Zohar Komargodski

On renormalization group flows in four dimensions

A bstractWe discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the effective action of the Nambu-Goldstone boson of broken conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly is “non-Abelian”, and leads to a positive-definite universal contribution to the S-matrix element of 2 → 2 dilaton scattering. Unitarity of the S-matrix results in a monotonically decreasing function that interpolates between the Euler anomalies in the ultraviolet and the infrared, thereby establishing the a-theorem.

Convexity and liberation at large spin

A bstractWe consider several aspects of unitary higher-dimensional conformal field theories (CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep inelastic scattering in the gapped phase leads to a convexity property of dimensions of spinning operators of the original CFT. We further investigate the dimensions of spinning operators via the crossing equations in the light-cone limit. We find that, in a sense, CFTs become free at large spin and 1/s is a weak coupling parameter. The spectrum of CFTs enjoys additivity: if two twists τ1, τ2 appear in the spectrum, there are operators whose twists are arbitrarily close to τ1 + τ2. We characterize how τ1 + τ2 is approached at large spin by solving the crossing equations analytically. We find the precise form of the leading correction, including the prefactor. We compare with examples where these observables were computed in perturbation theory, or via gauge-gravity duality, and find complete agreement. The crossing equations show that certain operators have a convex spectrum in twist space. We also observe a connection between convexity and the ratio of dimension to charge. Applications include the 3d Ising model, theories with a gravity dual, SCFTs, and patterns of higher spin symmetry breaking.

Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity

We analyze various supersymmetry multiplets containing the supercurrent and the energy-momentum tensor. The most widely known such multiplet, the Ferrara-Zumino (FZ) multiplet, is not always well-defined. This can happen once Fayet-Iliopoulos (FI) terms are present or when the Kähler form of the target space is not exact. We present a new multiplet

The Constraints of Conformal Symmetry on RG Flows

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Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories

which always exists. This understanding of the supersymmetry current allows us to obtain new results about the possible IR behavior of supersymmetric theories. Next, we discuss the coupling of rigid supersymmetric theories to supergravity. When the theory has an FZ-multiplet or it has a global R-symmetry the standard formalism can be used. But when this is not the case such simple gauging is impossible. Then, we must gauge the current

Supersymmetric field theories on three-manifolds

{\mathcal{S}_{\alpha \dot{\alpha }}}

Notes on SUSY and R-symmetry breaking in Wess-Zumino models

. The resulting theory has, in addition to the graviton and the gravitino, another massless chiral superfield Φ which is essential for the consistency of the theory. Some of the moduli of various string models play the role of Φ. Our general considerations, which are based on the consistency of supergravity, show that such moduli cannot be easily lifted thus leading to constraints on gravity/string models.

Comments on Chern-Simons contact terms in three dimensions

A bstractIf the coupling constants in QFT are promoted to functions of space-time, the dependence of the path integral on these couplings is highly constrained by conformal symmetry. We begin the present note by showing that this idea leads to a new proof of Zamolodchikov’s theorem. We then review how this simple observation also leads to a derivation of the a-theorem. We exemplify the general procedure in some interacting theories in four space-time dimensions. We concentrate on Banks-Zaks and weakly relevant flows, which can be controlled by ordinary and conformal perturbation theories, respectively. We compute explicitly the dependence of the path integral on the coupling constants and extract the change in the a-anomaly (this agrees with more conventional computations of the same quantity). We also discuss some general properties of the sum rule found in [1] and study it in several examples.

Exactly Marginal Deformations and Global Symmetries

A bstractWe consider three-dimensional

The geometry of supersymmetric partition functions

\mathcal{N}=2