Too much spacing after exponent

Question

I was trying to improve the visual on a double exponant (text associated to a tilde) and found the following solution online. The problem is that the spacing after seems a bit odd, any help would be appreciated!

\documentclass[10pt,a4paper]{article}
\begin{document}
The space after $\widetilde{G\mkern 0mu}^{\scriptscriptstyle def}$ is too large.
\end{document} 

Answer 1

There's not too much space, as far as TeX is concerned.

\documentclass[10pt,a4paper]{article}

\newcommand{\noic}[1]{\kern-\fontcharic\scriptscriptfont\fam`#1 }
\newcommand{\vr}{\kern-0.05pt\vrule width 0.1pt\kern-0.05pt}

\pagestyle{empty}
\begin{document}

$\widetilde{G\mkern 0mu}^{\scriptscriptstyle def}${\vr} x x

$\widetilde{G\mkern 0mu}^{\scriptscriptstyle def\noic{f}}${\vr} x x

\showoutput

\end{document}

The hairline is meant to show where TeX thinks the formula ends. If you look at the space between the hairline and “x”, you'll realize it's the same as the space between the two following letters.

What's the difference between top and bottom? At the end of the superscript, TeX, by rule, adds the italic correction pertaining to the last math letter. As you can see in the log file, from

....\hbox(3.47221+0.97221)x11.59406, shifted -7.2778
.....\OML/cmm/m/it/5 d
.....\OML/cmm/m/it/5 e
.....\OML/cmm/m/it/5 f
.....\kern0.59029
....\mathoff

the italic correction is about 0.6pt (that is, 0.21mm). In the bottom row the italic correction is removed

....\hbox(3.47221+0.97221)x11.00377, shifted -7.2778
.....\OML/cmm/m/it/5 d
.....\OML/cmm/m/it/5 e
.....\OML/cmm/m/it/5 f
.....\kern0.59029
.....\kern -0.59029
....\mathoff

by explicitly inserting a negative kern. The difference is very tiny even at the big magnification in the picture.

The visual problem is due to the shape of the math italic “f”. If you deem the produced hole is too big (I don't think so), then add yourself a negative kern after the formula.

With a proper setting of the “def” text, upright, you get

and the problem is much less evident. The italic correction is about 0.44pt (that is, 0.14mm).

Answer 2

The space after the exponent can be reduced using a negative \thinmuskip, which can be done with \!:

\documentclass{article}
\begin{document}

The space after $\widetilde{G\mkern 0mu}^{\scriptscriptstyle def}$ is large.

The space after $\widetilde{G\mkern 0mu}^{\scriptscriptstyle def}\!$ is less
large.

The space after $\widetilde{G\mkern 0mu}^{\scriptscriptstyle def}\!\!$ is even
narrower.

\bigskip
Other possibility: if ``def'' is text, better use
$\widetilde{G}^{\mathrm{def}}$,
$\widetilde{G}^{\scriptscriptstyle\mathrm{def}}$, or
$\widetilde{G\mkern 0mu}^{\scriptscriptstyle\mathrm{def}}$.

\end{document}

Answer 3

Consider the following screenshot:

The four math-y terms are generated by $\widetilde{G\mkern 0mu}^{\scriptscriptstyle def}$, $\widetilde{G}^{\scriptscriptstyle def}$,$\widetilde{G}^{\scriptscriptstyle \mathrm{def}}$, and $\widetilde{G}^{\textup{\tiny def}}$, respectively.

The first two terms differ only in the height of the superscript term "def" above the baseline; in both cases, the "def" particle is rendered in math mode. It is known that the letter f has very pronounced side-bearings when typeset in math mode. That's why you're getting the large gap to the next word ("is") -- as well as between "e" and "f". Speaking for myself, I wouldn't use (pure) math-mode "def", regardless of any horizontal spacing issues.

I'm assuming that you will prefer the look of either the third or the fourth term. The former uses math mode -- specifically: \scriptscriptstyle\mathrm{def} -- whereas the letter uses text mode -- \textup{\tiny def}. Observe that the trailing gap generated by the text mode approach is ever so slightly less than that of the math mode approach.

\documentclass{article}
\begin{document}
The space after $\widetilde{G\mkern0mu}^{\scriptscriptstyle def}$ is too large.

The space after $\widetilde{G}^{\scriptscriptstyle def}$ is too large.

The space after $\widetilde{G}^{\scriptscriptstyle \mathrm{def}}$ is too large.

The space after $\widetilde{G}^{\textup{\tiny def}}$ is too large.
\end{document}