Higher spin vortical Zilches from Kubo formulae

S. Golkar and D. T. Son, JHEP 02

Original

2015

Cited alongside, same era.

The helicity current in these works is sometimes defined through ∂ μ H μ = F μ ​ ν ​ \mathaccentV ​ t ​ i ​ l ​ d ​ e ​ 07 ​ E ​ F μ ​ ν , \partial_{\mu}H^{\mu}=F_{\mu\nu}\mathaccentV{tilde}07E{F}^{\mu\nu}, which gives the local expression of a Chern-Simons current H μ = 2 ​ ϵ μ ​ ν ​ ρ ​ σ ​ A ν ​ F ρ ​ σ H^{\mu}=2\epsilon^{\mu\nu\rho\sigma}A_{\nu}F_{\rho\sigma} . It is also useful to define a classically conserved helicity current \mathaccentV ​ t ​ i ​ l ​ d ​ e ​ 07 ​ E ​ H μ = 2 ​ ϵ μ ​ ν ​ ρ ​ σ ​ ( A ν ​ F ρ ​ σ − C ν ​ \mathaccentV ​ t ​ i ​ l ​ d ​ e ​ 07 ​ E ​ F ρ ​ σ ) \mathaccentV{tilde}07E{H}^{\mu}=2\epsilon^{\mu\nu\rho\sigma}\left(A_{\nu}F_{\rho\sigma}-C_{\nu}\mathaccentV{tilde}07E{F}_{\rho\sigma}\right) where the dual gauge field C C is defined through \mathaccentV ​ t ​ i ​ l ​ d ​ e ​ 07 ​ E ​ F = d ​ C \mathaccentV{tilde}07E{F}=dC . This is the current considered, for example, in [ 1 ] and the one to bring a close analogue to the axial current for fermions

Cited in the paper.

S. Iso, T. Morita, and H. Umetsu, Physical Review D 75

Cited in the paper.

S. Iso, T. Morita, and H. Umetsu, Physical Review D 76

Cited in the paper.

Our convention for symmetrization is V ( μ 1 ​ … ​ μ s ) = 1 s ! ​ ∑ π ∈ S n V π ⁡ ( μ 1 ) ​ … ​ π ​ ( μ s ) . V_{(\mu_{1}...\mu_{s})}=\frac{1}{s!}\sum\displaylimits_{\pi\in S_{n}}V_{\pi(\mu_{1})...\pi(\mu_{s})}. (38)

Cited in the paper.

The seagull contribution only comes from the covariantization of derivatives in the Zilch. Other contributions, which are due to the metric dependence of \mathaccentV ​ t ​ i ​ l ​ d ​ e ​ 07 ​ E ​ F \mathaccentV{tilde}07E{F} and the index contractions give terms independent of the external momentum

Cited in the paper.

X.-G. Huang and A. V. Sadofyev, (2018), arXiv:1805.08779 [hep-th]

Original

2018

Closest in time.