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Register a new userNotes on gravity multiplet correlators in $AdS_3 times S^3$
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We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in $(2,0)$ supergravity on $AdS_3 times S^3$, with two operators in tensor multiplet and the other two in gravity multiplet. This is achieved by solving the recursion relation arising from a hidden six-dimensional conformal symmetry. We note the compact expression is obtained after carefully analysing the analytic structures of the correlators. Various limits of the correlators are studied, including the maximally R-symmetry violating limit and flat-space limit.
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We study $AdS_3 times S^1 times Y$ supersymmetric string theory backgrounds with Neveu-Schwarz-Neveu-Schwarz flux that are dual to ${cal N}=2$ superconformal theories on the boundary. We classify all worldsheet vertex operators that correspond to space-time chiral primaries. We compute space-time chiral ring structure constants for operators in the zero spectral flow sector using the operator product expansion in the worldsheet theory. We find that the structure constants take a universal form that depends only on the topological data of the ${cal N}=2$ superconformal theory on $Y$.
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.
$SL(2,mathbb{Z})$ invariant action for probe $(m,n)$ string in $AdS_3times S^3times T^4$ with mixed three-form fluxes can be described by an integrable deformation of an one-dimensional Neumann-Rosochatius (NR) system. We present the deformed features of the integrable model and study general class of rotating and pulsating solutions by solving the integrable equations of motion. For the rotating string, the explicit solutions can be expressed in terms of elliptic functions. We make use of the integrals of motion to find out the scaling relation among conserved charges for the particular case of constant radii solutions. Then we study the closed $(m,n)$ string pulsating in $R_ttimes S^3$. We find the string profile and calculate the total energy of such pulsating string in terms of oscillation number $(cal{N})$ and angular momentum $(cal{J})$.
Sigma model in $AdS_3times S^3$ background supported by both NS-NS and R-R fluxes is one of the most distinguished integrable models. We study a class of classical string solutions for $N$-spike strings moving in $AdS_3 times S^1$ with angular momentum $J$ in $S^1 subset S^5$ in the presence of mixed flux. We observe that the addition of angular momentum $J$ or winding number $m$ results in the spikes getting rounded off and not end in cusp. The presence of flux shows no alteration to the rounding-off nature of the spikes. We also consider the large $N$-limit of $N$-spike string in $AdS_3 times S^1$ in the presence of flux and show that the so-called Energy-Spin dispersion relation is analogous to the solution we get for the periodic-spike in $AdS_3-pp-$wave $times S^1$ background with flux.
We consider string theory on AdS$_3$ $times$ (S$^3$ $times$ S$^3$ $times$ S$^1)/mathbb Z_2$, a background supporting $mathcal N=(3,3)$ spacetime supersymmetry. We propose that string theory on this background is dual to the symmetric product orbifold of $mathcal S_0/mathbb Z_2$ where $mathcal S_0$ is a theory of four free fermions and one free boson. We show that the BPS spectra of the two sides of the duality match precisely. Furthermore, we compute the elliptic genus of the dual CFT and that of the supergravity limit of string theory and demonstrate that they match, hence providing non-trivial support for the holographic proposal.
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