Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 307 / 1 / vi

Table of contents
- Solution vi

Solution

Under

Φ^{'} = e^{- 2 i Λ} Φ

, the conjugate field transforms as

Φ^{'}^{†} = Φ^{†} e^{2 i Λ^{†}}

. Invariance of the canonical Kähler term therefore requires

e^{2 i Λ^{†}} e^{2 V^{'}} e^{- 2 i Λ} = e^{2 V},

or

e^{2 V^{'}} = e^{- 2 i Λ^{†}} e^{2 V} e^{2 i Λ} .

This is the finite non-Abelian supergauge transformation of the vector superfield.

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