On the pulsating strings in AdS_4 x CP3

We study the class of pulsating strings on AdS_4 x CP3. Using a generalized ansatz for pulsating string configurations we find new solutions of this class. Further we quasi-classically quantize the theory and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual N=6 Chern-Simons theory.Comment: references adde

Large J expansion in ABJM theory revisited

Recently there has been progress in the computation of the anomalous dimensions of gauge theory operators at strong coupling by making use of AdS/CFT correspondence. On string theory side they are given by dispersion relations in the semiclassical regime. We revisit the problem of large charges expansion of the dispersion relations for simple semiclassical strings in $AdS_4\times\mathbb{CP}^3$ background. We present the calculation of the corresponding anomalous dimensions of the gauge theory operators to an arbitrary order using three different methods. Although the results of the three methods look different, power series expansions show their consistency.Comment: 24 pages, 2 figure

On the pulsating strings in Sasaki-Einstein spaces

We study the class of pulsating strings in AdS_5 x Y^{p,q} and AdS_5 x L^{p,q,r}. Using a generalized ansatz for pulsating string configurations, we find new solutions for this class in terms of Heun functions, and derive the particular case of AdS_5 x T^{1,1}, which was analyzed in arXiv:1006.1539 [hep-th]. Unfortunately, Heun functions are still little studied, and we are not able to quantize the theory quasi-classically and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual N=1 superconformal field theory.Comment: 9 pages, talk given at the 2nd Int. Conference AMiTaNS, 21-26 June 2010, Sozopol, Bulgaria, organized by EAC (Euro-American Consortium) for Promoting AMiTaNS, to appear in the Proceedings of 2nd Int. Conference AMiTaN

Generalized pulsating strings

In this paper we consider new solutions for pulsating strings. For this purpose we use tha idea of the generalized ansatz for folded and circular strings in hep-th/0311004. We find the solutions to the resulting Neumann-Rosochatius integrable system and the corrections to the energy. To do that we use the approach developed by Minahan in hep-th/0209047 and find that the corrections are quite different from those obtained in that paper and hep-th/0310188. We conclude with comments on our solutions and obtained corrections to the energy, expanded to the leading order in lambda.Comment: v.2 references added, citations corrected, 18 page

Monte Carlo Study of Particle Transport Problem in Air Pollution

2002 Mathematics Subject Classification: 65C05.The actual transport of the air pollutants is due to the wind. This normally called “advection of the air pollutants”. Diffusion and deposition are other two major physical processes, which take place during the transport of pollutants in the atmosphere. In this paper we study two classes of grid-free Monte Carlo (MC) algorithms for solving an elliptic boundary value problem, where the partial differential equation contains advection, diffusion and deposition parts. The grid-free MC approach to solve the above equation uses a local integral representation and leads to a stochastic process called a random “Walk on balls” (WOB). In the first class of algorithms, the choice of a transition density function in the Markov chain depends on the radius of the maximal ball, lying inside the domain, in which the problem is defined, and on the parameters of the differential operator. While the choice of a transition density function in the second class of algorithms does not depend on the deposition part of the problem. The computational complexity of both classes of grid-free MC algorithms was investigated using varied numerical tests on a PowerPC (G4 w/AltiVec) 450 MHz running YDL 2.0.Supported by Center of Excellence BIS-21 grant ICA1-2000-70016 and by the NSF of Bulgaria under Grants #I 811/98 and #MM 902/9

A note on spin chain/string duality

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N=4 SYM theory and rotating strings was made. The correspondence was established mainly using Bethe ansatz technique applied to the spin s Heisenberg model. In a recent paper Kruczenski (hep-th/0311203) suggested to solve the Heisenberg model by using of sigme model approach. In this paper we generalize the solutions obtained by Kruczenski and comment on the dual string theory. It turns out that our solutions are related to the so called Neumann-Rosochatius integrable system. We comment on the spin chain solutions and on the string/gauge theory correspondence.Comment: v.2 One reference added, typos corrected, 21 page