IR free or interacting? A proposed diagnostic

Abstract

Einstein Drive, Princeton NJ 08540We present and discuss a conjectured criterion for determining whether a 4d quantum field theory is IR free, or flows to an interacting conformal field theory in the infrared: "the correct infrared phase is that with the larger conformal anomaly a". A stronger conjecture is that "an operator can become IR free only if that results in a larger conformal anomaly a". We test these conjectures in the context of N = 1 supersymmetric theories. They are verified to indeed predict the correct IR phase in every tested case, for a plethora of examples for which the infrared phase could already be determined on other grounds.When applied to the still unsettled case of SU (2) with a chiral superfield in the isospin 3/2 representation, the conjecture suggest that the IR phase is conformal rather than confining. September 20051 Sabbatical address, Sept. '05 to June '06.

Supersymmetric asymptotic safety is not guaranteed

“…Indeed a 1 (R) = −a 1 (2 − R), so a 1 (R = 1) = 0, fitting with massive operators contributing a = 0. Note also that a 1 (R) is below the local maximum, a 1 (R) < a 1 (R = 2/3), for all R in the range R < 5/3 (see [48] for a related conjectured phase diagnostic). For unconstrained, i.e.…”

Cardy formula for 4d SUSY theories and localization

“…There are few known examples [43,44] so far of theories with V eff M 3 (a min ) < 0, and they share some intriguing features: 1) the unbroken R-symmetry has Tr(R) > 0, which implies that in absence of emergent symmetries the IR SCFTs will have c − a < 0; 2) they are examples of so-called "misleading anomaly matching" [43], meaning that all 't Hooft anomalies are matched by a putative confined phase, but various arguments rule out this possibility and point to the existence of an interacting IR phase (see also [45][46][47][48]). We will analyze a large class of examples and find that in all these theories the potential is minimized in the origin when Tr(R) ≤ 0.…”

Aspects of Supersymmetric Field Theories

“…[11]: that the correct IR phase is that with the larger value of the conformal anomaly a IR . The intuition is that the shorter IR flow is correct, and that ∆a measures the length of the RG flow.…”