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

Non-perturbative constraints on light sparticles from properties of the RG flow

This work was supported in part by the European Commission under the ERC Advanced Grant 226371 and the contract PITN-GA-2009-237920

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

On 4d rank-one N=3 superconformal field theories

We study the properties of 4d N=3 superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form C^3/Z_k for k=1,2,3,4,6, and that the supersymmetry automatically enhances to N=4 for k=1,2. In addition, we determine the central charges a and c in terms of k, and construct the associated 2d chiral algebras, which turn out to be exotic N=2 supersymmetric W-algebras.Comment: 24 page

Galois Conjugation and Multiboundary Entanglement Entropy

We revisit certain natural algebraic transformations on the space of 3D topological quantum field theories (TQFTs) called “Galois conjugations.” Using a notion of multiboundary entanglement entropy (MEE) defined for TQFTs on compact 3-manifolds with disjoint boundaries, we give these abstract transformations additional physical meaning. In the process, we prove a theorem on the invariance of MEE along orbits of the Galois action in the case of arbitrary Abelian theories defined on any link complement in S . We then give a generalization to non-Abelian TQFTs living on certain infinite classes of torus link com- plements. Along the way, we find an interplay between the modular data of non-Abelian TQFTs, the topology of the ambient spacetime, and the Galois action. These results are suggestive of a deeper connection between entanglement and fusion

Small deformation of a simple N=2 superconformal theory

We study an interesting relevant deformation of the simplest interacting N=2 SCFT---the original Argyres-Douglas (AD) theory. We argue that, although this deformation is not strictly speaking Banks-Zaks like (certain operator dimensions change macroscopically), there are senses in which it constitutes a mild deformation of the parent AD theory: the exact change in the "a" anomaly is small and is essentially saturated at one loop. Moreover, contributions from IR operators that have a simple description in the UV theory reproduce a particular limit of the IR index to a remarkably high order. These results lead us to conclude that the IR theory is an interacting N=1 SCFT with particularly small "a" and "c" central charges and that this theory sheds some interesting light on the spectrum of its AD parent.The work of M. B. is partially supported by the Royal Society under the grant “New Constraints and Phenomena in Quantum Field Theory” and by the U.S. Department of Energy under Grant No. DE-SC0009924. T. N. is partially supported by the Yukawa Memorial Foundation

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

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

On Irregular Singularity Wave Functions and Superconformal Indices

We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregu- lar singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU(N). As an application, we give closed-form expressions for the Schur indices of all (AN−1,AN(n−1)−1) Argyres-Douglas (AD) superconformal field theories (SCFTs), thus com- pleting the computation of these quantities for the (AN , AM ) SCFTs. With minimal effort, our wave functions also give new Schur indices of various infinite sets of “Type IV” AD theories. We explore the discrete symmetries of these indices and also show how highly intricate renormalization group (RG) flows from isolated theories and conformal manifolds in the ultraviolet to isolated theories and (products of) conformal manifolds in the infrared are encoded in these indices. We compare our flows with dimensionally reduced flows via a simple “monopole vev RG” formalism. Finally, since our expressions are given in terms of concise Lie algebra data, we speculate on extensions of our results that might be useful for probing the existence of hypothetical SCFTs based on other Lie algebras. We conclude with a discussion of some open problems