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FV-type action for AdS(5) mixed-symmetry fields

K. B. Alkalaev

TL;DR

This work extends Fradkin–Vasiliev theory to five-dimensional anti-de Sitter space by constructing a cubic-action for massless higher-spin fields that includes mixed-symmetry hook fields within the $\mathcal{N}=2$ Fradkin–Linetsky superalgebra. The authors develop an unfolded, oscillator-based description using auxiliary spinor variables, define a compatible higher-spin algebra $cu(2^{\mathcal{N}-1},2^{\mathcal{N}-1}|8)$ and its reduced version $hu_0(2^{\mathcal{N}-1},2^{\mathcal{N}-1}|8)$, and formulate a gauge-invariant FV-type action with an extra-field decoupling condition. They derive explicit coefficient functions, factorization and $C$-invariance constraints, and demonstrate cubic-order gauge invariance for hook fields, thereby providing a consistent framework for interactions among mixed-symmetry and symmetric higher-spin fields in $AdS_5$. The results pave the way for higher-$N$ and higher-dimensional generalizations and contribute to the understanding of higher-spin dynamics and their holographic connections in $AdS_5$.

Abstract

We formulate Fradkin-Vasiliev type theory of massless higher spin fields in AdS(5). The corresponding action functional describes cubic order approximation to gravitational interactions of bosonic mixed-symmetry fields of a particular "hook" symmetry type and totally symmetric bosonic and fermionic fields.

FV-type action for AdS(5) mixed-symmetry fields

TL;DR

This work extends Fradkin–Vasiliev theory to five-dimensional anti-de Sitter space by constructing a cubic-action for massless higher-spin fields that includes mixed-symmetry hook fields within the Fradkin–Linetsky superalgebra. The authors develop an unfolded, oscillator-based description using auxiliary spinor variables, define a compatible higher-spin algebra and its reduced version , and formulate a gauge-invariant FV-type action with an extra-field decoupling condition. They derive explicit coefficient functions, factorization and -invariance constraints, and demonstrate cubic-order gauge invariance for hook fields, thereby providing a consistent framework for interactions among mixed-symmetry and symmetric higher-spin fields in . The results pave the way for higher- and higher-dimensional generalizations and contribute to the understanding of higher-spin dynamics and their holographic connections in .

Abstract

We formulate Fradkin-Vasiliev type theory of massless higher spin fields in AdS(5). The corresponding action functional describes cubic order approximation to gravitational interactions of bosonic mixed-symmetry fields of a particular "hook" symmetry type and totally symmetric bosonic and fermionic fields.

Paper Structure

This paper contains 30 sections, 2 theorems, 172 equations.

Table of Contents

  1. Introduction
  2. Free fields
  3. Gauge description of $AdS_{5}$ spacetime
  4. Totally symmetric massless fields in $AdS_{5}$
  5. "Hook" massless fields in $AdS_{5}$
  6. Auxiliary spinor variables
  7. Gauge fields as polynomials in auxiliary variables
  8. Higher spin action functionals
  9. Generalized Weyl tensors and constraints
  10. Fradkin-Linetsky superalgebra
  11. Higher spin superalgebra $cu(2^{\mathcal{N}-1},2^{\mathcal{N}-1}|8)$
  12. Factorized higher spin superalgebra $hu_0(2^{\mathcal{N}-1},2^{\mathcal{N}-1}|8)$
  13. Gauging $cu(2^{\mathcal{N}-1},2^{\mathcal{N}-1}|8)$ superalgebra
  14. $\mathcal{N}=2$ higher spin supermultiplets
  15. A general view of FV-type action
  16. ...and 15 more sections

Key Result

Proposition 2.1

Variational equations of motion for spin-$(s_1,0)$ and spin-$(s_1,1/2)$ fields supplemented with the constraints for extra fields can be equivalently rewritten as and plus analogous expression for complex conjugated curvatures. Here $H_2{}_{\,\delta\rho} = h_\delta{}^\gamma \wedge h_{\gamma\rho}$. Totally symmetric multispinor $C_0^{\alpha_1 ... \alpha_{2s_1}}$ is a generalized bosonic Weyl tens

Theorems & Definitions (3)

  • Proposition 2.1
  • Proposition 2.2
  • proof