Sunday’s scene played out for about 20 minutes, and at least one woman granted the men’s request, setting off a roar as if the former star running back Curtis Martin had just scored a touchdown. Martin was actually nearby, being honored on the field in the official halftime show, which had a far less intense audience.

Throughout halftime, about 10 security guards in yellow jackets stood near the bottom of the circular, multilevel ramp, located beyond the stadium’s concourse of concession stands and restrooms. One of the guards was smoking a cigarette; many fans do the same during halftime on the giant ramps, which are located at each corner of the stadium. Another guard later said they were not permitted to do anything about the chants at Gate D because of free speech laws. Yet when a reporter tried to interview two security guards after halftime, he was detained in a holding room, threatened with arrest and asked to hand over his tape recorder.

The New Jersey Sports and Exposition Authority, which provides security at Giants Stadium for Jets and Giants games, is aware of the raucous and raunchy halftime show. Patrick C. Aramini, the authority’s vice president for security, parking and traffic for the Meadowlands Sports Complex, said men and women could be expelled and even turned over to the New Jersey State Police to be arrested for their participation — although he said he did not know if anyone was cited Sunday. He added that other measures, like blocking access to the ramps, were being considered.

“The problem is, you got to watch four or five hundred people sometimes in the one particular spiral,” Aramini said.