scholarly journals GAUGED WZW MODELS VIA EQUIVARIANT COHOMOLOGY

2011 ◽  
Vol 26 (18) ◽  
pp. 1343-1352
Author(s):  
HUGO GARCÍA-COMPEÁN ◽  
PABLO PANIAGUA
Keyword(s):  
Equivariant Cohomology ◽  
Higher Dimensions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Anomaly Cancellation ◽  
Gauge Invariant ◽  
Cancellation Condition ◽  
Four Dimensions ◽  
Invariant Extension

The problem of finding a systematic computation of the gauge-invariant extension of WZW term by using equivariant cohomology is addressed. Witten's analysis for the two-dimensional case is extended to higher dimensions, in particular to four dimensions. It is shown that Cartan's model is used to find the anomaly cancellation condition while Weil's model is more appropriated to express the gauge-invariant extension of the WZW term. In the process we point out that both models are also useful to emphasize some nice relations with the Abelian anomaly.

scholarly journals Random Harmonic Functions in Growth Spaces and Bloch-type Spaces

2014 ◽  
Vol 66 (2) ◽  
pp. 284-302
Author(s):  
Kjersti Solberg Eikrem
Keyword(s):  
Unit Ball ◽  
Unit Disk ◽  
Spherical Harmonics ◽  
Harmonic Functions ◽  
Higher Dimensions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Doubling Condition ◽  
Similar Characterization ◽  
Type Spaces

Abstract. Let h∞v (D) and h∞v (B) be the spaces of harmonic functions in the unit disk and multidimensional unit ball admitting a two-sided radial majorant v(r). We consider functions v that fulfill a doubling condition. In the two-dimensional case letwhere ξ ={ξji} is a sequence of random subnormal variables and aji are real. In higher dimensions we consider series of spherical harmonics. We will obtain conditions on the coefficients aji that imply that u is in h∞v (B) almost surely. Our estimate improves previous results by Bennett, Stegenga, and Timoney, and we prove that the estimate is sharp. The results for growth spaces can easily be applied to Bloch-type spaces, and we obtain a similar characterization for these spaces that generalizes results by Anderson, Clunie, and Pommerenke and by Guo and Liu.

scholarly journals On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Guojun Yang
Keyword(s):  
Higher Dimensions ◽  
Riemannian Metric ◽  
Dimensional Case ◽  
Finsler Metrics ◽  
Two Dimensional ◽  
Local Structures ◽  
Projectively Flat

We study a class of two-dimensional Finsler metrics defined by a Riemannian metricαand a 1-formβ. We characterize those metrics which are Douglasian or locally projectively flat by some equations. In particular, it shows that the known fact thatβis always closed for those metrics in higher dimensions is no longer true in two-dimensional case. Further, we determine the local structures of two-dimensional (α,β)-metrics which are Douglasian, and some families of examples are given for projectively flat classes withβbeing not closed.

HELICITY-CHIRALITY CORRELATION AND WEINBERG’S CONSTRAINT IN HIGHER DIMENSIONS

1992 ◽  
Vol 07 (26) ◽  
pp. 6679-6689
Author(s):  
VINEER BHANSALI
Keyword(s):  
Lorentz Group ◽  
Higher Dimensions ◽  
Gauge Invariant ◽  
Four Dimensions ◽  
Highest Weight ◽  
Invariant Representations ◽  
Massless Fields

We show a simple correspondence between massless fields transforming as representations of the higher (even) dimensional Lorentz group and highest weight states of the little group, under the assumption that the Euclidean translations of the little group act trivially. This yields the generalization to higher dimensions of Weinberg’s (1964) constraint which establishes a connection between helicity and chirality in four dimensions. As a bonus, we obtain restrictions on “gauge invariant” representations for physical particles.

H → γγ, gauge invariance, and the hierarchy problem

2016 ◽  
Vol 31 (26) ◽  
pp. 1630046 ◽  
Author(s):  
Jennifer Kile
Keyword(s):  
Gauge Invariance ◽  
Dimensional Regularization ◽  
Hierarchy Problem ◽  
Anomaly Cancellation ◽  
Gauge Invariant ◽  
Loop Contribution ◽  
Cancellation Condition ◽  
Interesting Possibility ◽  
Interesting Behavior ◽  
Finite Result

The calculation of [Formula: see text] displays interesting behavior which depends on the regulator used in the integration over loop momenta. If calculated using a gauge-invariant regulator, such as dimensional regularization, the calculation yields a unique, finite, gauge-invariant result. If four-dimensional symmetric regulation is used without finite subtractions, additional pieces occur which spoil QED gauge invariance. In both cases, a finite result is obtained, but the particular finite result depends on the regulator utilized in the calculation. While gauge-invariant regulators such as dimensional regularization are normally used, four-dimensional symmetric integration is also physically motivated. Also, the gauge-invariance-violating terms that arise using four-dimensional symmetric integration are of the same form for the fermionic, scalar, and the SM [Formula: see text] loop calculated in renormalizable gauge. This presents an interesting possibility. Inspired by anomaly cancellation, we ask if it is possible that these gauge-invariance-violating terms may cancel in certain models when contributions from all diagrams are included. Here, we calculate the regulator-dependent contributions to [Formula: see text] arising from generic fermion and scalar loops, as well as the Standard Model [Formula: see text] loop contribution, which we evaluate in renormalizable gauge for general [Formula: see text]. We find that a cancellation between such terms is possible, and derive the cancellation condition. Additionally, we find that this cancellation condition ensures QED gauge invariance without finite subtractions for any regulator used, not just for four-dimensional symmetric integration. We additionally relate the regulator-dependent terms in [Formula: see text] to the behavior of quadratically-divergent Higgs tadpole diagrams under shifts of internal loop momentum. Thus, the cancellation condition for the gauge-invariance-violating terms in [Formula: see text] implies a relation between the quadratic divergences in Higgs tadpole diagrams; this has consequences for hypothesized solutions to the hierarchy problem. Lastly, we find that the MSSM obeys our cancellation condition.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals AdS superprojectors

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
E. I. Buchbinder ◽  
D. Hutchings ◽  
S. M. Kuzenko ◽  
M. Ponds
Keyword(s):  
Shell Model ◽  
Differential Operators ◽  
Second Order ◽  
Projection Operators ◽  
De Sitter ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Higher Spin

Abstract Within the framework of $$ \mathcal{N} $$ N = 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$ V α m α ⋅ n ≔ V α 1 … αm α ⋅ 1 … α ⋅ n on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$ V α m α ⋅ n into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the $$ \mathcal{N} $$ N = 1 AdS4 superalgebra $$ \mathfrak{osp} $$ osp (1|4) in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.

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