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Register a new userProtected states in $mbox{AdS}_3$ backgrounds from integrability
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We write down the Algebraic Bethe Ansatz for string theory on $mbox{AdS}_3timesmbox{S}^3timesmbox{T}^4$ and $mbox{AdS}_3timesmbox{S}^3timesmbox{K3}$ in its orbifold limits. We use it to determine the wave-functions of protected closed strings in these backgrounds and prove that their energies are protected to all orders in $alpha$. We further apply the ABA to find the wave functions of protected states of $mbox{AdS}_3timesmbox{S}^3timesmbox{S}^3times mbox{S}^1$ and its $mathbf{Z}_2$ orbifold. Our findings match with protected spectrum calculations from supergravity, $mbox{Sym}^N$ orbifolds and apply to the complete moduli space of these theories, excluding orbifold blow-up modes for which further analysis is necessary.
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Minimal area surfaces in AdS$_3$ ending on a given curve at the boundary are dual to planar Wilson loops in N=4 SYM. In previous work it was shown that the problem of finding such surfaces can be recast as the one of finding an appropriate parameterization of the boundary contour that corresponds to conformal gauge. A. Dekel was able to find such reparameterization in a perturbative expansion around a circular contour. In this work we show that for more general contours such reparameterization can be found using a numerical procedure that does not rely on a perturbative expansion. This provides further checks and applications of the integrability method. An interesting property of the method is that it uses as data the Schwarzian derivative of the contour and therefore it has manifest global conformal invariance. Finally, we apply Shanks transformation to extend the near circular expansion to larger deformations, the results are in agreement with the new method.
In this paper we look for AdS solutions to generalised gravity theories in the bulk in various spacetime dimensions. The bulk gravity action includes the action of a non-minimally coupled scalar field with gravity, and a higher-derivative action of gravity. The usual Einstein-Hilbert gravity is induced when the scalar acquires a non-zero vacuum expectation value. The equation of motion in the bulk shows scenarios where AdS geometry emerges on-shell. We further obtain the action of the fluctuation fields on the background at quadratic and cubic orders.
The problem of computing the anomalous dimensions of a class of (nearly) half-BPS operators with a large R-charge is reduced to the problem of diagonalizing a Cuntz oscillator chain. Due to the large dimension of the operators we consider, non-planar corrections must be summed to correctly construct the Cuntz oscillator dynamics. These non-planar corrections do not represent quantum corrections in the dual gravitational theory, but rather, they account for the backreaction from the heavy operator whose dimension we study. Non-planar corrections accounting for quantum corrections seem to spoil integrability, in general. It is interesting to ask if non-planar corrections that account for the backreaction also spoil integrability. We find a limit in which our Cuntz chain continues to admit extra conserved charges suggesting that integrability might survive.
We present all the symmetry superalgebras $mathfrak{g}$ of all warped AdS$_ktimes_w M^{d-k}$, $k>2$, flux backgrounds in $d=10, 11$ dimensions preserving any number of supersymmetries. First we give the conditions for $mathfrak{g}$ to decompose into a direct sum of the isometry algebra of AdS$_k$ and that of the internal space $M^{d-k}$. Assuming this decomposition, we identify all symmetry superalgebras of AdS$_3$ backgrounds by showing that the isometry groups of internal spaces act transitively on spheres. We demonstrate that in type II and $d=11$ theories the AdS$_3$ symmetry superalgebras may not be simple and also present all symmetry superalgebras of heterotic AdS$_3$ backgrounds. Furthermore, we explicitly give the symmetry superalgebras of AdS$_k$, $k>3$, backgrounds and prove that they are all classical.
We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no $AdS_n$ backgrounds with $n ot=3$. Moreover the warp factor of AdS$_3$ backgrounds is constant, the geometry is a product $AdS_3times M^7$ and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of $M^7$ has been specified in all cases. For 2 supersymmetries, it has been found that $M^7$ admits a suitably restricted $G_2$ structure. For 4 supersymmetries, $M^7$ has an $SU(3)$ structure and can be described locally as a circle fibration over a 6-dimensional KT manifold. For 6 and 8 supersymmetries, $M^7$ has an $SU(2)$ structure and can be described locally as a $S^3$ fibration over a 4-dimensional manifold which either has an anti-self dual Weyl tensor or a hyper-Kahler structure, respectively. We also demonstrate a new Lichnerowicz type theorem in the presence of $alpha$ corrections.
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