The N=2 Vector–tensor Multiplet, Central Charge Superspace, and Chern–simons Couplings

Abstract

We present a new, alternative interpretation of the vector-tensor multiplet as a 2-form in central charge superspace. This approach provides a geometric description of the (non-trivial) central charge transformations ab initio and is naturally generalized to include couplings of Chern-Simons forms to the antisymmetric tensor gauge field, giving rise to a N = 2 supersymmetric version of the Green-Schwarz anomaly cancellation mechanism.

Hidden symmetries of supersymmetric p-form gauge theories

“…Furthermore, the transformations (10), and in fact all other transformations (7) as well, commute on-shell with the supersymmetry transformations,…”

“…Furthermore, Poincaré invariant models in flat 4-dimensional spacetime must have extended (N ≥ 2) supersymmetry in order that the commutator of two supersymmetry transformations can contain a symmetry (10). This is seen when one writes the supersymmetry transformations as…”

“…It contains one 1-form gauge potential, one 2-form gauge potential, one real scalar field and two Weyl fermions (one may add an auxiliary real scalar field). In that case one has {D i α , D j β } ≈ ε αβ ε ij δ hidden with δ hidden as in (10). Another example, the VTT-multiplet, will be given below.…”

“…Examples have been constructed in [10][11][12][13][14] where the central charge symmetry of the free VT multiplet is extended to a nonlinear global symmetry.…”

On non-linear superfield versions of the vector-tensor multiplet

“…As for the superfield formulations of the VT multiplet (which are most natural when dealing with off-shell supermultiplets), until recently they were constructed only for the linear version, both in the free case and in the presence of couplings to background vector multiplets [6], [7], [8], [9]. There exist formulations in the standard [6] - [8] as well as in harmonic [9] N = 2 superspaces 1 . Our purpose in this letter is to give such a formulation for the non-linear version, both for the pure VT multiplet and for the case when CS couplings to the background vector multiplets are switched on.…”