Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-12-23
Physics
High Energy Physics
High Energy Physics - Theory
Latex file
Scientific paper
We consider high spin, $s$, long twist, $L$, operators of the strong and planar ${\cal N}=4$ SYM. Precisely, we compute the minimal anomalous dimensions for large 't Hooft coupling $\lambda$ to the lowest order of the (string) scaling variable $\ell \sim L/ (\ln \mathcal{S} \sqrt{\lambda})$ with GKP string size $\ln \mathcal{S}\equiv \ln (s/\sqrt{\lambda})$. At the leading order $\ln (8\pi \mathcal{S}) \cdot \ell ^2 $, we can confirm the O(6) non-linear sigma model description for this (large size) bulk term, without boundary term $(\ln (8\pi \mathcal{S}))^0$. Going further, we derive, in this O(6) regime, the exact effect of having the size finite. In particular, we compute easily the first Casimir correction $\ell ^0/\ln \mathcal{S}$, which reveals, in the asymptotic regime, only one massless mode (instead of five). In fact, upon comparing with string theory expansion, at one loop our findings agree for large twist, while reveal for negligible twist, already at this order, the appearance of wrapping. At two loops, as well as for next loops and orders, we can produce predictions, which may guide string regularisations.
Fioravanti Davide
Rossi Marco
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