A poorly managed database table has grown to be enormous. 48+gigs of orphan records. I am trying to clean it up and put my dangerously full hard drive back to a normal state. I will be deleting approx 400 million records from this table. This is running as I type. I notice that I am not seeing any drop in my hard drive space but I am seeing the memory drop on system table queries, I am running to get table size. The database is using "Simple Recovery Model".

There are many questions similar to this with responses saying you need to shrink the database. But they go on to explain how bad/scary this is to do because of fragmented data etc. 


Since the database should not be this size. Is it still bad for me to shrink it?
This is a production database. If I shrink it will it cause downtime or lock the database?
In SQL Server Management Studio you have two options for shrink, database or files. Given my situation what would be the best option?
is there a rule on the percentage of free space a DB should have?


Even reading the tag description of shrink makes me not want to do it. Is there another way?


Question: $\theta$ term of anomaly related with topological insulators
Answer: The $\theta$-term is also known as the axion term and it's simply the $F\wedge F$ term known to particle physicists. In a more condensed-matter-friendly language,
$$\Delta {\mathcal L} = \theta\left( \frac{e^2}{2\pi h}  \right) \vec B \cdot \vec E $$
I don't know the optimum starting point but you may begin with 


  http://arxiv.org/abs/1001.3179


and its followups and references. More generally, the $\theta$-term means the integral of the anomaly polynomial. Note that the anomaly polynomial is a nice gauge-invariant expression - but in higher dimensions. The actual anomaly in the original spacetime is related to it by several operations.