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Register a new userFinite Size Effect from Classical Strings in deformed AdS$_3times$ S$^3$
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We study the finite size effect of rigidly rotating and spinning folded strings in $(AdS_3times S^3)_{varkappa}$ background. We calculate the leading order exponential corrections to the infinite size dispersion relation of the giant magnon, and single spike solutions. For the spinning folded strings we write the finite size effect in terms of the known Lambert $W$-function.
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We study the finite size effect of rigidly rotating strings and closed folded strings in $AdS_3times S^3$ geometry with NS-NS B-field. We calculate the classical exponential corrections to the dispersion relation of infinite size giant magnon and single spike in terms of Lambert $mathbf{W}-$function. We also write the analytic expression for the dispersion relation of finite size Gubser-Klebanov-Polyakov (GKP) string in the form of Lambert $mathbf{W}-$function.
We study solutions for the rotating strings on the sphere with a background NS-NS field and on the Anti-de-Sitter spacetime. We show the existence of magnon and single spike solutions on R$times$S$^2$ in the presence of constant magnetic field as two limiting cases. We also study the solution for strings on AdS$_3times$ S$^3$ with Melvin deformation. The dispersion relations among various conserved charges are shown to receive finite corrections due to the deformation parameter. We further study the rotating string on AdS$_3 times$ S$^3$ geometry with two conserved angular momenta on S$^3$ and one spin along the AdS$_3$. We show that there exists two kinds of solutions: a circular string solution and a helical string. We find out the dispersion relation among various charges and give physical interpretation of these solutions.
We study a giant magnon and a spike solution for the string rotating on AdS(4) X CP**3 geometry. We consider rigid rotating fundamental string in the SU(2) X SU(2) sector inside the CP**3 and find out the general form of all the conserved charges. We find out the dispersion relation corresponding to both the known giant magnon and the new spike solutions. We further study the finite size correction in both cases.
We discuss finite-size corrections to the spiky strings in $AdS$ space which is dual to the long $mathcal{N}=4$ SYM operators of the form Tr($Delta_+ ^{J_1}phi_1Delta_+ ^{J_2}phi_2...Delta_+ ^{J_n}phi_n$). We express the finite-size dispersion relation in terms of Lambert $mathbf{W}$-function. We further establish the finite-size scaling relation between energy and angular momentum of the spiky string in presence of mixed fluxes in terms of $mathbf{W}$-function. We comment on the solution in pure NS-NS background as well.
In this paper, considering the correspondence between spin chains and string sigma models, we explore the rotating string solutions over $ eta $ deformed $ AdS_5 times S^{5} $ in the so called fast spinning limit. In our analysis, we focus only on the bosonic part of the full superstring action and compute the relevant limits on both $(R times S^{3})_{eta} $ and $(R times S^{5})_{eta} $ models. The resulting system reveals that in the fast spinning limit, the sigma model on $ eta $ deformed $S^5$ could be $textit{approximately}$ thought of as the continuum limit of anisotropic $ SU(3) $ Heisenberg spin chain model. We compute the energy for a certain class of spinning strings in deformed $S^5$ and we show that this energy can be mapped to that of a similar spinning string in the purely imaginary $beta$ deformed background.
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