Spin-3/2 and spin-2 charged massive states in a constant electromagnetic background

Abstract

We develop in components the superspace action obtained in [1] describing the first massive level of the open charged superstring in a flat four-dimensional spacetime. In the absence of an electromagnetic background, we show how the Rarita-Schwinger and Fierz-Pauli Lagrangians are retrieved for spin-3/2 and 2, respectively. We then write different forms of the action in the presence of the electromagnetic background. The resulting equations of motion describe the propagation of fields of charged spin-3/2 and spin-1/2 on the one hand, and spin-2, 1 and 0 on the other.

Dilatonic (Anti-)de Sitter Black Holes and Weak Gravity Conjecture

“…In [18] an effective superspace action for the first mass level of a charged superstring, incorporating a massive spin-3/2 and a massive spin-2 particle within the same supermultiplet, was obtained. This action was subsequently expanded and simplified into its component form [15][16][17], which retains only physical degrees of freedom. The resulting Lagrangian includes a charged massive spin-3/2, described by the two-component spinor fields , , coupled to the two-component spinors , of a spin 1/2 Dirac fermion ,…”

“…We use indices , , as spacetime indices while , are spatial indices. More precisely, the string theory first excited level contains two copies of these fermions, and their couplings to the electromagnetic background differ by minus signs [15][16][17] with commutator [9,12] [D…”

“…A description of the propagation of charged massive spin-2 in 26 dimensions has been achieved by Argyres and Nappi [12,13] by deriving a Lagrangian for the first massive modes and subsequently by extracting the equations of motion and constraint from the Virasoro algebra operator constraints [19]. For the bosonic part of the open superstring, the Lagrangian in [15][16][17] features scalars, vectors and spin-2 physical degrees of freedom,…”

“…We will focus on the equation of motion for spin-2. Let us define P by P ≡ L/ H , with The rationale for using P instead of R has not been provided in [15][16][17], hence the interest in presenting it in these proceedings.…”

“…Despite many efforts, the problem of constructing a Lagrangian that only contains fields of higher spins remains unresolved to this day. However, progress was made for the original problem posed by Dirac, Fierz and Pauli of simply writing down the equations of motion [15][16][17][18] which we will be concerned with here.…”