Free-electron laser: advancement into the X-ray region

Abstract

We study the Penrose limit of ODp theory. There are two different PPwave limits of the theory. One of them is a ten dimensional PP-wave and the other a four dimensional one. We observe the later one leads to an exactly solvable background for type-II string theories where we have both NS and RR fields. The Penrose limit of different branes of string (M-theory) in a nonzero B/E field (C field) is also studied. These backgrounds are conjectured to provide dual description of NCSYM, NCOS and OM theory. We see that under S-duality the subsector of NCSYM 4 and NCOS 4 which are dual to the corresponding string theory on PP-wave coming from NCYM 4 and NCOS 4 map to each other for given null geodesic.Keywords: Superstring Vacua, Penrose limit and pp-wave background.Recently, PP-wave backgrounds in string theory have attracted much interest, since they possess several interesting features, such as exact solvability in Green-Schwarz formalism etc.. In fact an interesting observation in [1] is that type-IIB string theory on the 10-dimensional PP-wave background with constant five-form RR field strength is exactly solvable. Moreover it has also been shown [2] that this background is a maximally supersymmetric solution of type-IIB supergravity.Another interesting fact is that such a D = 10 maximally supersymmetric PP-wave background can be obtained as a Penrose limit of another one with maximal supersymmetry, namely AdS 5 × S 5 [3, 4]. On the other hand type-IIB string theory on AdS 5 × S 5 is believed to be dual to the N = 4 SYM theory in four dimensions. Indeed it has been shown [4] that taking Penrose limit of AdS 5 × S 5 has a corresponding limit for the gauge theory as well. By making use of this fact the authors of [4] have been able to identify the excited string states with a class of gauge invariant operators in the large-N limit of N = 4 SYM SU(N ) theory in four dimensions. Such an identification is very difficult for AdS 5 × S 5 itself mainly because the string theory in this maximally supersymmetric background has not proved to be exactly solvable yet.Considering the fact that the string theory on a PP-wave background, obtained by taking the Penrose limit of AdS 5 × S 5 , is exactly solvable one might wonder if this is the case for other gravity backgrounds of string theory. Therefore it would be important to study the Penrose limit of different known supergravity solution in string theory. Actually soon after [4], several papers appeared discussing Penrose limit of different gravity solutions in string theory [5] (see also [6]).Recently the Penrose limit of supergravity solutions which are supposed to be dual to some non-local theories have been studied in [7], where the authors considered little string