AdS7_7/CFT6_6 with orientifolds

AdS$_7$ solutions of massive type IIA have been classified, and are dual to a large class of six-dimensional $(1,0)$ SCFT's whose tensor branch deformations are described by linear quivers of SU groups. Quivers and AdS vacua depend solely on the group theory data of the NS5-D6-D8 brane configurations engineering the field theories. This has allowed for a direct holographic match of their $a$ conformal anomaly. In this paper we extend the match to cases where O6 and O8-planes are present, thereby introducing SO and USp groups in the quivers. In all of them we show that the $a$ anomaly computed in supergravity agrees with the holographic limit of the exact field theory result, which we extract from the anomaly polynomial. As a byproduct we construct special AdS$_7$ vacua dual to nonperturbative F-theory configurations. Finally, we propose a holographic $a$-theorem for six-dimensional Higgs branch RG flows.Comment: 91 pages, 6 figures, 4 tables, 4 appendices; v2: typos fixed, version published in JHE

Flux backreaction in supergravity : heterotic Calabi-Yau compactifications and new type II anti-de-Sitter vacua

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Green-Schwarz Automorphisms and 6D SCFTs

All known interacting 6D superconformal field theories (SCFTs) have a tensor branch which includes anti-chiral two-forms and a corresponding lattice of string charges. Automorphisms of this lattice preserve the Dirac pairing and specify discrete global and gauge symmetries of the 6D theory. In this paper we compute this automorphism group for 6D SCFTs. This discrete data determines the geometric structure of the moduli space of vacua. Upon compactification, these automorphisms generate Seiberg-like dualities, as well as additional theories in discrete quotients by the 6D global symmetries. When a perturbative realization is available, these discrete quotients correspond to including additional orientifold planes in the string construction.Comment: v2: 66 pages, 5 figures, updated references and clarifications adde

All AdS_7 solutions of type II supergravity

In M-theory, the only AdS_7 supersymmetric solutions are AdS_7 x S^4 and its orbifolds. In this paper, we find and classify new supersymmetric solutions of the type AdS_7 x M_3 in type II supergravity. While in IIB none exist, in IIA with Romans mass (which does not lift to M-theory) there are many new ones. We use a pure spinor approach reminiscent of generalized complex geometry. Without the need for any Ansatz, the system determines uniquely the form of the metric and fluxes, up to solving a system of ODEs. Namely, the metric on M_3 is that of an S^2 fibered over an interval; this is consistent with the Sp(1) R-symmetry of the holographically dual (1,0) theory. By including D8 brane sources, one can numerically obtain regular solutions, where topologically M_3 = S^3.Comment: 45 pages, 4 figures. v2: solution with single D8 added; references added; minor correction

Supersymmetric AdS_5 solutions of massive IIA supergravity

Motivated by a recently found class of AdS_7 solutions, we classify AdS_5 solutions in massive IIA, finding infinitely many new analytical examples. We reduce the general problem to a set of PDEs, determining the local internal metric, which is a fibration over a surface. Under a certain simplifying assumption, we are then able to analytically solve the PDEs and give a complete list of all solutions. Among these, one class is new and regular. These spaces can be related to the AdS_7 solutions via a simple universal map for the metric, dilaton and fluxes. The natural interpretation of this map is that the dual CFT_6 and CFT_4 are related by twisted compactification on a Riemann surface $\Sigma_g$. The ratio of their free energy coefficients is proportional to the Euler characteristic of $\Sigma_g$. As a byproduct, we also find the analytic expression for the AdS_7 solutions, which were previously known only numerically. We determine the free energy for simple examples: it is a simple cubic function of the flux integers.Comment: 56 pages, 2 figures, LaTeX; v3: subsection 4.3.1 revised, minor correction

Wilson lines and Chern-Simons flux in explicit heterotic Calabi-Yau compactifications

We study to what extent Wilson lines in heterotic Calabi-Yau compactifications lead to non-trivial H-flux via Chern-Simons terms. Wilson lines are basic ingredients for Standard Model constructions but their induced H-flux may affect the consistency of the leading order background geometry and of the two-dimensional worldsheet theory. Moreover H-flux in heterotic compactifications would play an important role for moduli stabilization and could strongly constrain the supersymmetry breaking scale. We show how to compute H-flux and the corresponding superpotential, given an explicit complete intersection Calabi-Yau compactification and choice of Wilson lines. We do so by classifying special Lagrangian submanifolds in the Calabi-Yau, understanding how the Wilson lines project onto these submanifolds, and computing their Chern-Simons invariants. We illustrate our procedure with the quintic hypersurface as well as the split-bicubic, which can provide a potentially realistic three generation model.Comment: 41 pages, 7 figures. v2: Minor corrections, published versio

Nilpotent Networks and 4D RG Flows

Starting from a general $\mathcal{N} = 2$ SCFT, we study the network of $\mathcal{N} = 1$ SCFTs obtained from relevant deformations by nilpotent mass parameters. We also study the case of flipper field deformations where the mass parameters are promoted to a chiral superfield, with nilpotent vev. Nilpotent elements of semi-simple algebras admit a partial ordering connected by a corresponding directed graph. We find strong evidence that the resulting fixed points are connected by a similar network of 4D RG flows. To illustrate these general concepts, we also present a full list of nilpotent deformations in the case of explicit $\mathcal{N} = 2$ SCFTs, including the case of a single D3-brane probing a $D$- or $E$-type F-theory 7-brane, and 6D $(G,G)$ conformal matter compactified on a $T^2$, as described by a single M5-brane probing a $D$- or $E$-type singularity. We also observe a number of numerical coincidences of independent interest, including a collection of theories with rational values for their conformal anomalies, as well as a surprisingly nearly constant value for the ratio $a_{\mathrm{IR}} / c_{\mathrm{IR}}$ for the entire network of flows associated with a given UV $\mathcal{N} = 2$ SCFT. The $\texttt{arXiv}$ submission also includes the full dataset of theories which can be accessed with a companion $\texttt{Mathematica}$ script.Comment: v2: 73 pages, 12 figures, clarifications and references adde

AdS_6 solutions of type II supergravity

Very few AdS_6 x M_4 supersymmetric solutions are known: one in massive IIA, and two IIB solutions dual to it. The IIA solution is known to be unique; in this paper, we use the pure spinor approach to give a classification for IIB supergravity. We reduce the problem to two PDEs on a two-dimensional space Sigma. M_4 is then a fibration of S^2 over Sigma; the metric and fluxes are completely determined in terms of the solution to the PDEs. The results seem likely to accommodate near-horizon limits of (p,q)-fivebrane webs studied in the literature as a source of CFT_5's. We also show that there are no AdS_6 solutions in eleven-dimensional supergravity.Comment: 37 pages; v2: references and equations (5.1) added, version published in Journal of High Energy Physics; v3: equation (5.1b) correcte

UV Completions for Non-Critical Strings

Compactifications of the physical superstring to two dimensions provide a general template for realizing 2D conformal field theories coupled to worldsheet gravity, i.e. non-critical string theories. Motivated by this observation, in this paper we determine the quasi-topological 8D theory which governs the vacua of 2D N = (0,2) gauged linear sigma models (GLSMs) obtained from compactifications of type I and heterotic strings on a Calabi-Yau fourfold. We also determine the quasi-topological 6D theory governing the 2D vacua of intersecting 7-branes in compactifications of F-theory on an elliptically fibered Calabi-Yau fivefold, where matter fields and interaction terms localize on lower-dimensional subspaces, i.e. defect operators. To cancel anomalies / cancel tadpoles, these GLSMs must couple to additional chiral sectors, which in some cases do not admit a known description in terms of a UV GLSM. Additionally, we find that constructing an anomaly free spectrum can sometimes break supersymmetry due to spacetime filling anti-branes. We also study various canonical examples such as the standard embedding of heterotic strings on a Calabi-Yau fourfold and F-theoretic "rigid clusters" with no local deformation moduli of the elliptic fibration.Comment: v4: 102 pages, 2 figures, clarifications adde

Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations

We initiate the systematic investigation of non-flat resolutions of non-minimal singularities in elliptically fibered Calabi--Yau threefolds. Compactification of M-theory on these geometries provides an alternative approach to studying phases of five-dimensional superconformal field theories (5d SCFTs). We argue that such resolutions capture non-trivial holonomies in the circle reduction of the 6d conformal matter theory that is the F-theory interpretation of the singular fibration. As these holonomies become mass deformations in the 5d theory, non-flat resolutions furnish a novel method in the attempt to classify 5d SCFTs through 6d SCFTs on a circle. A particularly pleasant aspect of this proposal is the explicit embedding of the 5d SCFT's enhanced flavor group inside that of the parent 6d SCFT, which can be read off from the geometry. We demonstrate these features in toric examples which realize 5d theories up to rank four.Comment: 49 pages + appendix and references, 10 figures; v2: discussion of prepotentials improved, references added, typos corrected; v3+v4: typos fixed, accepted for publication in JHE