coupled to two Wilson lines. For the special case of the topological coset G/G we arrive at the conclusion that the phase space of the N-fold product of the topological coset G/G on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of Chern–Simons theory on a Riemann surface of the genus N-1 times the time-line with four Wilson lines.

SUSY coherent states and enhanced canonical quantizations for Pauli model

2021 ◽  
pp. 2150105
Author(s):  
Jean Vignon Hounguevou ◽  
Daniel Sabi Takou ◽  
Gabriel Y. H. Avossevou
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coherent States ◽  
Differential Operators ◽  
Canonical Quantization ◽  
Point Of View ◽  
Supersymmetric Quantum Mechanics ◽  
Geometric Properties

In this paper, we study coherent states for a quantum Pauli model through supersymmetric quantum mechanics (SUSYQM) method. From the point of view of canonical quantization, the construction of these coherent states is based on the very important differential operators in SUSYQM call factorization operators. The connection between classical and quantum theory is given by using the geometric properties of these states.

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