# Gauge fixing while preserving supersymmetry

In supersymmetric gauge theories, the vector potential is a part of a vector supermultiplet which is represented by a real superfield $$V$$. Expanded out in components, the Lagrangian for such a field is given by

$$\mathcal{L}=-\frac{1}{4g^2}F_{\mu\nu}^a F^{\mu\nu a}+\cdots,$$

Where the extra terms are in terms of the extra superpartners in this multiplet.

Upon gauge fixing, one introduces Faddeev-Popov ghosts to counter the overcounting in the path integral. The gauge-fixed Lagurangian in, say, the Lorenz gauge takes the form

$$\mathcal{L}_{\text{g.f.}}=\text{Tr}\left[-\frac{1}{4g^2}F_{\mu\nu} F^{\mu\nu}+\overline{c}D_{\mu}\partial^{\mu}c+\cdots\right].$$

Thus, since the vector potential $$A$$ transforms nontrivially under SUSY transformations, but the ghosts do not, it is clear that the introduction of ghost fields has broken supersymmetry at ghost level $$n_g\neq 0$$.

Is there a gauge-fixing method which circumvents this and allows for intrinsically supersymmetric perturbative calculations (for instance introducing a super partner for the ghosts and absorbing the broken supersymmetry into a $$\mathbb{Z}_2$$-graded version of extended BRST symmetry)?

• Can you give a reference where I can read how the overcounting problem occurs? – my2cts Dec 18 '18 at 13:06
• This paper might be useful. – Nogueira Dec 18 '18 at 13:20
• @my2cts Any QFT book will discuss this in the quantization of non-abelian gauge theories in the path integral formalism (cf section 16.2 of Peskin and Schroeder). – Bob Knighton Dec 18 '18 at 14:13