* May PPI falls unexpectedly, weekly jobless claims at 10-month high

* Broadcom soars after FY forecast raise on AI chips strength

NEW YORK, June 13 (Reuters) - The S&P 500 and Nasdaq registered record closing highs for a fourth session in a row on Thursday as technology shares extended their recent rally.

The number of Americans filing new claims for unemployment benefits increased last week and another report showed producer prices unexpectedly fell in May, helping to keep alive hopes of a September rate cut by the Federal Reserve.

The Fed on Wednesday projected only one rate cut this year after its outlook in March included three quarter-percentage-point reductions.

Both the S&P 500 technology sector and an index of semiconductors rose sharply.

Shares of Broadcom jumped and hit a record high after the chipmaker raised its forecast for revenue from semiconductors used in artificial intelligence technology. It also announced a 10-for-1 forward stock split.

Shares of Nvidia rallied as well.

"We're seeing a little bit more of a decline in yields, but it's still very much a tech story" in stocks, said Paul Nolte, senior wealth advisor and market strategist for Murphy & Sylvest in Elmhurst, Illinois. "When you look at the broader market, you're not seeing the participation you would like to see from a healthier market."

According to preliminary data, the S&P 500 gained 11.94 points, or 0.22%, to end at 5,432.97 points, while the Nasdaq Composite gained 59.12 points, or 0.34%, to 17,667.56. The Dow Jones Industrial Average fell 70.48 points, or 0.19%, to 38,639.92.

The yield on the 10-year Treasury note eased further on Thursday.

Some investors are wondering whether the economy may be slowing too quickly.

The industrials index fell along with the small-cap Russell 2000 index.

UBS Global Research said it expects the Fed to cut rates in December instead of September, while Goldman Sachs and Morgan Stanley continue to expect the first cut in September.

(Additional reporting by Lisa Mattackal and Johann M Cherian in Bengaluru; Editing by Devika Syamnath and Richard Chang)