Plamen Bozhilov

On the multi-spin magnon and spike solutions from membranes

Abstract Recently important classes of solitonic string solutions were obtained—giant magnons and single spikes. In previous study we showed the existence of giant magnon-like membrane solutions and studied their properties. In this paper we investigate classical rotating membranes representing analog of a specific class of string spiky solutions. Using the reduction to the Neumann–Rosochatius integrable system we find analog of the string single spike solutions. In contrast to the magnon-like solutions, this case is characterized with finite difference of energy and “winding number” and finite spins as well.

Neumann and Neumann-Rosochatius integrable systems from membranes on AdS4 × S7

It is known that large class of classical string solutions in the type IIB AdS5 × S5 background is related to the Neumann and Neumann-Rosochatius integrable systems, including spiky strings and giant magnons. It is also interesting if these integrable systems can be associated with some membrane configurations in M-theory. We show here that this is indeed the case by presenting explicitly several types of membrane embedding in AdS4 × S7 with the searched properties.

Magnon-like dispersion relation from M-theory

Abstract We investigate classical rotating membranes in two different backgrounds. First, we obtain membrane solution in AdS 4 × S 7 background, analogous to the solution obtained by Hofman and Maldacena in the case of string theory. We find a magnon type dispersion relation similar to that of Hofman and Maldacena and to the one found by Dorey for the two spin case. In the appendix of the paper, we consider membrane solutions in AdS 7 × S 4 , which give new relations between the conserved charges.

More three-point correlators of giant magnons with finite size

In the framework of the semiclassical approach, we compute the normalized structure constants in three-point correlation functions, when two of the vertex operators correspond to heavy string states, while the third vertex corresponds to a light state. This is done for the case when the heavy string states are finite-size giant magnons with one or two angular momenta, and for two different choices of the light state, corresponding to dilaton operator and primary scalar operator. The relevant operators in the dual gauge theory are

Finite-size dyonic giant magnons in TsT-transformed AdS5 × S5

Tr\left( {F_{\mu \nu }^2{Z^j} + \ldots } \right)

Membrane solutions in M-theory

and Tr(Zj). We first consider the case of AdS5 × S5 and

Three-point correlators: Finite-size giant magnons and singlet scalar operators on higher string levels

\mathcal{N} = 4

Exact rotating membrane solutions on a G2 manifold and their semiclassical limits

super Yang-Mills. Then we extend the obtained results to the γ-deformed AdS5 × Sγ5, dual to

Rotating strings and D2-branes in type IIA reduction of M-theory on G2 manifold and their semiclassical limits

\mathcal{N} = 1

A note on two-spin magnon-like energy-charge relations from M-theory viewpoint

super Yang-Mills theory, arising as an exactly marginal deformation of