Custom taxonomy wp_query woes.

Before I start, you should not use capital letters in your names, and also, don’t use hyphens, the correct way is to separate words with underscores

What you are trying to do doesn’t work. Do a var_dump() to get the available query variables on your single page

?><pre><?php var_dump($wp_query->query_vars); ?></pre><?php

You will see that the following are invalid

$term_slug = get_query_var( 'the-art' );
$taxonomyName = get_query_var( 'art-category' );

I don’t know of any means to get the taxonomy from a term name, so this you will need to hardcode and you will also need to do a check to see if a post term belongs to the taxonomy.

To get the post terms, you can make use of one of the following

I would most probably also make use of a proper tax_query, the reason is, the way you are doing it will not work if you have more than one term.