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Register a new userTwisted Supergravity and Koszul Duality: A case study in AdS$_3$
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In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS$_3times S^3times T^4$ and the SCFT (on the moduli space of) the symmetric orbifold theory $Sym^N(T^4)$ as $N rightarrow infty$. This variant arises conjecturally from a twist proposed by the first author and Si Li. We recover a number of results concerning protected subsectors of the original duality working directly in the twisted bulk theory. Moreover, we identify the symmetry algebra arising in the $Nrightarrow infty$ limit of the twisted gravitational theory. We emphasize the role of $textit{Koszul duality}$---a ubiquitous mathematical notion to which we provide a friendly introduction---in field theory and string theory. After illustrating the appearance of Koszul duality in the toy example of holomorphic Chern-Simons theory, we describe how (a deformation of) Koszul duality relates bulk and boundary operators in our twisted setup, and explain how one can compute algebra OPEs diagrammatically using this notion. Further details, results, and computations will appear in a companion paper.
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We show that an $SL(2,R)_L times SL(2,R)_R$ Chern-Simons theory coupled to a source on a manifold with the topology of a disk correctly describes the entropy of the AdS$_3$ black hole. The resulting boundary WZNW theory leads to two copies of a twisted Kac-Moody algebra, for which the respective Virasoro algebras have the same central charge $c$ as the corresponding untwisted theory. But the eigenvalues of the respective $L_0$ operators are shifted. We show that the asymptotic density of states for this theory is, up to logarithmic corrections, the same as that obtained by Strominger using the asymptotic symmetry of Brown and Henneaux.
We have extended previous analysis of the bulk/brane supersymmetrizations involving non-zero brane mass terms of bulk fermions (gravitini) and twisting of boundary conditions. We have constructed new brane/bulk models that may be relevant for realistic model building. In particular, we have built a model with the Randall-Sundrum bosonic sector, orthogonal projection operators on the branes in the fermionic sector, and an unbroken N=1 supersymmetry. We have also constructed 5d super-bigravity with static vacuum and unbroken N=1 supersymmetry, which may be viewed as a deconstruction of 5d supergravity.
Starting from the dual Lagrangians recently obtained for (partially) massless spin-2 fields in the Stueckelberg formulation, we write the equations of motion for (partially) massless gravitons in (A)dS in the form of twisted-duality relations. In both cases, the latter admit a smooth flat limit. In the massless case, this limit reproduces the gravitational twisted-duality relations previously known for Minkowski spacetime. In the partially-massless case, our twisted-duality relations preserve the number of degrees of freedom in the flat limit, in the sense that they split into a decoupled pair of dualities for spin-1 and spin-2 fields. Our results apply to spacetimes of any dimension greater than three. In four dimensions, the twisted-duality relations for partially massless fields that appeared in the literature are recovered by gauging away the Stueckelberg field.
We find non-supersymmetric AdS$_8$ solutions of type IIA supergravity. The internal space is topologically an $S^2$ with a U(1) isometry. The only non-zero flux is $F_0$; an O8 sourcing it is present at the equator of the $S^2$. The warping function and dilaton are non-constant. It is also possible to add D8-branes on top of the O8. Possible destabilizing brane bubbles (whose presence would be suggested by the weak-gravity conjecture) are either absent or collapsing. Our solutions are candidate holographic duals to unitary interacting CFTs in seven dimensions with exceptional global symmetry. We also present analogous non-supersymmetric AdS$_{d}$ solutions for general $d$ which are supported only by $F_0$.
We study near-extremal n-point correlation functions of chiral primary operators, in which the maximal scale dimension k is related to the others by k=sum_i k_i-m with m equal to or smaller than n-3. Through order g^2 in field theory, we show that these correlators are simple sums of terms each of which factors into products of lower-point correlators. Terms which contain only factors of two- and three-point functions are not renormalized, but other terms have non-vanishing order g^2 corrections. We then show that the contributing AdS exchange diagrams neatly match this factored structure. In particular, for n=4,5 precise agreement in form and coefficient is established between supergravity and the non-renormalized factored terms from field theory. On the other hand, contact diagrams in supergravity would produce a non-factored structure. This leads us to conjecture that the corresponding bulk couplings vanish, so as to achieve full agreement between the structure of these correlators in supergravity and weak-coupling field theory.
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