**New Penrose Limits and AdS/CFT**

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*$^1$ Dipartimento di Fisica, Università di Perugia,\
I.N.F.N. Sezione di Perugia,\
Via Pascoli, I-06123 Perugia, Italy\
0.4cm *$^2$ NORDITA\
Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden 0.4cm *$^3$ The Niels Bohr Institute\
*Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark\
****

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grignani@pg.infn.it, harmark@nordita.org, andrea.marini@fisica.unipg.it, orselli@nbi.dk

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**Abstract**

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We find a new Penrose limit of $\mbox{AdS}_5 \times S^5$ giving the maximally supersymmetric pp-wave background with two explicit space-like isometries. This is an important missing piece in studying the AdS/CFT correspondence in certain subsectors. In particular whereas the Penrose limit giving one space-like isometry is useful for the $SU(2)$ sector of ${\mathcal{N}}=4$ SYM, this new Penrose limit is instead useful for studying the $SU(2|3)$ and $SU(1,2|3)$ sectors. In addition to the new Penrose limit of $\mbox{AdS}_5 \times S^5$ we also find a new Penrose limit of $\mbox{AdS}_4 \times {\mathbb{C}}P^3$.

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Introduction {#sec:intro}
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AdS/CFT duality identifies ${\mathcal{N}}=4$ superconformal Yang-Mills (SYM) theory with gauge group $SU(N)$ to type IIB superstring theory on the $\mbox{AdS}_5\times S^5$ background [@Maldacena:1997re; @Gubser:1998bc; @Witten:1998qj]. The AdS/CFT correspondence relates gauge theory and string theory in different regimes, thus, on the one hand, this makes it powerful as it can be used to compute 