Deformations of superconformal theories

Abstract

We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in d ≥ 3 dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and noncentral charges. Second, many theories with a sufficient amount of supersymmetry do not admit relevant or marginal deformations, and some admit neither. The classification is complicated by the fact that short superconformal multiplets display a rich variety of sporadic phenomena, including supersymmetric deformations that reside in the middle of a multiplet. We illustrate our results with examples in diverse dimensions. In particular, we explain how the classification of irrelevant supersymmetric deformations can be used to derive known and new constraints on moduli-space effective actions.

Holographic RG flows for four-dimensional $$ \mathcal{N}=2 $$ SCFTs

“…While these results present interesting holographic predictions for strongly interacting SCFTs it should be noted that some of the supergravity results can also be shown more generally, without a reference to holography, using purely algebraic techniques [13]. Questions about the structure of RG flows triggered by relevant deformations on the other hand are less accessible with field theory tools and thus the supergravity results derived here should teach us important general lessons for the structure of supersymmetric RG flows.…”

“…The latter is related to the cosmological constant, which in our conventions is the same as the critical value of the scalar potential, V = −6/ 2 . The supersymmetry conditions for solutions of this form (and with ξ M = 0) read [28] −A γ 5 i + i P i j j = 0 , (2.10) 13) where i are the supersymmetry parameters, satisfying the symplectic-Majorana condition…”

N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs

“…This is because TrR 2 F = 0 for any global symmetry F in an N = 2 SCFT [39], and it also implies TrF = 0 so that the flavor symmetry F is "baryonic". 4 Baryonic symmetries cannot be mixed with the R-symmetry [3]. Therefore, we pick the trial U(1) R symmetry as…”

“…Let us briefly comment on the method to test the enhancement of supersymmetry from computing the N = 1 superconformal index. 8 In the section 5.5.1 of the recent paper [59], they list the conserved current multiplets of four-dimensional N = 1 superconformal theory. Once there is a flavor symmetry, we have a conserved current multiplet in the theory.…”

Universal bounds on operator dimensions from the average null energy condition

“…The representation theory of these algebras is known [26][27][28][29][30], and there are a variety of short multiplets that do not occur in known superconformal field theories. 2 Finally, it would be interesting to investigate our conjectures further, and to develop a more direct perspective on the anomalous dimensions of chiral operators.…”