generally the behavior of string theory above the Hagedorn temperature and to study the connection between gauge theory and black holes in $\mbox{AdS}_5 \times S^5$ [@Grignani:2009ua][^4].

Interesting related work in other less supersymmetric gauge theories can be found in Refs. [@Grignani:2007xz; @Larsen:2007bm; @Hamilton:2007he].

The paper is organized as follows. In Section \[sec:stringtheory\] we first review the Penrose limit of string theory that lead to pp-wave backgrounds with zero and one spatial isometry. Then, we find a new Penrose limit giving rise to a pp-wave background with two space-like isometries in which string theory can be quantized. In Section \[sec:stringrotspectra\] we obtain a general form for a pp-wave metric that reproduces all the pp-wave backgrounds analyzed in the previous section. We moreover show that string theory can be directly quantized on this background which we dub “[*rotated pp-wave background*]{} " and we compute the spectrum. In Section \[sec:decsectors\] we show that, after taking an appropriate limit, the spectrum of type IIB string theory on the rotated pp-wave background can be exactly matched to the spectrum of the dual gauge theory operators in certain decoupled sectors of ${\mathcal{N}}=4$ SYM. Finally, in Section \[sec:ads4\] we find a new Penrose limit of the ${\mbox{AdS}}_4\times 