Four-dimensional vector multiplets in arbitrary signature (II)

2020 ◽  
Vol 17 (10) ◽  
pp. 2050151 ◽  
Author(s):  
V. Cortés ◽  
L. Gall ◽  
T. Mohaupt
Keyword(s):  
Dimensional Reduction ◽  
Companion Paper ◽  
Lie Superalgebras ◽  
Dimensional Vector ◽  
Vector Multiplet ◽  
Four Dimensions ◽  
Underlying Space ◽  
Arbitrary Signature ◽  
Minkowski Signature ◽  
Field Redefinition

Following the classification up to isomorphism of [Formula: see text] Poincaré Lie superalgebras in four dimensions with arbitrary signature obtained in a companion paper, we present off-shell vector multiplet representations and invariant Lagrangians realizing these algebras. By dimensional reduction of five-dimensional off-shell vector multiplets, we obtain two representations in each four-dimensional signature. In Euclidean and neutral signature, these representations can be mapped to each other by a field redefinition induced by the action of the Schur group on the space of superbrackets. In Minkowski signature, we show that the superbrackets underlying the two vector multiplet representations belong to distinct open orbits of the Schur group and are therefore inequivalent. Our formalism allows to answer questions about the possible relative signs between terms in the Lagrangian systematically by relating them to the underlying space of superbrackets.

scholarly journals Four-dimensional vector multiplets in arbitrary signature (I)

2020 ◽  
Vol 17 (10) ◽  
pp. 2050150 ◽  
Author(s):  
V. Cortés ◽  
L. Gall ◽  
T. Mohaupt
Keyword(s):  
Vector Space ◽  
Classification Problem ◽  
Lie Superalgebras ◽  
Symmetry Groups ◽  
Sufficient Condition ◽  
Dimensional Vector ◽  
Necessary And Sufficient Condition ◽  
Arbitrary Signature ◽  
Necessary And Sufficient ◽  
R Symmetry

We derive a necessary and sufficient condition for Poincaré Lie superalgebras in any dimension and signature to be isomorphic. This reduces the classification problem, up to certain discrete operations, to classifying the orbits of the Schur group on the vector space of superbrackets. We then classify four-dimensional [Formula: see text] supersymmetry algebras, which are found to be unique in Euclidean and in neutral signature, while in Lorentz signature there exist two algebras with R-symmetry groups [Formula: see text] and [Formula: see text], respectively.

The quantum consistency of the 12-dimensional theory

2016 ◽  
Vol 31 (04n05) ◽  
pp. 1650010
Author(s):  
Simon Davis
Keyword(s):  
Cosmological Constant ◽  
Moduli Space ◽  
Dimensional Reduction ◽  
Text Structure ◽  
Three Dimensions ◽  
Supersymmetric Theory ◽  
Particle Spectrum ◽  
Dimensional Theory ◽  
Cosmological Constant Problem ◽  
Four Dimensions

By considering the 12-dimensional superalgebra, inferences are drawn about the finiteness of the 12-dimensional theory unifying the superstring models. The dimensional reduction of the nonsupersymmetric theory in four dimensions to a supersymmetric action in three dimensions is established for the bosonic sector. It is found to be the quotient by [Formula: see text] of the integration over the fiber coordinate of a theory with [Formula: see text] supersymmetry. Consequently, a flow on the moduli space of Spin(7) manifolds from a [Formula: see text] structure with [Formula: see text] supersymmetry yielding a phenomelogically realistic particle spectrum to a [Formula: see text] holonomy manifold compatible with supersymmetry in three dimensions and a nonsupersymmetric action in four dimensions, solving the quantum cosmological constant problem, is proven to exist. The projection of the representations of the [Formula: see text] superalgebra of the 12-dimensional theory to four dimensions include nonperturbative string solitons that are more stable because the dynamics is described by supersymmetric theory with a higher degree of finiteness.

Supplement to “The group E6(q) and graphs with a locally linear group of automorphisms” by V. I. Trofimov and R. M. Weiss

2009 ◽  
Vol 148 (1) ◽  
pp. 33-45 ◽  
Author(s):  
V. I. TROFIMOV
Keyword(s):  
Normal Subgroup ◽  
Vector Space ◽  
Permutation Group ◽  
Linear Group ◽  
Prime Power ◽  
Companion Paper ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Group Of Automorphisms ◽  
Locally Linear

AbstractLet q be a prime power and let G be a group acting faithfully and vertex transitively on a graph such that for each vertex x, the stabilizer Gx is finite and contains a normal subgroup inducing on the set of neighbours of x a permutation group isomorphic to the linear group L5(q) acting on the 2-dimensional subspaces of a 5-dimensional vector space over Fq. In a companion paper, it is shown, except in some special situations where q = 2, that the kernel of the action of a vertex stabilizer Gx on the ball of radius 3 around x is trivial. In this paper we show that these special situations cannot occur.

scholarly journals Improved Passive Microwave Retrievals of Rain Rate over Land and Ocean. Part I: Algorithm Description

2013 ◽  
Vol 30 (11) ◽  
pp. 2493-2508 ◽  
Author(s):  
Grant W. Petty ◽  
Ke Li
Keyword(s):  
Dimensional Reduction ◽  
Rain Rate ◽  
A Priori ◽  
Companion Paper ◽  
Passive Microwave ◽  
Effective Density ◽  
Retrieval Algorithm ◽  
Current Standard ◽  
Surface Rain Rate ◽  
Microwave Imager

Abstract A new approach to passive microwave retrievals of precipitation is described that relies on an objective dimensional reduction procedure to filter, normalize, and decorrelate geophysical background noise while retaining the majority of radiometric information concerning precipitation. The dimensional reduction also sharply increases the effective density of any a priori database used in a Bayesian retrieval scheme. The method is applied to passive microwave data from the Tropical Rainfall Measuring Mission (TRMM), reducing the original nine channels to three “pseudochannels” that are relatively insensitive to most background variations occurring within each of seven surface classes (one ocean plus six land and coast) for which they are defined. These pseudochannels may be used in any retrieval algorithm, including the current standard Goddard profiling algorithm (GPROF), in place of the original channels. The same methods are also under development for the Global Precipitation Measurement (GPM) Core Observatory Microwave Imager (GMI). Starting with the pseudochannel definitions, a new Bayesian algorithm for retrieving the surface rain rate is described. The algorithm uses an a priori database populated with matchups between the TRMM precipitation radar (PR) and the TRMM Microwave Imager (TMI). The explicit goal of the algorithm is to retrieve the PR-derived best estimate of the surface rain rate in portions of the TMI swath not covered by the PR. A unique feature of the new algorithm is that it provides robust posterior Bayesian probabilities of pixel-averaged rain rate exceeding various thresholds. Validation and intercomparison of the new algorithm is the subject of a companion paper.

NEW N=2 MATTER COUPLINGS IN SUPERSPACE

1988 ◽  
Vol 03 (03) ◽  
pp. 703-719 ◽  
Author(s):  
S.V. KETOV
Keyword(s):  
Sigma Models ◽  
Dimensional Reduction ◽  
Two Dimensional ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Four Dimensions ◽  
Yang Mills ◽  
Quaternionic Kähler ◽  
Nonlinear Sigma Models

The generalized N=2 tensor multiplets are defined and the corresponding interacting models are constructed in N=2 superspace in four dimensions. The couplings with the N=2 Yang-Mills fields are given too. The two-dimensional nonlinear N=4 supersymmetric sigma models obtained via dimensional reduction are known to be finite. The construction gives rise to a variety of explicitly constructed quaternionic-Kähler metrics. Some two-dimensional N=4 supersymmetric sigma models with nonvanishing torsion turn out to be equivalent to the ordinary N=4 hyper-Kähler nonlinear sigma models without torsion.

On ω-Lie superalgebras

2018 ◽  
Vol 17 (11) ◽  
pp. 1850212
Author(s):  
Jia Zhou ◽  
Liangyun Chen ◽  
Yao Ma ◽  
Bing Sun
Keyword(s):  
Bilinear Form ◽  
Characteristic Zero ◽  
Jacobi Identity ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Complex Numbers ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional

Let [Formula: see text] be a finite-dimensional vector space over a field [Formula: see text] of characteristic zero, [Formula: see text] an anti-commutative product on [Formula: see text] and [Formula: see text] a bilinear form on [Formula: see text]. The triple [Formula: see text] is called an [Formula: see text]-Lie algebra if [Formula: see text] (graded [Formula: see text]-Jacobi identity) for all [Formula: see text] In this paper, we introduce the notion of an [Formula: see text]-Lie superalgebra. We study elementary properties and representations of [Formula: see text]-Lie superalgebras. We classify all 3- and 4-dimensional [Formula: see text]-Lie superalgebras over the field of complex numbers.

Gravitational aspects of a conformally coupled field theory in five space–time dimensions

1982 ◽  
Vol 383 (1785) ◽  
pp. 457-464 ◽  
Keyword(s):  
Field Theory ◽  
Vacuum State ◽  
Space Time ◽  
Large Space ◽  
Four Dimensions ◽  
Underlying Space ◽  
Higher Dimensional ◽  
Newtonian Constant ◽  
Cosmological Constants ◽  
Newtonian Gravitational Constant

Where a field with broken symmetry is coupled to the scalar curvature of the underlying space–time, we may expect, in general, that the resulting effective Newtonian gravitational constant is dependent upon the vacuum state of the field theory. Except in regions of large space–time curvature or high temperature, physical field theories in four dimensions predict only negligible vacuum contributions to the Newtonian constant whereas in the higher-dimensional model considered here, this is not the case. We discover also that both the Newtonian and the cosmological constants may be influenced by the presence of an electromagnetic field.

The group E6(q) and graphs with a locally linear group of automorphisms

2009 ◽  
Vol 148 (1) ◽  
pp. 1-32 ◽  
Author(s):  
V. I. TROFIMOV ◽  
R. M. WEISS
Keyword(s):  
Normal Subgroup ◽  
Vector Space ◽  
Permutation Group ◽  
Linear Group ◽  
Prime Power ◽  
Companion Paper ◽  
Dimensional Vector ◽  
Exceptional Group ◽  
Dimensional Vector Space ◽  
Group Of Automorphisms

AbstractLet q be a prime power and let G be a group acting faithfully and vertex transitively on a graph such that for each vertex x, the stabilizer Gx is finite and contains a normal subgroup inducing on the set of neighbours of x a permutation group isomorphic to the linear group L5(q) acting on the 2-dimensional subspaces of a 5-dimensional vector space over Fq. It is shown, except in some special situations where q = 2, that the kernel of the action of a vertex stabilizer Gx on the ball of radius 3 around x is trivial. (These special situations are eliminated in a companion paper by the first author.) An example coming from the exceptional group E6(q) shows that the kernel of the action of Gx on the ball of radius 2 around x can be non-trivial.

scholarly journals Logarithmic corrections to the entropy of non-extremal black holes in $$ \mathcal{N} $$ = 1 Einstein-Maxwell supergravity

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Gourav Banerjee ◽  
Binata Panda
Keyword(s):  
Black Holes ◽  
Four Dimensions ◽  
The Third ◽  
Link Type ◽  
Logarithmic Corrections ◽  
Extremal Black Holes ◽  
Field Redefinition

Abstract We reviewed the field redefinition approach of Seeley-DeWitt expansion for the determination of Seeley-DeWitt coefficients from arXiv:1505.01156. We apply this approach to compute the first three Seeley-DeWitt coefficients for “non-minimal” $$ \mathcal{N} $$ N = 1 Einstein-Maxwell supergravity in four dimensions. Finally, we use the third coefficient for the computation of the logarithmic corrections to the Bekenstein-Hawking entropy of non-extremal black holes following arXiv:1205.0971. We determine the logarithmic corrections for non-extremal Kerr-Newman, Kerr, Reissner-Nordström and Schwarzschild black holes in “non-minimal” $$ \mathcal{N} $$ N = 1, d = 4 Einstein-Maxwell supergravity.

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