The research looked at how people did on a cognitive ability test after each of three workouts: 10-minute cycle at moderate intensity, 20-minute cycle at moderate intensity and 45-minute cycle at moderate intensity, with each of the rides preceded by a 5-minute warm-up and followed by a 5-minute cooldown. The participants' scores on the cognitive ability test were compared to their performance on the test when they hadn't exercised.
The cognitive ability task was what's known as a Stroop test. In it, words representing colors are presented, and the test taker is required to say what color the word is printed in, regardless of what color the word represents. For example, if the word "green" is presented in red ink, the correct answer is "red." The Stroop effect describes the phenomenon in which it takes longer or is harder to give the right answer when the word is printed in a different color than the color it names (as in the example above) than when the word and the color it's printed in are the same (for example, if "green" were printed in green ink).
When the participants did the Stroop test after their 20-minute ride, they scored significantly better than when they'd taken it without working out first. The 10-minute and 45-minute workouts, however, had negligible effect on their test performance, as measured by accuracy and speed of response.
Of course, if you look at the original research you see that the sample size was very small- only 26 individuals and all "healthy young men." So.... not sure if this is universally applicable. But most of us can probably identify that "sweet spot" of workout length and intensity that helps get us through our day. So go ahead and justify that lunch-time workout by saying "it's helping me work."