1,720,989 research outputs found
Phases of 5d SCFTs from M-/F-theory on non-flat fibrations
Full text linkWe 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
AdS7/CFT6 with orientifolds
Full text linkAbstract AdS7 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 AdS7 vacua dual to nonperturbative F-theory configurations. Finally, we propose a holographic a-theorem for six-dimensional Higgs branch RG flows
5d SCFTs from decoupling and gluing
Full text linkWe systematically analyse 5d superconformal field theories (SCFTs) obtained by dimensional reduction from 6d N = (1, 0) SCFTs. Such theories have a realization as M-theory on a singular Calabi-Yau threefold, from which we determine the so-called combined fiber diagrams (CFD) introduced in [1–3]. The CFDs are graphs that encode the superconformal flavor symmetry, BPS states, low energy descriptions, as well as descendants upon flavor matter decoupling. To obtain a 5d SCFT from 6d, there are two approaches: the first is to consider a circle-reduction combined with mass deformations. The second is to circle-reduce and decouple an entire gauge sector from the theory. The former is applicable e.g. for very Higgsable theories, whereas the latter is required to obtain a 5d SCFT from a non-very Higgsable 6d theory. In the M-theory realization the latter case corresponds to decompactification of a set of compact surfaces in the Calabi-Yau threefold. To exemplify this we consider the 5d SCFTs that descend from non-Higgsable clusters and non-minimal conformal matter theories. Finally, inspired by the quiver structure of 6d theories, we propose a gluing construction for 5d SCFTs from building blocks and their CFDs
4D gauge theories with conformal matter
No full textOne of the hallmarks of 6D superconformal field theories (SCFTs) is that on a partial tensor branch, all known theories resemble quiver gauge theories with links comprised of 6D conformal matter, a generalization of weakly coupled hypermultiplets. In this paper we construct 4D quiverlike gauge theories in which the links are obtained from compactifications of 6D conformal matter on Riemann surfaces with flavor symmetry fluxes. This includes generalizations of super QCD with exceptional gauge groups and quarks replaced by 4D conformal matter. Just as in super QCD, we find evidence for a conformal window as well as confining gauge group factors depending on the total amount of matter. We also present F-theory realizations of these field theories via elliptically fibered Calabi-Yau fourfolds. Gauge groups (and flavor symmetries) come from 7-branes wrapped on surfaces, conformal matter localizes at the intersection of pairs of 7-branes, and Yukawas between 4D conformal matter localize at points coming from triple intersections of 7-branes. Quantum corrections can also modify the classical moduli space of the F-theory model, matching expectations from effective field theory
Nilpotent networks and 4D RG flows
Full text linkStarting from a general N= 2 SCFT, we study the network of 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 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 T2, 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 aIR/cIR for the entire network of flows associated with a given UV N= 2 SCFT. The arXiv submission also includes the full dataset of theories which can be accessed with a companion Mathematica script
Supersymmetric AdS5 solutions of massive IIA supergravity
Full text linkMotivated by a recently found class of AdS7 solutions, we classify AdS5 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 AdS7 solutions via a simple universal map for the metric, dilaton and fluxes. The natural interpretation of this map is that the dual CFT6 and CFT4 are related by twisted compactification on a Riemann surface Σg. The ratio of their free energy coefficients is proportional to the Euler characteristic of Σg. As a byproduct, we also find the analytic expression for the AdS7 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
AdS6 solutions of type II supergravity
Full text linkVery few AdS6 × M4 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 Σ. M4 is then a fibration of S2 over Σ; 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 CFT5’s. We also show that there are no AdS6 solutions in eleven-dimensional supergravity
Wilson lines and Chern-Simons flux in explicit heterotic Calabi-Yau compactifications
Full text linkWe 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 identifying large classes of 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
All AdS7 solutions of type II supergravity
Full text linkIn M-theory, the only AdS7 supersymmetric solutions are AdS7 × S4 and its orbifolds. In this paper, we find and classify new supersymmetric solutions of the type AdS7 × M3 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 M3 is that of an S2 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 M3 ≅ S3
From 6D superconformal field theories to dynamic gauged linear sigma models
No full textCompactifications of six-dimensional (6D) superconformal field theories (SCFTs) on four- manifolds generate a large class of novel two-dimensional (2D) quantum field theories. We consider in detail the case of the rank-one simple non-Higgsable cluster 6D SCFTs. On the tensor branch of these theories, the gauge group is simple and there are no matter fields. For compactifications on suitably chosen Kähler surfaces, we present evidence that this provides a method to realize 2D SCFTs with N=(0,2) supersymmetry. In particular, we find that reduction on the tensor branch of the 6D SCFT yields a description of the same 2D fixed point that is described in the UV by a gauged linear sigma model (GLSM) in which the parameters are promoted to dynamical fields, that is, a “dynamic GLSM” (DGLSM). Consistency of the model requires the DGLSM to be coupled to additional non-Lagrangian sectors obtained from reduction of the antichiral two-form of the 6D theory. These extra sectors include both chiral and antichiral currents, as well as spacetime filling noncritical strings of the 6D theory. For each candidate 2D SCFT, we also extract the left- and right-moving central charges in terms of data of the 6D SCFT and the compactification manifold
- …
