Kenneth Intriligator

Dynamical SUSY breaking in meta-stable vacua

Dynamical supersymmetry breaking in a long-lived meta-stable vacuum is a phenomenologically viable possibility. This relatively unexplored avenue leads to many new models of dynamical supersymmetry breaking. Here, we present a surprisingly simple class of models with meta-stable dynamical supersymmetry breaking: = 1 supersymmetric QCD, with massive flavors. Though these theories are strongly coupled, we definitively demonstrate the existence of meta-stable vacua by using the free-magnetic dual. Model building challenges, such as large flavor symmetries and the absence of an R-symmetry, are easily accommodated in these theories. Their simplicity also suggests that broken supersymmetry is generic in supersymmetric field theory and in the landscape of string vacua.

Lectures on supersymmetry breaking

We review the subject of spontaneous supersymmetry breaking. First we consider supersymmetry breaking in a semiclassical theory. We illustrate it with several examples, demonstrating different phenomena, including metastable supersymmetry breaking. Then we give a brief review of the dynamics of supersymmetric gauge theories. Finally, we use this dynamics to present various mechanisms for dynamical supersymmetry breaking. This paper is based on lectures given by the authors in 2007, at various schools.

Bonus symmetries of N = 4 super-Yang-Mills correlation functions via AdS duality

General conjectures about the SL(2,cZ) modular transformation properties of N = 4 superYang-Mills correlation functions are presented. It is shown how these modular transformation properties arise from the conjectured duality with IIB string theory on AdS5 × S5. We discuss in detail a prediction of the AdS duality: that N = 4 field theory, in an appropriate limit, must exhibit bonus symmetries, corresponding to the enhanced symmetries of IIB string theory in its supergravity limit.

Supersymmetry breaking, R-symmetry breaking and metastable vacua

Models of spontaneous supersymmetry breaking generically have an R-symmetry, which is problematic for obtaining gaugino masses and avoiding light R-axions. The situation is improved in models of metastable supersymmetry breaking, which generically have only an approximate R-symmetry. Based on this we argue, with mild assumptions, that metastable supersymmetry breaking is inevitable. We also illustrate various general issues regarding spontaneous and explicit R-symmetry breaking, using simple toy models of supersymmetry breaking.

Comments on Unparticles

Abstract We comment on several points concerning unparticles which have been overlooked in the literature. One regards Macks unitarity constraint lower bounds on CFT operator dimensions, e.g., d V ⩾ 3 for primary, gauge invariant, vector unparticle operators. We correct the results in the literature to account for this, and also for a needed correction in the form of the propagator for vector and tensor unparticles. We show that the unitarity constraints can be directly related to unitarity requirements on scattering amplitudes of particles, e.g., those of the Standard Model, coupled to the CFT operators. We also stress the existence of explicit Standard Model contact terms, which are generically induced by the coupling to the CFT (or any other hidden sector), and are subject to LEP bounds. Barring an unknown mechanism to tune away these contact interactions, they can swamp interference effects generated by the CFT. We illustrate these points in the context of a weakly coupled CFT example. A significant amount of the unparticle literature should be reconsidered or revised in light of the observations in this note.

Bonus symmetry and the operator product expansion of N = 4 super-Yang-Mills

Abstract The superconformal group of N = 4 super-Yang-Mills has two types of operator representations: short and long. We conjecture that operator product expansions for which at least two of the three operators are short exactly respect a bonus U (1) y R-symmetry, which acts as an automorphism of the superconformal group. This conjecture is for arbitrary gauge group G and gauge coupling g YM . A consequence is that n ⩽ 4-point functions involving only short operators exactly respect the U (1) Y symmetry, as has been previously conjectured based on AdS duality. This, in turn, would imply that all n ⩽ 3-point functions involving only short operators are not renormalized, as has also been previously conjectured and subjected to perturbative checks. It is argued that instantons are compatible with our conjecture. Some perturbative checks of the conjecture are presented and SL(2, Z ) modular transformation properties are discussed.

Aspects of 3d \mathcal{N}=2 Chern-Simons-Matter theories

A bstractWe comment on various aspects of the the dynamics of 3d

Anomaly Matching and a Hopf-Wess-Zumino Term in 6d, N =( 2; 0) Field Theories

\mathcal{N}=2

Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories

Chern-Simons gauge theories and their possible phases. Depending on the matter content, real masses and FI parameters, there can be non-compact Higgs or Coulomb branches, compact Higgs or Coulomb branches, and isolated vacua. We compute the Witten index of the theories, and show that it does not change when the system undergoes a phase transition. We study aspects of monopole operators and solitons in these theories, and clarify subtleties in the soliton collective coordinate quantization. We show that solitons are compatible with a mirror symmetry exchange of Higgs and Coulomb branches, with BPS solitons on one branch related to the modulus of the other. Among other results, we show how to derive Aharony duality from Giveon-Kutasov duality.

RG fixed points and flows in SQCD with adjoints

Abstract We point out that the low energy theory of 6d N =(2,0) field theories, when away from the origin of the moduli space of vacua, necessarily includes a new kind of Wess–Zumino term. The form of this term is related to the Hopf invariant associated with π 7 ( S 4 ). The coefficient of the Wess–Zumino term is fixed by an anomaly matching relation for a global flavor symmetry. For example, in the context of a single M5 brane probe in the background of N distant M5 branes, the probe must have the Hopf–WZ term with coefficient proportional to N ( N +1). Various related checks and observations are made. We also point out that there are skyrmionic strings, and propose that they are the W -boson strings.