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P. Bozhilov

Publications and source records attributed to P. Bozhilov.

At least 19 recordsLinked to original sources
arXiv2012

On the semiclassical 3-point function in AdS_3

We reconsider the problem of determining the semiclassical 3-point function in the Euclidean AdS_3 model. Exploiting the affine symmetry of the model we use solutions of the classical Knizhnik-Zamolodchikov (KZ) equation to compute the saddle point of the action in the presence of three vertex operators. This alternative derivation reproduces the "heavy charge" classical limit of the quantum 3-point correlator. It is different from the recently proposed expression obtained by generalised Pohlmeyer reduction in AdS_2

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arXiv2008

M2-brane Perspective on N=6 Super Chern-Simons Theory at Level k

Recently, O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena (ABJM) proposed three-dimensional super Chern-Simons-matter theory, which at level k is supposed to describe the low energy limit of N M2-branes. For large N and k, but fixed 't Hooft coupling λ=N/k, it is dual to type IIA string theory on AdS_4 x CP^3. For large N but finite k, it is dual to M theory on AdS_4 x S^7/Z_k. In this paper, relying on the second duality, we find exact giant magnon and single spike solutions of membrane configurations on AdS_4 x S^7/Z_k by reducing the system to the Neumann-Rosochatius integrable model. We derive the dispersion relations and their finite-size corrections with explicit dependence on the level k.

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arXiv2008

Finite-size Effect of the Dyonic Giant Magnons in N=6 super Chern-Simons Theory

We consider finite-size effects for the dyonic giant magnon of the type IIA string theory on AdS_4 x CP^3 by applying Luscher mu-term formula which is derived from a recently proposed S-matrix for the N=6 super Chern-Simons theory. We compute explicitly the effect for the case of a symmetric configuration where the two external bound states, each of A and B particles, have the same momentum p and spin J_2. We compare this with the classical string theory result which we computed by reducing it to the Neumann-Rosochatius system. The two results match perfectly.

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arXiv2008

Neumann-Rosochatius integrable system for strings on AdS_4 x CP^3

We use the reduction of the string dynamics on AdS_4 x CP^3 to the Neumann-Rosochatius integrable system. All constraints can be expressed simply in terms of a few parameters. We analyze the giant magnon and single spike solutions on R_t x CP^3 with two angular momenta in detail and find the energy-charge relations. The finite-size effects of the giant magnon and single spike solutions are analyzed.

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arXiv2008

Finite-size Effects for Single Spike

We use the reduction of the string dynamics on R_t x S^3 to the Neumann-Rosochatius integrable system to map all string solutions described by this dynamical system onto solutions of the complex sine-Gordon integrable model. This mapping relates the parameters in the solutions on both sides of the correspondence. In the framework of this approach, we find finite-size string solutions, their images in the (complex) sine-Gordon system, and the leading finite-size effects of the single spike "E-Δϕ" relation for both R_t x S^2 and R_t x S^3 cases.

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arXiv2008

Finite-size effects of Membranes on AdS_4 x S_7

We consider semi-classical solution of membranes on the AdS_4 x S^7. This is supposed to be dual to the N=6 super Chern-Simons theory with k=1 in a planar limit recently proposed by Aharony, Bergmann, Jafferis, and Maldacena (ABJM). We have identified giant magnon and single spike states on the membrane by reducing them to the Neumamm - Rosochatius integrable system. We also connect these to the complex sine-Gordon integrable model. Based on this approach, we find finite-size membrane solutions and obtain their images in the complex sine-Gordon system along with the leading finite-size corrections to the energy-charge relations.

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arXiv2008

Integrable systems from membranes on AdS_4 x S^7

We describe how Neumann and Neumann-Rosochatius type integrable systems, as well as the continuous limit of the SU(2) integrable spin chain, can be obtained from membranes on AdS_4 x S^7 background, in the framework of AdS/CFT correspondence.

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arXiv2007

On the multi-spin magnon and spike solutions from membranes

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.

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arXiv2007

Spin chain from membrane and the Neumann-Rosochatius integrable system

We find membrane configurations in AdS_4 x S^7, which correspond to the continuous limit of the SU(2) integrable spin chain, considered as a limit of the SU(3) spin chain, arising in N=4 SYM in four dimensions, dual to strings in AdS_5 x S^5. We also discuss the relationship with the Neumann-Rosochatius integrable system at the level of Lagrangians, comparing the string and membrane cases.

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arXiv2007

Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7

It is known that large class of classical string solutions in the type IIB AdS_5xS^5 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 AdS_4xS^7 with the searched properties.

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arXiv2007

Magnon-Like Dispersion Relation from M-Theory

We investigate classical rotating membranes in two different backgrounds. First, we obtain membrane solution in $AdS_4\times S^7$ 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 $AdS_7\times S^4$, which give new relations between the conserved charges.

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arXiv2006

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

We consider rotating strings and D2-branes on type IIA background, which arises as dimensional reduction of M-theory on manifold of G2 holonomy, dual to N=1 gauge theory in four dimensions. We obtain exact solutions and explicit expressions for the conserved charges. By taking the semiclassical limit, we show that the rotating strings can reproduce only one type of semiclassical behavior, exhibited by rotating M2-branes on G2 manifolds. Our further investigation leads to the conclusion that the rotating D2-branes reproduce two types of the semiclassical energy-charge relations known for membranes in eleven dimensions.

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arXiv2006

Exact rotating membrane solutions on a G_2 manifold and their semiclassical limits

We obtain exact rotating membrane solutions and explicit expressions for the conserved charges on a manifold with exactly known metric of G_2 holonomy in M-theory, with four dimensional N=1 field theory dual. After that, we investigate their semiclassical limits and derive different relations between the energy and the other conserved quantities, which is a step towards M-theory lift of the semiclassical string/gauge theory correspondence for N=1 field theories.

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arXiv2005

Membrane solutions in M-theory

Motivated by the recent achievements in the framework of the semiclassical limit of the M-theory/field theory correspondence, we propose an approach for obtaining exact membrane solutions in general enough M-theory backgrounds, having field theory dual description. As an application of the derived general results, we obtain several types of membrane solutions in AdS_4xS^7 M-theory background.

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arXiv2005

String Solutions in General Backgrounds

Motivated by the recent interest in the different aspects of the string/field theory duality, we describe an approach for obtaining exact string solutions in general backgrounds, based on two types of string embedding, allowing for separation of the worldsheet variables.

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arXiv2005

On the Open String Ending on D-brane

We obtain background independent solutions for an open string ending on D-brane, in variable external fields. Explicit solution of the boundary conditions is given for background metric and NS-NS two-form gauge field, depending on the coordinates of the transverse to the Dp-brane directions. Extension of the constraint algebra is proposed and discussed from both Hamiltonian and Lagrangian approach viewpoint.

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arXiv2004

On the Classical String Solutions and String/Field Theory Duality II

Based on the recently considered classical string configurations, in the framework of the semi-classical limit of the string/gauge theory correspondence, we describe a procedure for obtaining exact classical string solutions in general string theory backgrounds, when the string embedding coordinates depend non-linearly on the worldsheet spatial parameter. The tensionless limit, corresponding to small t'Hooft coupling on the field theory side, is also considered. Applying the developed approach, we first reproduce some known results. Then, we find new string solutions - with two spins in AdS_5 black hole background and in AdS_5 x S^5 with two spins and up to nine independent conserved R-charges.

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