https://www.nejm.org/doi/pdf/10.1056/NEJMoa2109072
A large medical center in Israel had previously done a study in which they took blood samples from employees to measure antibody levels at intervals after vaccination with Pfizer.
Subsequently, 39 fully vaccinated people tested positive via PCR (although not all were symptomatic -- red dots in the graph indicate symptoms). They had recent (within a week) samples from some, and for the rest they took blood samples immediately upon testing positive. So from those sources they have what they call "peri-infection" antibody levels.
These cases were matched to controls from the earlier study (that is, they found people who were similar in terms of age, sex, days since vaccine, health status) that had not gotten breakthrough infections.
Those who had tested positive for the virus had about one-third the level of antibodies in their "peri-infection" blood as the controls. Antibodies were measured as IgG, and also as neutralizing titers. They did not use a standardized test, however, so you can't compare your levels to theirs.
They also went back to the earlier samples to determine peak antibody levels, and these were also lower for those that had breakthrough infections. All of the symptomatic breakthrough cases had peak neutralizing antibody levels that were at the average or below.
In general, those with higher peri-infection neutralizing antibody levels had higher Ct values, which correlates with less shedding of virus. There were no known cases of the vaccinated person giving the virus to someone else.
Some of the "peri-infection" levels almost certainly had started to change due to the infection, but the combination of this data with peak antibody data fits with the data from the AZ trial showing that higher neutralizing antibody titers are an indication of higher resistance to symptomatic breakthrough infection.
The bad news is that 19% of these breakthrough cases had long covid (with symptoms lasting 6 weeks or more). Quoting from the text: "At 6 weeks after their diagnosis, 19% reported having “long Covid-19” symptoms, which included a prolonged loss of smell, persistent cough, fatigue, weakness, dyspnea, or myalgia. Nine
workers (23%) took a leave of absence from work beyond the 10 days of required quarantine; of these workers, 4 returned to work within 2 weeks. One worker had not yet returned after 6 weeks."
If breakthrough cases that are mostly alpha variant produce that much long covid, delta is likely to be at least as bad, given the higher viral loads seen with it.