Abstract
We find new solutions to real cubic constraints on N=1 chiral superfields transforming under global abelian symmetries. These solutions describe the low-energy dynamics of a goldstino interacting with an axion (both belonging to the same chiral superfield) with non-linearly realized supersymmetry. We show the relation between our model and the approach of Komargodski and Seiberg for describing goldstino-axion dynamics which uses orthogonal nilpotent superfields.
Highlights
The outline of our paper is as follows
In this work we found non-trivial solutions to real cubic constraints on chiral superfields transforming under global U (1) symmetries
For a chiral superfield S transforming by an imaginary shift we considered the invariant constraint (S + S − 2a)3 = 0, which is solved by Eq (21) – this eliminates the real part of the scalar S ≡ S| in terms of the goldstino and the axion which is the imaginary part of S
Summary
The minimal globally supersymmetric Lagrangian for a nilpotent chiral superfield is given by (we use Wess–Bagger [39] conventions). Where the leading term is the usual contribution from the superpotential, while the fermionic terms come from the solution to the nilpotency constraint. Plugging this back into the Lagrangian yields, L. This minimal Lagrangian describes non-linear dynamics of the goldstino which transforms under SUSY as, δ χα = −μ α − i μ−1σαmα ̄α (χ ∂m χ ) + O(χ 2, χ 2),. In terms of the components of S, the solution to constraint (4) is S = χ 2/(2F) This relation eliminates S in terms of the fermion χ , which can be identified as the goldstino because the corresponding auxiliary field F must be nonvanishing.
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