NONLINEAR REALIZATION OF THE $\mathcal{N}=2$, D = 6 SUPERGRAVITY

We have applied the method of dualization to construct the coset realization of the bosonic sector of the [Formula: see text], D = 6 supergravity which is coupled to a tensor multiplet. The bosonic field equations are regained through the Cartan–Maurer equation which the Cartan form satisfies. The first-order formulation of the theory is also obtained as a twisted self-duality condition within the nonlinear coset construction.

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T-dualization of Gödel string cosmologies via Poisson–Lie T-duality approach

The European Physical Journal C ◽

10.1140/epjc/s10052-020-08797-9 ◽

2021 ◽

Vol 81 (1) ◽

Author(s):

Ali Eghbali ◽

Reza Naderi ◽

Adel Rezaei-Aghdam

Keyword(s):

Lie Groups ◽

Effective Action ◽

Three Dimensional ◽

Target Space ◽

Loop Order ◽

Field Equations ◽

First Order ◽

Self Duality ◽

Duality Approach ◽

Dual Models

AbstractUsing the homogeneous Gödel spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in $$\alpha '$$ α ′ including both dilaton and axion fields. We then discuss in detail the (non-)Abelian T-dualization of Gödel string cosmologies via the Poisson–Lie (PL) T-duality approach. In studying Abelian T-duality of the models we get seven dual models in such a way that they are constructed by one-, two- and three-dimensional Abelian Lie groups acting freely on the target space manifold. The results of our study show that the Abelian T-dual models are, under some of the special conditions, self-dual; moreover, by applying the usual rules of Abelian T-duality without further corrections, we are still able to obtain two-loop solutions. We also study the Abelian T-duality of Gödel string cosmologies up to $$\alpha '$$ α ′ -corrections by using the T-duality rules at two-loop order derived by Kaloper and Meissner. Afterwards, non-Abelian duals of the Gödel spacetimes are constructed by two- and three-dimensional non-Abelian Lie groups such as $$A_2$$ A 2 , $$A_2 \oplus A_1$$ A 2 ⊕ A 1 and $$SL(2, \mathbb {R})$$ S L ( 2 , R ) . In this way, the PL self-duality of $$AdS_3 \times \mathbb {R}$$ A d S 3 × R space is discussed.

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INTEGRATED FIELD EQUATIONS OF HETEROTIC SUPERGRAVITIES

International Journal of Modern Physics A ◽

10.1142/s0217751x08038494 ◽

2008 ◽

Vol 23 (06) ◽

pp. 871-879

Author(s):

NEJAT T. YILMAZ

Keyword(s):

Low Energy ◽

Heterotic String ◽

Field Equations ◽

Bosonic Field ◽

First Order ◽

Energy Theory

The first-order bosonic field equations of the D-dimensional effective low energy theory which describes the massless background coupling of the D-dimensional fully Higgsed heterotic string are derived.

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On Conformally Covariant Spinor Field Equations

Canadian Journal of Physics ◽

10.1139/p72-280 ◽

1972 ◽

Vol 50 (18) ◽

pp. 2100-2104 ◽

Cited By ~ 2

Author(s):

Mark S. Drew

Keyword(s):

Minkowski Space ◽

Invariant Mass ◽

Spinor Field ◽

Dimensional Space ◽

Flat Space ◽

Field Equations ◽

First Order ◽

Conformally Invariant ◽

Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

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Strength of the Poincaré gauge field equations in first order formalism

Physics Letters A ◽

10.1016/0375-9601(89)90600-2 ◽

1989 ◽

Vol 139 (1-2) ◽

pp. 21-26 ◽

Cited By ~ 9

Author(s):

Michael Sué ◽

Eckehard W. Mielke

Keyword(s):

Gauge Field ◽

Field Equations ◽

First Order

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WEAK SOLUTIONS FOR WEAK SINGULARITIES

International Journal of Modern Physics A ◽

10.1142/s0217751x02011965 ◽

2002 ◽

Vol 17 (20) ◽

pp. 2769-2769

Author(s):

B. C. NOLAN

Keyword(s):

Existence And Uniqueness ◽

Finite Measure ◽

Generalized Solutions ◽

Functions Of Bounded Variation ◽

Field Equations ◽

Finite Radius ◽

Locally Finite ◽

Naked Singularities ◽

First Order ◽

Bounded Functions

We revisit the problem of the development of singularities in the gravitational collapse of an inhomogeneous dust sphere. As shown by Yodzis et al1, naked singularities may occur at finite radius where shells of dust cross one another. These singularities are gravitationally weak 2, and it has been claimed that at these singularities, the metric may be written in continuous form 2, with locally L∞ connection coefficients 3. We correct these claims, and show how the field equations may be reformulated as a first order, quasi-linear, non-conservative, non-strictly hyperbolic system. We discuss existence and uniqueness of generalized solutions of this system using bounded functions of bounded variation (BV) 4, where the product of a BV function and the derivative of another BV function may be interpreted as a locally finite measure. The solutions obtained provide a dynamical extension to the future of the singularity.

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FUZZY INSTANTONS

International Journal of Modern Physics A ◽

10.1142/s0217751x02010595 ◽

2002 ◽

Vol 17 (15) ◽

pp. 2095-2111 ◽

Cited By ~ 10

Author(s):

HARALD GROSSE ◽

MARCO MACEDA ◽

JOHN MADORE ◽

HAROLD STEINACKER

Keyword(s):

Real Number ◽

Matrix Model ◽

Matrix Algebra ◽

Quantization Condition ◽

Constant Factor ◽

Arbitrary Real Number ◽

Self Duality ◽

Duality Condition ◽

The Matrix ◽

Fixed Constant

We present a series of instanton-like solutions to a matrix model which satisfy a self-duality condition and possess an action whose value is, to within a fixed constant factor, an integer l2. For small values of the dimension n2 of the matrix algebra the integer resembles the result of a quantization condition but as n → ∞ the ratio l/n can tend to an arbitrary real number between zero and one.

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Pair creation of neutral Dirac particle in (1 + 2)d noncommutative spacetime

Modern Physics Letters A ◽

10.1142/s0217732318500177 ◽

2018 ◽

Vol 33 (03) ◽

pp. 1850017 ◽

Cited By ~ 2

Author(s):

B. Hamil

Keyword(s):

Neutral Particle ◽

Pair Creation ◽

Dirac Particle ◽

Bogoliubov Transformation ◽

Quantum Fields ◽

Field Equations ◽

First Order ◽

Noncommutative Spacetime

In this paper, we study the influence of the noncommutativity on the pairs creation of neutral particle–antiparticle in (1 + 2)d. Using the Seiberg–Witten maps, the modified Euler–Lagrange field equations up to first-order in the noncommutativity, parameter [Formula: see text] is obtained and the Nikishov method based on Bogoliubov transformation is applied to calculate the density number of created neutral fermions. It is shown that the noncommutativity amplifies the density number N. In addition, when [Formula: see text], we obtain the known results corresponding to the undeformed quantum fields.

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