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Register a new userPulsating strings in $Schr_5 times T^{1,1}$ background
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The quest for extension of holographic correspondence to non-relativistic sectors naturally includes Schrodinger backgrounds and their field theory duals. In this paper we study the holography by probing the correspondence with pulsating strings. The case we consider is pulsating strings in five-dimensional Schrodinger space times five-torus $T^{1,1}$, which has as field theory dual a dipole CFT. First we find particular pulsating string solutions and then semi-classically quantize the theory. We obtain the wave function of the problem and thoroughly study the corrections to the energy, which by duality are supposed to give anomalous dimensions of certain operators in the dipole CFT.
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We study a general class of spinning pulsating strings in $(AdS_5 times S^5)_{varkappa}$ background. For these family of solitons, we examine the scaling relation between the energy, spin or angular momentum. We verify that in $varkappa rightarrow 0 $ limit these relations reduce to the undeformed $AdS_5 times S^5$ case. We further study an example of a string which is spinning in the $varkappa$-deformed AdS$_5$ and S$^5$ simultaneously and find out the scaling relation among various conserved charges.
Recently, Arutyunov, Bassi and Lacroix have shown that 2D non-linear sigma model with a deformed $T^{1,1}$ background is classically integrable [arXiv:2010.05573 [hep-th]]. This background includes a Kalb-Ramond two-form with a critical value. Then the sigma model has been conjectured to be non-integrable when the two-form is off critical. We confirm this conjecure by explicitly presenting classical chaos. With a winding string ansatz, the system is reduced to a dynamical system described by a set of ordinary differential equations. Then we find classical chaos, which indicates non-integrability, by numerically computing Poincar{e} sections and Lyapunov spectra for some initial conditions.
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 manuscript we study Liouvillian non-integrability of strings in $AdS_{6}times S^{2}timesSigma$ background and its 5D Holographic Duals. For this we consider soliton strings and look for simple solutions in order to reduce the equations to only one linear second order differential equation called NVE (Normal Variation Equation ). We show that, differently of previous studies, the correct truncation is given by $eta=0$ and not $sigma=0$. With this we are able to study many recent cases considered in the literature: the abelian and non-abelian T-duals, the $(p,q)$-5-brane system, the T$_{N}$, $+_{MN}$ theories and the $tilde{T}_{N,P}$ and $+_{P,N}$ quivers. We show that all of them, and therefore the respective field theory duals, are not integrable. Finally, we consider the general case at the boundary $eta=0$ and show that we can get general conclusions about integrability. For example, beyond the above quivers, we show generically that long quivers are not integrable. In order to stablish the results, we numerically study the string dynamical system seeking by chaotic behaviour. Such a characteristic gives one more piece of evidence for non-integrability for the background studied.
We consider quantum global vortex string correlation functions, within the Kalb-Ramond framework, in the presence of a background field-strength tensor and investigate the conditions under which this yields a nontrivial contribution to those correlation functions. We show that a background field must be supplemented to the Kalb-Ramond theory, in order to correctly describe the quantum properties of the vortex strings. The explicit form of this background field and the associated quantum vortex string correlation function are derived. The complete expression for the quantum vortex creation operator is explicitly obtained. We discuss the potential applicability of our results in the physics of superfluids and rotating Bose-Einstein condensates.
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