G-theory: The generator of M-theory and supersymmetry

2018 ◽  
Vol 33 (10n11) ◽  
pp. 1850058
Author(s):  
Alireza Sepehri ◽  
Richard Pincak
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Negative Energy ◽  
Gauge Fields ◽  
Tensor Fields ◽  
Physical Reason ◽  
Four Dimensions ◽  
M Theory ◽  
Nonlinear Gravity

In string theory with ten dimensions, all Dp-branes are constructed from D0-branes whose action has two-dimensional brackets of Lie 2-algebra. Also, in M-theory, with 11 dimensions, all Mp-branes are built from M0-branes whose action contains three-dimensional brackets of Lie 3-algebra. In these theories, the reason for difference between bosons and fermions is unclear and especially in M-theory there is not any stable object like stable M3-branes on which our universe would be formed on it and for this reason it cannot help us to explain cosmological events. For this reason, we construct G-theory with M dimensions whose branes are formed from G0-branes with N-dimensional brackets. In this theory, we assume that at the beginning there is nothing. Then, two energies, which differ in their signs only, emerge and produce 2M degrees of freedom. Each two degrees of freedom create a new dimension and then M dimensions emerge. M-N of these degrees of freedom are removed by symmetrically compacting half of M-N dimensions to produce Lie-N-algebra. In fact, each dimension produces a degree of freedom. Consequently, by compacting M-N dimensions from M dimensions, N dimensions and N degrees of freedom is emerged. These N degrees of freedoms produce Lie-N-algebra. During this compactification, some dimensions take extra i and are different from other dimensions, which are known as time coordinates. By this compactification, two types of branes, Gp and anti-Gp-branes, are produced and rank of tensor fields which live on them changes from zero to dimension of brane. The number of time coordinates, which are produced by negative energy in anti-Gp-branes, is more sensible to number of times in Gp-branes. These branes are compactified anti-symmetrically and then fermionic superpartners of bosonic fields emerge and supersymmetry is born. Some of gauge fields play the role of graviton and gravitino and produce the supergravity. The question may arise that what is the physical reason which shows that this theory is true. We shown that G-theory can be reduced to other theories like nonlinear gravity theories in four dimensions. Also, this theory, can explain the physical properties of fermions and bosons. On the other hand, this theory explains the origin of supersymmetry. For this reason, we can prove that this theory is true. By reducing the dimension of algebra to three and dimension of world to 11 and dimension of brane to four, G-theory is reduced to F(R)-gravity.

G-theory and its reduction to F(R)-gravity in FRW universe

2018 ◽  
Vol 15 (09) ◽  
pp. 1850144 ◽  
Author(s):  
Alireza Sepehri ◽  
Richard Pincak
Keyword(s):  
General Theory ◽  
Degrees Of Freedom ◽  
Negative Energy ◽  
Positive Energy ◽  
Tensor Fields ◽  
Frw Universe ◽  
Four Dimensions ◽  
The World ◽  
The Universe

A new theory, named G(General)-theory in 14 dimensions, has been proposed that is reduced to [Formula: see text]-gravity and produces the metric of FRW universe in four dimensions. In this theory, the Universe is born in six stages. First, there is nothing in the world. Then, two strings, one with positive energy and one with negative energy in 14th, dimension are created such that the sum over their energies is zero. These strings are excited and for flowing their energies, other dimensions are produced. Second, these strings decay to G0-branes. Third, these branes join each other and construct Gp-branes which tensor fields live on. The rank of these fields can change from zero to p for [Formula: see text] and from zero to six for [Formula: see text]. Four, by compacting Gp-branes on three circles, supersymmetry is born which contains the equal number of degrees of freedom for fermions and bosons. Six, by reducing G-theory to four dimensions, FRW universe is emerges and initial tensor fields produce the predicted shape of [Formula: see text]-gravity.

Investigation of Train Dynamics in Passing Through Curves Using a Full Model

Joint Rail ◽  
2004 ◽  
Author(s):  
Mohammad Durali ◽  
Mohammad Mehdi Jalili Bahabadi
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Full Model ◽  
Bogie Frame ◽  
Nonlinear Characteristics ◽  
Train Derailment ◽  
Train Dynamics

In this article a train model is developed for studying train derailment in passing through bends. The model is three dimensional, nonlinear, and considers 43 degrees of freedom for each wagon. All nonlinear characteristics of suspension elements as well as flexibilities of wagon body and bogie frame, and the effect of coupler forces are included in the model. The equations of motion for the train are solved numerically for different train conditions. A neural network was constructed as an element in solution loop for determination of wheel-rail contact geometry. Derailment factor was calculated for each case. The results are presented and show the major role of coupler forces on possible train derailment.

scholarly journals Topologically Protected Duality on The Boundary of Maxwell-BF Theory

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 921 ◽  
Author(s):  
Alberto Blasi ◽  
Nicola Maggiore
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
General Boundary Conditions ◽  
Planar Boundary ◽  
Dimensional Theory ◽  
Electromagnetic Structure ◽  
Bf Theory ◽  
Gauge Symmetries ◽  
Dimensional Spacetime

The Maxwell-BF theory with a single-sided planar boundary is considered in Euclidean four-dimensional spacetime. The presence of a boundary breaks the Ward identities, which describe the gauge symmetries of the theory, and, using standard methods of quantum field theory, the most general boundary conditions and a nontrivial current algebra on the boundary are derived. The electromagnetic structure, which characterizes the boundary, is used to identify the three-dimensional degrees of freedom, which turn out to be formed by a scalar field and a vector field, related by a duality relation. The induced three-dimensional theory shows a strong–weak coupling duality, which separates different regimes described by different covariant actions. The role of the Maxwell term in the bulk action is discussed, together with the relevance of the topological nature of the bulk action for the boundary physics.

STOCHASTIC QUANTIZATION OF ANTISYMMETRIC TENSOR FIELDS

1986 ◽  
Vol 01 (02) ◽  
pp. 111-118 ◽  
Author(s):  
P.A. AMUNDSSEN ◽  
P.H. DAMGAARD ◽  
B.-S. SKAGERSTAM
Keyword(s):  
Stochastic Process ◽  
Initial Data ◽  
Langevin Equation ◽  
Degrees Of Freedom ◽  
Mass Shell ◽  
Symmetric Tensor ◽  
Gauge Fields ◽  
Stochastic Quantization ◽  
Tensor Fields ◽  
Abelian Gauge

We extend the stochastic quantization procedure of Parisi and Wu to the case of anti-symmetric tensor fields of arbitrary rank. It is shown that the correct number of physical degrees of freedom on mass shell is automatically projected out. The gauge degrees of freedom can be buried in the initial data of the Langevin equation describing the stochastic process in analogy with the treatment of Abelian and non-Abelian gauge fields.

scholarly journals Incidences with Curves in $\mathbb{R}^d$

10.37236/5840 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Micha Sharir ◽  
Adam Sheffer ◽  
Noam Solomon
Keyword(s):  
Recent Result ◽  
Degrees Of Freedom ◽  
Algebraic Curves ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Bounded Degree ◽  
Four Dimensions ◽  
Mild Conditions ◽  
Point Line ◽  
Special Case

We prove that the number of incidences between $m$ points and $n$ bounded-degree curves with $k$ degrees of freedom in ${\mathbb R}^d$ is\[ O\left(m^{\frac{k}{dk-d+1}+\varepsilon}n^{\frac{dk-d}{dk-d+1}}+ \sum_{j=2}^{d-1} m^{\frac{k}{jk-j+1}+\varepsilon}n^{\frac{d(j-1)(k-1)}{(d-1)(jk-j+1)}} q_j^{\frac{(d-j)(k-1)}{(d-1)(jk-j+1)}}+m+n\right),\]for any $\varepsilon>0$, where the constant of proportionality depends on $k, \varepsilon$ and $d$, provided that no $j$-dimensional surface of degree $\le c_j(k,d,\varepsilon)$, a constant parameter depending on $k$, $d$, $j$, and $\varepsilon$, contains more than $q_j$ input curves, and that the $q_j$'s satisfy certain mild conditions. This bound generalizes the well-known planar incidence bound of Pach and Sharir to $\mathbb{R}^d$. It generalizes a recent result of Sharir and Solomon concerning point-line incidences in four dimensions (where d=4 and k=2), and partly generalizes a recent result of Guth (as well as the earlier bound of Guth and Katz) in three dimensions (Guth's three-dimensional bound has a better dependency on $q_2$). It also improves a recent d-dimensional general incidence bound by Fox, Pach, Sheffer, Suk, and Zahl, in the special case of incidences with algebraic curves. Our results are also related to recent works by Dvir and Gopi and by Hablicsek and Scherr concerning rich lines in high-dimensional spaces. Our bound is not known to be tight in most cases.

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.

scholarly journals From Chern–Simons to Tomonaga–Luttinger

2018 ◽  
Vol 33 (02) ◽  
pp. 1850013 ◽  
Author(s):  
Nicola Maggiore
Keyword(s):  
Degrees Of Freedom ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons ◽  
Weyl Fermion

A single-sided boundary is introduced in the three-dimensional Chern–Simons model. It is shown that only one boundary condition for the gauge fields is possible, which plays the twofold role of chirality condition and bosonization rule for the two-dimensional Weyl fermion describing the degrees of freedom of the edge states of the Fractional Quantum Hall Effect. The symmetry on the boundary is derived, which determines the effective two-dimensional action, whose equation of motion coincides with the continuity equation of the Tomonaga–Luttinger theory. The role of Lorentz symmetry and of discrete symmetries on the boundary is also discussed.

scholarly journals N = 2 SUPERSYMMETRIC YANG–MILLS AND THE QUANTUM HALL EFFECT

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4807-4821 ◽  
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Phase Diagram ◽  
Hall Effect ◽  
Strong Coupling ◽  
Quantum Hall Effect ◽  
Modular Group ◽  
Degrees Of Freedom ◽  
Quantum Hall ◽  
Four Dimensions ◽  
Yang Mills

It is argued that there are strong similarities between the infrared physics of N = 2 supersymmetric Yang–Mills and that of the quantum Hall effect, both systems exhibit a hierarchy of vacua with a subgroup of the modular group mapping between them. The coupling flow for pure SU(2) N = 2 supersymmetric Yang–Mills in four dimensions is reexamined and an earlier suggestion in the literature, that was singular at strong coupling, is modified to a form that is well behaved at both weak and strong coupling and describes the crossover in an analytic fashion. Similarities between the phase diagram and the flow of SUSY Yang–Mills and that of the quantum Hall effect are then described, with the Hall conductivity in the latter playing the role of the θ-parameter in the former. Hall plateaux, with odd denominator filling fractions, are analogous to fixed points at strong coupling in N = 2 SUSY Yang–Mills, where the massless degrees of freedom carry an odd monopole charge.

scholarly journals On symmetries and dynamics of exotic supermultiplets

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ruben Minasian ◽  
Charles Strickland-Constable ◽  
Yi Zhang
Keyword(s):  
Field Theory ◽  
Extended Supersymmetry ◽  
Degrees Of Freedom ◽  
Three Dimensions ◽  
Tensor Fields ◽  
Time Section ◽  
Mixed Symmetry ◽  
Dimensional Gravity ◽  
M Theory ◽  
Chern Simons

Abstract Among the allowed representations of extended supersymmetry in six dimensions there are exotic chiral multiplets that, instead of a graviton, contain mixed-symmetry spin-2 tensor fields. Notably, an $$ \mathcal{N} $$ N = (4, 0) multiplet has a four index exotic graviton and it was conjectured that an interacting theory based on this multiplet could arise as a strong coupling limit of M theory compactified on T6. We present an algebraic study of these multiplets and their possible embedding into the framework of exceptional field theory, finding in particular that the six-dimensional momenta do not correspond to a conventional space-time section. When compactified on a circle, the six-dimensional multiplets give rise to the same degrees of freedom as five-dimensional supergravity theories with the same number of supersymmetries. However, by considering anomalies (computed using the product multiplets construction) and the generation of Chern-Simons couplings, we find reason to doubt that their dynamics will agree with the five-dimensional gravity theories. We propose an alternative picture, similar to F-theory, in which particular fixed-volume T3-fibered space-times play a central role, suggesting that only on compactification to three-dimensions will one make contact with the dynamics of supergravity.

scholarly journals The birth of the universe in a new G-theory approach

2017 ◽  
Vol 32 (05) ◽  
pp. 1750033 ◽  
Author(s):  
Alireza Sepehri ◽  
Richard Pincak
Keyword(s):  
Degrees Of Freedom ◽  
Boundary Surface ◽  
Negative Energy ◽  
Positive Energy ◽  
Theory Approach ◽  
Superstring Theory ◽  
Extra Energy ◽  
Extended Theories Of Gravity ◽  
The Difference ◽  
M Theory

Recently, Padmanabhan has discussed that the expansion of the cosmic space is due to the difference between the number of degrees of freedom on the boundary surface and the number of degrees of freedom in a bulk region. Now, a natural question arises that how these degrees of freedom emerged from nothing? We try to address this issue in a new theory which is more complete than M-theory and reduces to it with some limitations. In M-theory, there is no stable object like stable M3-branes that our universe is formed on it and for this reason cannot help us to explain cosmological events. In this research, we propose a new theory, named G-theory which could be the mother of M-theory and superstring theory. In G-theory, at the beginning, two types of G0-branes, one with positive energy and one with negative energy are produced from nothing in 14 dimensions. Then, these branes are compactified on three circles via two different ways (symmetrically and anti-symmetrically), and two bosonic and fermionic parts of action for M0-branes are produced. By joining M0-branes, supersymmetric Mp-branes are created which contain the equal number of degrees of freedom for fermions and bosons. Our universe is constructed on one of Mp-branes and other Mp-brane and extra energy play the role of bulk. By dissolving extra energy which is produced by compacting actions of Gp-branes, into our universe, the number of degrees of freedom on it and also its scale factor increase and universe expands. We test G-theory with observations and find that the magnitude of the slow-roll parameters and the tensor-to-scalar ratio in this model are very much smaller than one which are in agreement with predictions of experimental data. Finally, we consider the origin of the extended theories of gravity in G-theory and show that these theories could be anomaly free.

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