# HEP/Astro Journal Club, Friday 28th January 2000

## Sergey Frolov (U. of Alabama)




### Abstract

All quartic couplings of scalar fields $s^I$ that are dual to extended
chiral primary operators in ${\cal N}=4$ SYM$_4$ are derived by using the
covariant equations of motion for type IIB supergravity on $AdS_5\times S^5$.
It is shown that despite some expectations if one keeps the structure of
the cubic terms untouched, the quartic action obtained contains terms with
$two$ and $four$ derivatives.
It is shown that the quartic action vanishes on shell in
the extremal case, e.g. $k_1=k_2+k_3+k_4$.
Consistency of the truncation of the quartic couplings to the
massless multiplet of the ${\cal N}=8$, $d=5$ supergravity
is proven and the explicit values of the couplings are found.
It is argued that the consistency of the KK reduction implies
non-renormalization of $n$-point functions of $n-1$ operators dual
to the fields from the massless multiplet and one operator dual to
a field from a massive multiplet.


## Note time 12:30pm, Smith Lab 4079

Jens O. Andersen( jensoa@pacific.mps.ohio-state.edu), last updated 27-APRIL-99.