scholarly journals A NOTE ON SUPERSYMMETRIC WZW TERM IN FOUR DIMENSIONS

2000 ◽  
Vol 15 (38n39) ◽  
pp. 2327-2333 ◽  
Author(s):  
MUNETO NITTA
Keyword(s):  
Equations Of Motion ◽  
Total Derivative ◽  
Four Dimensions ◽  
Anomalous Term ◽  
Higher Derivative ◽  
Derivative Term ◽  
Chiral Superfields

We reconsider the supersymmetric Wess–Zumino–Witten (SWZW) term in four dimensions. It has been known that the manifestly supersymmetric form of the SWZW term includes derivative terms on auxiliary fields, the highest components of chiral superfields, and then we cannot eliminate them by their equations of motion. We discuss a possibility for the elimination of such derivative terms by adding total derivative terms. Although most of the derivative terms can be eliminated in this way, we find that all the derivative terms can be canceled, if and only if an anomalous term in SWZW term vanishes. As a by-product, we find the first example of a higher derivative term free from such problem.

scholarly journals Higher-derivative f(R,□R,T) theories of gravity

2017 ◽  
Vol 26 (03) ◽  
pp. 1750024 ◽  
Author(s):  
M. J. S. Houndjo ◽  
M. E. Rodrigues ◽  
N. S. Mazhari ◽  
D. Momeni ◽  
R. Myrzakulov
Keyword(s):  
Modified Gravity ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
De Sitter ◽  
Higher Derivative ◽  
Stress Energy ◽  
Derivative Term ◽  
Theories Of Gravity ◽  
Tensor Formula ◽  
Stress Energy Momentum Tensor

In literature, there is a model of modified gravity in which the matter Lagrangian is coupled to the geometry via trace of the stress–energy–momentum tensor [Formula: see text]. This type of modified gravity is denoted [Formula: see text] in which [Formula: see text] is Ricci scalar [Formula: see text]. We extend manifestly this model to include the higher derivative term [Formula: see text]. We derived equations of motion (EOM) for the model by starting from the basic variational principle. Later we investigate FLRW cosmology for our model. We show that de Sitter (dS) solution is unstable for a generic type of [Formula: see text] model. Furthermore we investigate an inflationary scenario based on this model. A graceful exit from inflation is guaranteed in this type of modified gravity.

scholarly journals Actions, topological terms and boundaries in first-order gravity: A review

2016 ◽  
Vol 25 (04) ◽  
pp. 1630011 ◽  
Author(s):  
Alejandro Corichi ◽  
Irais Rubalcava-García ◽  
Tatjana Vukašinac
Keyword(s):  
Boundary Conditions ◽  
Symplectic Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Action Principle ◽  
Internal Boundary ◽  
Four Dimensions ◽  
First Order ◽  
Conserved Charges ◽  
Boundary Terms

In this review, we consider first-order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad [Formula: see text] and a [Formula: see text] connection [Formula: see text]. We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein–Hilbert–Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space [Formula: see text] is given by solutions to the equations of motion. For each of the possible terms contributing to the action, we consider the well-posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges. The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way, we point out and clarify some issues that have not been clearly understood in the literature.

UNCONSTRAINED HIGHER SPINS IN FOUR DIMENSIONS

2011 ◽  
Vol 08 (03) ◽  
pp. 511-556 ◽  
Author(s):  
GIUSEPPE BANDELLONI
Keyword(s):  
Equations Of Motion ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Geometrical Meaning ◽  
Four Dimensions ◽  
Spin Field ◽  
Angular Momenta ◽  
Higher Spin ◽  
Spin Fields ◽  
The Right

The relativistic symmetric tensor fields are, in four dimensions, the right candidates to describe Higher Spin Fields. Their highest spin content is isolated with the aid of covariant conditions, discussed within a group theory framework, in which auxiliary fields remove the lower intrinsic angular momenta sectors. These conditions are embedded within a Lagrangian Quantum Field theory which describes an Higher Spin Field interacting with a Classical background. The model is invariant under a (B.R.S.) symmetric unconstrained tensor extension of the reparametrization symmetry, which include the Fang–Fronsdal algebra in a well defined limit. However, the symmetry setting reveals that the compensator field, which restore the Fang–Fronsdal symmetry of the free equations of motion, is in the existing in the framework and has a relevant geometrical meaning. The Ward identities coming from this symmetry are discussed. Our constraints give the result that the space of the invariant observables is restricted to the ones constructed with the Highest Spin Field content. The quantum extension of the symmetry reveals that no new anomaly is present. The role of the compensator field in this result is fundamental.

scholarly journals Twisted characters and holomorphic symmetries

2020 ◽  
Vol 110 (10) ◽  
pp. 2779-2853
Author(s):  
Ingmar Saberi ◽  
Brian R. Williams
Keyword(s):  
Riemann Surfaces ◽  
Flavor Symmetry ◽  
Four Dimensions ◽  
Infinite Dimensional ◽  
Topological Quantum ◽  
Hopf Manifolds ◽  
Local Operators ◽  
Free Fields ◽  
Supersymmetric Theories ◽  
Chiral Superfields

Abstract We consider holomorphic twists of arbitrary supersymmetric theories in four dimensions. Working in the BV formalism, we rederive classical results characterizing the holomorphic twist of chiral and vector supermultiplets, computing the twist explicitly as a family over the space of nilpotent supercharges in minimal supersymmetry. The BV formalism allows one to work with or without auxiliary fields, according to preference; for chiral superfields, we show that the result of the twist is an identical BV theory, the holomorphic $$\beta \gamma $$ β γ system with superpotential, independent of whether or not auxiliary fields are included. We compute the character of local operators in this holomorphic theory, demonstrating agreement of the free local operators with the usual index of free fields. The local operators with superpotential are computed via a spectral sequence and are shown to agree with functions on a formal mapping space into the derived critical locus of the superpotential. We consider the holomorphic theory on various geometries, including Hopf manifolds and products of arbitrary pairs of Riemann surfaces, and offer some general remarks on dimensional reductions of holomorphic theories along the $$(n-1)$$ ( n - 1 ) -sphere to topological quantum mechanics. We also study an infinite-dimensional enhancement of the flavor symmetry in this example, to a recently studied central extension of the derived holomorphic functions with values in the original Lie algebra, that generalizes the familiar Kac–Moody enhancement in two-dimensional chiral theories.

scholarly journals A COHOMOLOGICAL INTERPRETATION OF THE MIGDAL–MAKEENKO EQUATIONS

2002 ◽  
Vol 17 (08) ◽  
pp. 481-489 ◽  
Author(s):  
A. AGARWAL ◽  
S. G. RAJEEV
Keyword(s):  
Lie Algebra ◽  
Equations Of Motion ◽  
Generating Functional ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Change Of Variables ◽  
Anomalous Term ◽  
Large N ◽  
Infinite Dimensional Lie Algebra ◽  
Cohomological Interpretation

The equations of motion of quantum Yang–Mills theory (in the planar "large-N" limit), when formulated in loop-space are shown to have an anomalous term, which makes them analogous to the equations of motion of WZW models. The anomaly is the Jacobian of the change of variables from the usual ones, i.e. the connection one-form A, to the holonomy U. An infinite-dimensional Lie algebra related to this change of variables (the Lie algebra of loop substitutions) is developed, and the anomaly is interpreted as an element of the first cohomology of this Lie algebra. The Migdal–Makeenko equations are shown to be the condition for the invariance of the Yang–Mills generating functional Z under the action of the generators of this Lie algebra. Connections of this formalism to the collective field approach of Jevicki and Sakita are also discussed.

QUANTUM GRAVITATIONAL EFFECTS AND THE COMPACTIFICATION SCALE IN THE HETEROTIC SUPERSTRING THEORY

1999 ◽  
Vol 14 (01) ◽  
pp. 119-127 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Black Holes ◽  
Wormhole Solution ◽  
Superstring Theory ◽  
Gravitational Effects ◽  
Parity Symmetry ◽  
Anomalous Term ◽  
Higher Derivative ◽  
Euclidean Action ◽  
Model Independent ◽  
Virtual Black Holes

It is known that quantum gravitational effects due to virtual black holes and wormholes can exert an important influence by violating global symmetries. These processes have recently been investigated by Kallosh et al., who found, for the heterotic superstring theory, that there is a sufficient suppression of deleterious effects via the Euclidean action S E from the presence of higher-derivative terms occurring as a topological invariant, the Euler characteristic χ, regardless of the precise details of the underlying wormhole solution. Here, we consider this result further, arguing, in the absence of inflation, that there are no large wormholes in the heterotic superstring theory for which the wormhole action per se is large enough, topological suppression being the only possibility. The model-independent superstring axion may be susceptible to these corrections, because, as shown by Witten, it possesses a non-linearly realized, global U(1) symmetry, being a real scalar field coupled to the anomalous term [Formula: see text] from the outset, and they are relevant to the R-parity symmetry. Allowing for the unknown effect of the black holes, however, we conjecture that these quantum gravitational effects produce no observable consequences.

scholarly journals Scalar-Torsion Theories in Four Dimensional Static Spacetimes

2021 ◽  
Vol 32 (2) ◽  
pp. 12-15
Author(s):  
Mulyanto . ◽  
Fiki Taufik Akbar ◽  
Bobby Eka Gunara
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Exact Solution ◽  
Master Equation ◽  
Equations Of Motion ◽  
Scalar Potential ◽  
Torsion Theory ◽  
Linear Ordinary Differential Equation ◽  
Four Dimensions ◽  
Torsion Theories

In this paper, we consider a class of static spacetimes scalar-torsion theories in four dimensioanal static spacetimes with the scalar potential turned on. We discover that the 2-dimensional submanifold must admit constant triplet structures, one of which is the torsion scalar. This indicates that these equations of motion can be reduced to a single highly non-linear ordinary differential equation known as the master equation. Then, we show that there are no exact solution of the scalar-torsion theory in four dimensions considering the Sinh-Gordon potential.

scholarly journals A pure connection formulation with real fields for gravity

2020 ◽  
pp. 2050114
Author(s):  
J. E. Rosales-Quintero
Keyword(s):  
Lie Algebra ◽  
Lagrange Multipliers ◽  
General Class ◽  
Equations Of Motion ◽  
Conformally Flat ◽  
Einstein Manifolds ◽  
De Sitter ◽  
Killing Form ◽  
Dual Approach ◽  
Four Dimensions

We study an [Formula: see text] pure connection formulation in four dimensions for real-valued fields, inspired by the Capovilla, Dell and Jacobson complex self-dual approach. By considering the CMPR BF action, also, taking into account a more general class of the Cartan–Killing form for the Lie algebra [Formula: see text] and by refining the structure of the Lagrange multipliers, we integrate out the metric variables in order to obtain the pure connection action. Once we have obtained this action, we impose certain restrictions on the Lagrange multipliers, in such a way that the equations of motion led us to a family of torsionless conformally flat Einstein manifolds, parametrized by two numbers. Finally, we show that, by a suitable choice of parameters, self-dual spaces (Anti-) de Sitter can be obtained.

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