(Corrects spelling to FHN Financial, instead of FTN Financial, in paragraph 3 of May 20 story) By Herbert Lash NEW YORK, May 20 (Reuters) - Yields on nominal U.S. Treasury debt and inflation-linked securities fell on Thursday after factory activity in the U.S. mid-Atlantic region slowed in May from a record pace, casting doubt on how fast the economy can continue to roar. The breakeven rate on 10-year Treasury inflation-protected securities, or TIPS, fell to a session low of 2.44% after the auction of $13 billion in 10-year TIPS securities. "To continue to buy protection against inflation requires either a belief or additional evidence that inflation is continuing to go higher, above where you bought the last time," said Jim Vogel, interest rate strategist at FHN Financial. The market needs to see confirmation of faster inflation after so much optimism about the recovery, the economy reopening and the impact of government stimulus on growth was incorporated into expectations in a very short period, Vogel said. The Philadelphia Federal Reserve Bank said its business activity index fell to 31.5 from 50.2 in April, its highest pace in nearly half a century. The reading was shy of economists" expectations of 43.0, a Reuters poll found. The yield on benchmark 10-year Treasury notes fell 5.1 basis points to 1.632%. The breakeven rate on five-year TIPS slid to 2.598%, after closing at 2.646% on Wednesday. The rate hit its highest close in just over a decade on Monday. Market expectations of a further rise in inflation would need evidence of the economy moving past full employment very, very rapidly, said Steven Ricchiuto, U.S. chief economist at Mizuho Securities USA LLC. If you don"t "reach full peak employment very, very quickly, then you have to rethink, reset your overall expectations on the market," he said, adding the U.S. economy probably reached its peak level of activity in March and April. The number of Americans filing new claims for unemployment benefits dropped further below 500,000 last week, suggesting job growth picked up this month. But companies are desperate for workers, which could affect how quickly the economy grows. Initial claims for state unemployment benefits totaled a seasonally adjusted 444,000 for the week ended May 15, compared to 478,000 in the prior week, the Labor Department said on Thursday. That was the lowest since mid-March 2020. Bond yields jumped on Wednesday after minutes of the Federal Reserve"s April meeting mentioned a number of policymakers found that "at some point" in the future discussion of adjusting the pace of bond purchases might be appropriate. The market"s reaction to "taper talk" is now seen as knee-jerk. But on Wednesday it conjured memories of the volatile reaction to Fed efforts in 2013 to ease an accommodative policy. The yield on the 30-year Treasury bond was down 4.7 basis points to 2.340%. The 10-year TIPS breakeven rate was last at 2.457%, indicating the market sees inflation averaging just under 2.5% a year for the next decade. May 20 Thursday 3:04PM New York / 1904 GMT Price Current Net Yield % Change (bps) Three-month bills 0.0075 0.0076 -0.007 Six-month bills 0.02 0.0203 -0.005 Two-year note 99-243/256 0.1512 -0.008 Three-year note 99-200/256 0.3237 -0.029 Five-year note 99-176/256 0.8146 -0.048 Seven-year note 99-208/256 1.2783 -0.055 10-year note 99-240/256 1.6318 -0.051 20-year bond 99-244/256 2.2529 -0.052 30-year bond 100-196/256 2.3393 -0.048 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) GooU.S. 2-year dollar swap 9.75 -0.25 spread U.S. 3-year dollar swap 11.75 0.50 spread U.S. 5-year dollar swap 8.75 1.25 spread U.S. 10-year dollar swap -3.00 1.00 spread U.S. 30-year dollar swap -30.00 1.75 spread (Reporting by Herbert Lash; editing by Barbara Lewis, Kirsten Donovan and Jonathan Oatis) Our Standards: The Thomson Reuters Trust Principles.