On the Geometry of Metastable Supersymmetry Breaking

We give a concise geometric recipe for constructing D-brane gauge theories that exhibit metastable SUSY breaking. We present two simple examples in terms of branes at deformed CY singularities.Comment: 31 pages, 9 figures, v2: references adde

A Conjectured Bound on Accidental Symmetries

In this note, we study a large class of four-dimensional R-symmetric theories, and we describe a new quantity, \tau_U, which is well-defined in these theories. Furthermore, we conjecture that this quantity is larger in the ultraviolet (UV) than in the infrared (IR), i.e. that \tau_U^{UV}>\tau_U^{IR}. While we do not prove this inequality in full generality, it is straightforward to show that our conjecture holds in the subset of theories that do not have accidental symmetries. In addition, we subject our inequality to an array of non-trivial tests in theories with accidental symmetries and dramatically different dynamics both in N=1 and N=2 supersymmetry and find that our inequality is obeyed. One interesting consequence of this conjecture is that the mixing of accidental symmetries with the IR superconformal R current is bounded by the UV quantity, \tau_U^{UV}. To demonstrate the potential utility of this bound, we apply it to the somewhat mysterious SU(2) gauge theory of Intriligator, Seiberg, and Shenker and show that our conjecture, if correct, implies that this theory flows in the IR to an interacting superconformal field theory.Comment: 50 pages; additional discussion; minor changes; results unchange

Non-Perturbative Explorations of Chiral Rings in 4d N=2\mathcal{N}=2 SCFTs

We study the conditions under which 4d $\mathcal{N}=2$ superconformal field theories (SCFTs) have multiplets housing operators that are chiral with respect to an $\mathcal{N}=1$ subalgebra. Our main focus is on the set of often-ignored and relatively poorly understood $\overline{\mathcal{B}}$ representations. These multiplets typically evade direct detection by the most popular non-perturbative 4d $\mathcal{N}=2$ tools and correspondences. In spite of this fact, we demonstrate the ubiquity of $\overline{\mathcal{B}}$ multiplets and show they are associated with interesting phenomena. For example, we give a purely algebraic proof that they are present in all local unitary $\mathcal{N}>2$ SCFTs. We also show that $\overline{\mathcal{B}}$ multiplets exist in $\mathcal{N}=2$ theories with rank greater than one and a conformal manifold or a freely generated Coulomb branch. Using recent topological quantum field theory results, we argue that certain $\overline{\mathcal{B}}$ multiplets exist in broad classes of theories with the $\mathbb{Z}_2$-valued 't Hooft anomaly for $Sp(N)$ global symmetry. Motivated by these statements, we then study the question of whether $\overline{\mathcal{B}}$ multiplets exist in rank-one SCFTs with exactly $\mathcal{N}=2$ SUSY. We conclude with various open questions.Comment: 44 page

D-branes at Singularities, Compactification, and Hypercharge

We report on progress towards the construction of SM-like gauge theories on the world-volume of D-branes at a Calabi-Yau singularity. In particular, we work out the topological conditions on the embedding of the singularity inside a compact CY threefold, that select hypercharge as the only light U(1) gauge factor. We apply this insight to the proposed open string realization of the SM of hep-th/0508089, based on a D3-brane at a dP_8 singularity, and present a geometric construction of a compact Calabi-Yau threefold with all the required topological properties. We comment on the relevance of D-instantons to the breaking of global U(1) symmetries.Comment: 39 pages, 9 figures. Minor correction

Argyres-Douglas Avatars of Coulomb Branch Physics

We study ultraviolet (UV) incarnations of deep infrared (IR) physics on the Coulomb branch of the simplest interacting 4D $\mathcal{N}=2$ superconformal field theory: the minimal Argyres-Douglas (MAD) theory. One of the most basic properties of the Coulomb branch is an emergent infinite-dimensional higher-spin symmetry. While the MAD theory is interacting and therefore does not have such a symmetry, we find UV operators that encode the emergent complex higher-spin symmetry on the Coulomb branch. Moreover, we show that cousins of these UV operators give rise to cousins of the IR higher-spin multiplets. In terms of superconformal representation theory, we are led to a conjecture on the exact spectrum of $\bar{\mathcal{C}}_{R,r(j,\bar j)}$ multiplets in the MAD theory for all $R$, $r$, $j$, and $\bar j$ satisfying $R+\bar j -j+1=0$, thereby making progress towards a full characterization of the protected spectrum. Along the way, we give a geometrical interpretation of these operators and include them in an extension of the Coulomb branch / $\mathcal{N}=2$ chiral operator correspondence.Comment: 36 pages; 3 figures; 2 table

4D Free Fields and the Minimal Argyres-Douglas Theory

The minimal Argyres-Douglas (MAD) theory is the "simplest" interacting 4d N=2 superconformal field theory (SCFT). Although it lacks an N=2 Lagrangian, the theory's simplicity suggests a close relationship with the free super-Maxwell SCFT on its Coulomb branch. We describe a precise realization of this idea by constructing a bijection between all MAD Schur operators and a subsector of free vector Schur operators. The ultraviolet dynamics governing infinitely many MAD null states manifest in the infrared (IR) via Fermi statistics of free gauginos. Using the concept of an arc space, this bijection allows us to compute the exact MAD Macdonald index from the IR. We conclude with generalizations and implications for the MAD local operator algebra.Comment: 10 pages and 1 figur

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction

On R-symmetric Fixed Points and Superconformality

An important unanswered question in quantum field theory is to understand precisely under which conditions scale invariance implies invariance under the full conformal group. While the general answer in two dimensions has been known for over twenty years, a precise non-perturbative relation between scale and conformal invariance in higher dimensions has been lacking. In this note, we specialize to four dimensions and give a full quantum mechanical proof that certain unitary R-symmetric fixed points are necessarily superconformal. Among other consequences, this result implies that the infrared fixed points of N=1 supersymmetric quantum chromodynamics are superconformal.Comment: 21 pages; references added; brief additional comments; results unchange