# What symmetries are in the following action:

by bagherihan
Tags: action, symmetries
 P: 7 $$S=\int d^4x\frac{m}{12}A_μ ε^{μ \nu ρσ} H_{\nu ρσ} + \frac{1}{8} m^2A^μA_μ$$ Where $$H_{\nu ρσ} = \partial_\nu B_{ρσ} + \partial_ρ B_{σ\nu} + \partial_σ B_{\nu ρ}$$ And $B^{μ \nu}$ is an antisymmetric tensor. What are the global symmetries and what are the local symmetries? p.s how many degrees of freedom does it have? Thank you!
 P: 895 Has $A_{\mu}$ anything to do with the $B_{\mu \nu}$? And what does it have dofs? The Action is a (real) scalar quantity, so it has 1 dof. if $A_{\mu}$ is a massive bosonic field, it should have 3 dofs. and about $B^{\mu \nu}$ just by being an antisymmetric tensor (in Lorentz repr it is a 4x4 in your case matrix) will have: $\frac{D^{2}}{2}-D = \frac{D(D-1)}{2}$ free parameters. So for D=4, you have 6 dofs...
 P: 7 Thanks ChrisVer, $A^\mu$ has nothing to do with $B_{\mu \nu}$ I meant the number dof of the thoery. $H_{\nu ρσ}$ is antisymmetric, so it has only $\binom{4}{3}=4$ dof, doesn't it? thus in total it's 3X4=12 dof, isn't it? And more important for me is to know the action symmetries, both the global and the local ones. thanks.
 P: 895 Also I don't think you need the dofs of the strength field tensor anywhere, do you? It gives the kinetic term of your field $B_{\mu \nu}$ I am not sure though about the dofs now...you might be right.
 P: 895 For the H you were right. $H$ is a p=3-form, and a general p-form in n dimensions has: $\frac{n!}{(n-p)!p!}$ ind. components.