Deriving Field Theories for Particles of Arbitrary Spin With and Without Supersymmetry

Abstract

We review the derivation of light-cone interaction vertices for fermionic and bosonic fields of arbitrary spin. The resulting amplitudes and their factorization properties are discussed. We then show how this symmetry-based approach works for theories with extended supersymmetry like N = 4 Yang-Mills theory and N = 8 supergravity.

Gravitation and quadratic forms

“…We are left with This is a clear point of contrast from Yang-Mills theory where both the pure and maximally supersymmetric theories are described by quadratic form structures composed of covariant derivatives [1]. From the MHV literature [15][16][17][18][19][20], we know that all treelevel scattering amplitudes in Yang-Mills theory may be expressed entirely in terms of the "square" or "angular" brackets. In gravity, the cubic amplitude does indeed have the same property but the quartic and higher vertices involve a mixture of both brackets.The derivatives we have introduced in the quadratic form for gravity do not transform covariantly beyond order κ and this is very likely, another way of stating what the amplitude structures have already taught us.…”

“…which we integration by parts 20) which is the expected kinetic term for the Hamiltonian. We refer the reader to [24] for details at order κ 2 and simply reproduce the relevant results here.…”

Towards a tensionless string field theory for the $$ \mathcal{N}=\left(2,0\right) $$ CFT in d = 6

“…This idea of determining the interacting Hamiltonian by requiring the closure of the symmetry algebra has proven extremely fruitful in the past [41][42][43][44]. In particular, the entire N = 4 SYM theory -for which the light-cone superspace formulation was first obtained in [23,45] can be derived from closure of the superconformal algebra [46].…”