Gauge-invariant description of massive higher-spin particles by dimensional reduction

Massive higher spin fermionic actions are studied by dimensionally reducing the corresponding massless, gauge-invariant actions in one higher dimension. Auxiliary fields are identified and the higher-spin Higgs effect is discussed.

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DIMENSIONAL REDUCTION OF SYMMETRIC HIGHER SPIN ACTIONS I: BOSONS

Modern Physics Letters A ◽

10.1142/s0217732389000332 ◽

1989 ◽

Vol 04 (03) ◽

pp. 265-273 ◽

Cited By ~ 19

Author(s):

S. D. RINDANI ◽

D. SAHDEV ◽

M. SIVAKUMAR

Keyword(s):

Dimensional Reduction ◽

Light Cone ◽

Gauge Invariant ◽

Higher Spin

The dimensional reduction of massless gauge-invariant free Lagrangians for totally symmetric and totally antisymmetric tensors of arbitrary integral spins is carried out for the covariant and light-cone gauges. The structure of the auxiliary fields for the massive Lagrangians so obtained is elucidated.

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THE GAUGE-INVARIANT THEORY OF HIGHER SPIN FIELDS IN CURVED SPACE

International Journal of Modern Physics A ◽

10.1142/s0217751x91000897 ◽

1991 ◽

Vol 06 (10) ◽

pp. 1693-1700 ◽

Cited By ~ 1

Author(s):

I.G. AVRAMIDI

Keyword(s):

Invariant Theory ◽

Gauge Invariant ◽

Curved Space ◽

Invariant Action ◽

Invariant Description ◽

Higher Spin ◽

Spin Fields ◽

Higher Spin Fields

It is shown that the gauge-invariant description of higher spin fields requires a nonlocal generalisation of the theory. Nonlocal gauge-invariant action functionals for spin 3/2 field and tensor spin 2 field in curved space are constructed.

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AdS superprojectors

Journal of High Energy Physics ◽

10.1007/jhep04(2021)074 ◽

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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Notes on cluster algebras and some all-loop Feynman integrals

Journal of High Energy Physics ◽

10.1007/jhep06(2021)119 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Song He ◽

Zhenjie Li ◽

Qinglin Yang

Keyword(s):

Configuration Space ◽

Strong Evidence ◽

Wilson Loop ◽

Cluster Algebra ◽

Cluster Algebras ◽

Gauge Invariant ◽

Feynman Integrals ◽

Cluster Function ◽

Invariant Description ◽

Cluster Configuration

Abstract We study cluster algebras for some all-loop Feynman integrals, including box-ladder, penta-box-ladder, and double-penta-ladder integrals. In addition to the well-known box ladder whose symbol alphabet is $$ {D}_2\simeq {A}_1^2 $$ D 2 ≃ A 1 2 , we show that penta-box ladder has an alphabet of D3 ≃ A3 and provide strong evidence that the alphabet of seven-point double-penta ladders can be identified with a D4 cluster algebra. We relate the symbol letters to the u variables of cluster configuration space, which provide a gauge-invariant description of the cluster algebra, and we find various sub-algebras associated with limits of the integrals. We comment on constraints similar to extended-Steinmann relations or cluster adjacency conditions on cluster function spaces. Our study of the symbol and alphabet is based on the recently proposed Wilson-loop d log representation, which allows us to predict higher-loop alphabet recursively; by applying it to certain eight-point and nine-point double-penta ladders, we also find D5 and D6 cluster functions respectively.

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LOOP VARIABLES AND GAUGE-INVARIANT INTERACTIONS — II

International Journal of Modern Physics A ◽

10.1142/s0217751x01002762 ◽

2001 ◽

Vol 16 (10) ◽

pp. 1679-1701 ◽

Cited By ~ 2

Author(s):

B. SATHIAPALAN

Keyword(s):

Scattering Amplitudes ◽

String Theory ◽

Gauge Transformation ◽

Dimensional Reduction ◽

Mass Shell ◽

Bosonic String ◽

Higher Dimension ◽

Gauge Invariant ◽

Gauge Transformations ◽

Variable Approach

We continue the discussion of our previous paper on writing down gauge-invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space–time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba–Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the free mass shell).

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SUPER-τ3QED AND THE DIMENSIONAL REDUCTION OF N=1SUPER-QED2+2

International Journal of Modern Physics A ◽

10.1142/s0217751x96000638 ◽

1996 ◽

Vol 11 (08) ◽

pp. 1367-1389 ◽

Cited By ~ 7

Author(s):

M.A. DE ANDRADE ◽

O.M. DEL CIMA

Keyword(s):

Vector Field ◽

Imaginary Part ◽

Gauge Invariance ◽

Dimensional Reduction ◽

Complex Vector ◽

Gauge Invariant ◽

Invariant Action ◽

Supersymmetric Version ◽

Supersymmetric Gauge ◽

Weyl Symmetry

In this work the supersymmetric gauge-invariant action for the massive Abelian N=1 super-QED 2+2 in the Atiyah-Ward space-time (D=2+2) is formulated. The questions concerning the scheme of the gauge invariance in D=2+2 by means of gauging the massive N=1 super-QED 2+2 are investigated. We study how to ensure the gauge invariance at the expense of the introduction of a complex vector superfield. We discuss the Wess-Zumino gauge and thereupon we conclude that, in this gauge, only the imaginary part of the complex vector field, Bμ, gauges a U(1) symmetry. whereas its real part gauges a Weyl symmetry. We build up the gauge-invariant massive term by introducing a pair of chiral and antichiral superfields with opposite U(1) charges. We carry out a dimensional reduction à la Scherk of the massive N=1 super-QED 2+2 action from D=2+2 to D=1+2. Truncations are needed in order to suppress nonphysical modes, and we end up with a parity-preserving N=1 super-QED 1+2 (rather than N=2) in D=1+2. Finally, we show that the N=1 super-QED 1+2 we have obtained is the supersymmetric version of τ3 QED .

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