Five-brane Webs Research Articles

Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers

We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifold five-planes. We propose a generalization of the rules to derive magnetic quivers from brane webs pioneered in [1], by analyzing theories that can be described with a brane web with and without O5 planes. Our proposed magnetic quivers include novel features, such as hypermultiplets transforming in the fundamental-fundamental representation of two gauge nodes, antisymmetric matter, and ℤ2 gauge nodes. We test our results by computing the Coulomb and Higgs branch Hilbert series of the magnetic quivers obtained from the two distinct constructions and find agreement in all cases.

Brane webs and magnetic quivers for SQCD

It is widely considered that the classical Higgs branch of 4d mathcal{N} = 2 SQCD is a well understood object. However there is no satisfactory understanding of its structure. There are two complications: (1) the Higgs branch chiral ring contains nilpotent elements, as can easily be checked in the case of SU(N) with 1 flavour. (2) the Higgs branch as a geometric space can in general be decomposed into two cones with nontrivial intersection, the baryonic and mesonic branches. To study the second point in detail we use the recently developed tool of magnetic quivers for five-brane webs, using the fact that the classical Higgs branch for theories with 8 supercharges does not change through dimensional reduction. We compare this approach with the computation of the hyper-Kähler quotient using Hilbert series techniques, finding perfect agreement if nilpotent operators are eliminated by the computation of a so called radical. We study the nature of the nilpotent operators and give conjectures for the Hilbert series of the full Higgs branch, giving new insights into the vacuum structure of 4d mathcal{N} = 2 SQCD. In addition we demonstrate the power of the magnetic quiver technique, as it allows us to identify the decomposition into cones, and provides us with the global symmetries of the theory, as a simple alternative to the techniques that were used to date.

Five-brane webs and highest weight representations

We consider BPS-counting functions mathcal{Z} N,M of N parallel M5-branes probing a transverse ℤM orbifold geometry. These brane web configurations can be dualised into a class of toric non-compact Calabi-Yau threefolds which have the structure of an elliptic fibration over (affine) AN −1. We make this symmetry of mathcal{Z} N,M manifest in particular regions of the parameter space of the setup: we argue that for specific choices of the deformation parameters, the supercharges of the system acquire particular holonomy charges which lead to infinitely many cancellations among states contributing to the partition function. The resulting (simplified) mathcal{Z} N,M can be written as a sum over weights forming a single irreducible representation of the Lie algebra mathfrak{a} N −1 (or its affine counterpart). We show this behaviour explicitly for an extensive list of examples for specific values of (N, M ) and generalise the arising pattern for generic configurations. Finally, for a particular compact M5-brane setup we use this form of the partition function to make the duality N ↔ M manifest.

(p,q)-strings probing five-brane webs

In recent work, globally well-defined Type IIB supergravity solutions with geometry AdS6 × S2 warped over a Riemann surface Σ were constructed and conjectured to describe the near-horizon geometry of (p, q) five-brane webs in the conformal limit. In the present paper, we offer more evidence for this interpretation of the supergravity solutions in terms of five-brane webs. In particular, we explore the behavior of probe (p, q)-strings in certain families of these AdS6 × S2 × Σ backgrounds and compare this behavior to that predicted by microscopic, brane web considerations. In the microscopic picture, we argue that the embedding of a probe string may give rise to the formation of string junctions involving open strings anchored on the branes of the web. We then identify a quantity on the supergravity side that is conjectured to be equivalent to the total junction tension in a class of backgrounds corresponding to brane webs with four semi-infinite external five-branes. In the process, we will show that for general brane web backgrounds, the minimal energy probe string embeddings do not coincide with the embeddings preserving half of the background supersymmetries.

Warped AdS6 \xd7 S2 in Type IIB supergravity II: global solutions and five-brane webs

Motivated by the construction of holographic duals to five-dimensional superconformal quantum field theories, we obtain global solutions to Type IIB supergravity invariant under the superalgebra F (4) on a space-time of the form AdS6 × S2 warped over a two-dimensional Riemann surface Σ. In earlier work, the general local solutions were expressed in terms of two locally holomorphic functions mathcal{A} ± on Σ and global solutions were sketched when Σ is a disk. In the present paper, the physical regularity conditions on the supergravity fields required for global solutions are implemented on mathcal{A} ± for arbitrary Σ. Global solutions exist only when Σ has a non-empty boundary ∂Σ. The differentials ∂ mathcal{A} ± are allowed to have poles only on ∂Σ and each pole corresponds to a semi-infinite (p, q) five-brane. The construction for the disk is carried out in detail and the conditions for the existence of global solutions are articulated for surfaces with more than one boundary and higher genus.

AdS6 solutions of type II supergravity

Abstract Very 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.

Relating conifold geometries to NS5-branes

We construct the first known example of a near horizon supergravity solution for a pair of NS5-branes, intersecting on R 1 , 3 and localised in all directions except a single transverse circle. We do this by establishing an explicit map between the conifold metric and the near horizon geometry of two intersecting NS5-branes, clarifying and correcting a number of open issues in the literature en route. Our technique is general in nature and may be applied to a whole class of 1/4-BPS five-brane webs and their geometric duals. These 1/4-BPS solutions may have an interesting holographic interpretation in terms of little string theory.