What does this notation mean: $F$ at the matrix norm and $Q$ under the $\arg\min$ I am trying to figuring out what is meant by Q and F in the 4th equation mentioned in this paper:
Diachronic Word Embeddings Reveal Statistical Laws of Semantic Change

They haven't define in the paper what is meant by Q and F. So, I am assuming that they are some fixed mathematical notations.
 A: The answers have already been provided in the comments. Just so this question has an answer attached...
$Q$ is defined in the optimization problem itself as the variable we're minimizing with respect to. The expression
$$\underset{Q^T Q = I}{\text{argmin }} f(Q)$$
could also be written as:
$$\underset{Q}{\text{argmin }} f(Q) \quad
\text{s.t. } Q^T Q = I$$
That is: find the value of $Q$ that minimizes the objective function $f$, subject to the constraint that $Q^T Q =I$. This means that $Q$ is an orthogonal matrix.
$\| \cdot \|_F$ denotes the Frobenius norm. For a matrix $A$:
$$\| A \|_F =
\left ( \sum_i \sum_j A_{ij}^2 \right)^\frac{1}{2}$$
A: The commenters essentially answered this question, but I will memorialize it here.
The argmin (or argmax) notation can be a bit confusing, because it often introduces a dummy variable (much like the dx or dt in an integral).  As Matthew Drury's comment indicates, the $\mathbf{Q}$ is the dummy variable here (so it won't be introduced elsewhere in the paper, as it only serves a place holder function).
Next, the argmin operator asks you to figure out which value of $\mathbf{Q}$ gives the smallest value.  However, instead of returning the smallest value for the expression in the argmin, you instead want the value generating this smallest number.  With this in mind, your $\mathbf{Q}$ is essentially your $\mathbf{R}^{(t)}$...so, $\mathbf{Q}$ is defined however $\mathbf{R}^{(t)}$ is defined.
Lastly the $F$ subscript on the norm function $||·||$ most likely indicates the Frobenius norm (https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm; as suggested by @Flounderer).  This is just the square-root of the sum of the squares of all of the entries in the matrix inside the norm function.
