Kappa-Symmetry of Green-Schwarz Actions in Coset Superspaces

TL;DR

This paper investigates the nature of -symmetry in Green-Schwarz p-brane actions within coset superspaces, revealing a natural implementation via a subgroup right action and connecting it to the brane classification.

Contribution

It introduces a novel interpretation of -symmetry as a right action of an enlarged supergroup subgroup, linking it to the brane scan and superspace geometry.

Findings

-symmetry can be understood through a right action of a subgroup of G.

An enlarged isotropy subgroup includes fermionic generators, facilitating  transformations.

Closure of the subgroup generators reproduces the known p-brane spectrum.

Abstract

The nature of $\kappa$-symmmetry transformations is examined for p-branes embedded in a class of coset superspaces G/H, where G is an appropriate supergroup and H is the Lorentz subgroup. It is shown that one of the conditions $\delta Z^M E_M{}^a = 0$ which characterizes $\kappa$-symmetry transformations arises very naturally if they are implemented in terms of a right action of a subgroup of the supergroup G on the supergroup elements which represent the coset. Unlike the global left action of G on G/H (which gives rise to supersymmetry on the coset superspace), there is no canonically defined right action of G on G/H. However, an interpretation of this right action involving an enlargement of the isotropy group from the Lorentz subgroup to a subgroup of G with generators which include some of the fermionic generators of G is suggested. Closure of the generators of this larger subgroup under commutation leads to the usual `brane scan' for p-branes which have bosonic degrees of freedom which are worldvolume scalars.