We review the status of the integrability and solvability of the geodesics equations of motion on symmetric coset spaces that appear as sigma models of supergravity theories when reduced over respectively the timelike and spacelike direction. Such geodesic curves describe respectively timelike and spacelike brane solutions. We emphasize the applications to black holes.
We explore analytic integrability criteria for $ D1 $ branes probing 4D relativistic background with a null isometry direction. We use both the Kovacic's algorithm of classical (non)integrability as well as the standard formulation of Lax connections to show the analytic integrability of the associated dynamical configuration. We further use the notion of double null reduction and obtain the world-volume action corresponding to a torsional Newton-Cartan (TNC) $ D0 $ brane probing a 3D torsional Newton-Cartan geometry. Moreover, following Kovacic's method, we show the classical integrability of…
In previous work we demonstrated that the enlarged super-Poincare algebras which underlie p-brane and D-brane actions in superstring theory can be directly determined based on the integrability of supersymmetry transformations assigned to fields appearing in Wess-Zumino terms. In that work we derived p-brane superalgebras for p = 2 and 3. Here we extend our previous results and give a compact expression for superalgebras for all valid p.
(Non)-Integrability of Geodesics in D-brane Backgrounds
出于对可积弦论的新背景的探索，我们对D-膜几何进行了分类，从而得到了可积测地线。我们的分析表明，无质量测地线的Hamilton-Jacobi方程只能在椭圆或球坐标系中分离，并且所有已知的可积背景都被这种分离所覆盖。特别地，我们确定了AdS_p X S^q的标准参数化与椭圆坐标在一个平坦的基地。我们还发现了新的几何承认分离的哈密顿-雅可比方程在椭圆坐标。由于这个方程的可分性是弦的可积性的必要条件，我们的分析对可积弦论的潜在候选者给出了严格的限制。
ABJM theory in the presence of a half-BPS domain wall is dual to the D2-D4 probe brane system with nonzero worldvolume flux. The ABJM domain wall was recently shown to be integrable to lowest order in perturbation theory and bond dimension. In the present paper we show that the string theory dual of this system is integrable, namely that the string boundary conditions on the probe D4-brane preserve the integrability of the Green-Schwarz sigma model. Our result suggests that the ABJM domain wall is integrable to all loop orders and for any value of the bond dimension.
We investigate classical integrability on two recently discovered classes of backgrounds in massive IIA supergravity. These vacua are of the form AdS$_3\times\,$S$^2\times\mathbb{R}\times\,$CY$_2$, they preserve small $\mathcal{N}=(0,4)$ supersymmetry and are associated with D8$-$D6$-$D4$-$D2 Hanany-Witten brane set-ups. We choose an appropriate string embedding and use differential Galois theory on its associated Hamiltonian system, intending to produce the conditions under which Liouvillian solutions may occur. By constraining the parameters of the system according to the consistency of the …
We consider type 0A matrix model in the presence of a spacelike D brane,localized in matter direction at any arbitrary point. It appears that in order to have an appropriate string/MQM correspondence we must need to impose a constraint on the matrix model side which is equivalent to an operator constraint on the matter part of the boundary state that arises from open string boundary condition. This condition constrains the Hilbert space generated by the macroscopic loop operator but the bulk matrix model remains unaffected, thereby describing a situation parallel to string theory. We have anal…
The D3-D5 probe-brane system is holographically dual to a defect CFT which is known to be integrable. The evidence comes mainly from the study of correlation functions at weak coupling. In the present work we shed light on the emergence of integrability on the string theory side. We do so by constructing the double row transfer matrix which is conserved when the appropriate boundary conditions are imposed. The corresponding reflection matrix turns out to be dynamical and depends both on the spectral parameter and the string embedding coordinates.
We construct integrable deformations of the $λ$-type for asymmetrically gauged WZW models. This is achieved by a modification of the Sfetsos gauging procedure to account for a possible automorphism that is allowed in $G/G$ models. We verify classical integrability, derive the one-loop beta function for the deformation parameter and give the construction of integrable D-brane configurations in these models. As an application, we detail the case of the $λ$-deformation of the cigar geometry corresponding to the axial gauged $SL(2,R)/U(1)$ theory at large $k$. Here we also exhibit a range of both …
