Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFeynman rules for higher-spin gauge fields on AdS$_{d+1}$
161
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We determine the Feynman rules for the minimal type A higher-spin gauge theory on AdS$_{d+1}$ at cubic order. In particular, we establish the quantum action at cubic order in de Donder gauge, including ghosts. We also give the full de Donder gauge propagators of higher-spin gauge fields and their ghosts. This provides all ingredients needed to quantise the theory at cubic order.
rate research
Read More
Lagrangian descriptions of irreducible and reducible integer higher-spin representations of the Poincare group subject to a Young tableaux $Y[hat{s}_1,hat{s}_2]$ with two columns are constructed within a metric-like formulation in a $d$-dimensional flat space-time on the basis of a BRST approach extending the results of [arXiv:1412.0200[hep-th]]. A Lorentz-invariant resolution of the BRST complex within both the constrained and unconstrained BRST formulations produces a gauge-invariant Lagrangian entirely in terms of the initial tensor field $Phi_{[mu]_{hat{s}_1}, [mu]_{hat{s}_2}}$ subject to $Y[hat{s}_1,hat{s}_2]$ with an additional tower of gauge parameters realizing the $(hat{s}_1-1)$-th stage of reducibility with a specific dependence on the value $(hat{s}_1-hat{s}_2)=0,1,...,hat{s}_1$. Minimal BRST--BV action is suggested, being proper solution to the master equation in the minimal sector and providing objects appropriate to construct interacting Lagrangian formulations with mixed-antisymmetric fields in a general framework.
In this short note we present a Lagrangian formulation for free bosonic Higher Spin fields which belong to massless reducible representations of D-dimensional Anti de Sitter group using an ambient space formalism.
We develop the BRST approach to gauge invariant Lagrangian construction for the massive mixed symmetry integer higher spin fields described by the rank-two Young tableaux in arbitrary dimensional Minkowski space. The theory is formulated in terms of auxiliary Fock space. No off-shell constraints on the fields and the gauge parameters are imposed. The approach under consideration automatically leads to a gauge invariant Lagrangian for massive theory with all appropriate Stuckelberg fields. It is shown that all the restrictions defining an irreducible representation of the Poincare group arise from Lagrangian formulation as a consequence of the equations of motion and gauge transformations. As an example of the general procedure, we derive the gauge-invariant Lagrangian for massive rank-2 antisymmetric tensor field containing the complete set of auxiliary fields and gauge parameters.
We propose a method of construction of a cubic interaction in massless Higher Spin gauge theory both in flat and in AdS space-times of arbitrary dimensions. We consider a triplet formulation of the Higher Spin gauge theory and generalize the Higher Spin symmetry algebra of the free model to the corresponding algebra for the case of cubic interaction. The generators of this new algebra carry indexes which label the three Higher Spin fields involved into the cubic interaction. The method is based on the use of oscillator formalism and on the Becchi-Rouet-Stora-Tyutin (BRST) technique. We derive general conditions on the form of cubic interaction vertex and discuss the ambiguities of the vertex which result from field redefinitions. This method can in principle be applied for constructing the Higher Spin interaction vertex at any order. Our results are a first step towards the construction of a Lagrangian for interacting Higher Spin gauge fields that can be holographically studied.
We compute the one-loop free energies of the type-A$_ell$ and type-B$_ell$ higher-spin gravities in $(d+1)$-dimensional anti-de Sitter (AdS$_{d+1}$) spacetime. For large $d$ and $ell$, these theories have a complicated field content, and hence it is difficult to compute their zeta functions using the usual methods. Applying the character integral representation of zeta function developed in the companion paper arXiv:1805.05646 to these theories, we show how the computation of their zeta function can be shortened considerably. We find that the results previously obtained for the massless theories ($ell=1$) generalize to their partially-massless counterparts (arbitrary $ell$) in arbitrary dimensions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
