On non-supersymmetric fixed points in five dimensions

Abstract

We generalize recent results regarding the phase space of the mass deformed E1 fixed point to a full class of five-dimensional superconformal field theories, known as X1,N. As in the E1 case, a phase transition occurs as a supersymmetry preserving and a supersymmetry breaking mass deformations are appropriately tuned. The order of such phase transition could not be unequivocally determined in the E1 case. For X1,N, instead, we can show that at large N there exists a regime where the phase transition is second order. Our findings give supporting evidence for the existence of non-supersymmetric fixed points in five dimensions.

Complete prepotentials of 5d higher rank theories

“…. Moreover, very recently, the existence of five dimensional non-supersymmetric conformal field theories was investigated using several techiques, such as the ϵ-expansion, the bootstrap [36][37][38][39][40][41][42][43][44], and soft supersymmety breaking of known superconformal fixed points [45][46][47].…”

“…This aspect becomes particularly useful when supersymmetry is softly broken and we lack control over the non-perturbative dynamics of the theory, as was observed recently for the E 1 theory subject to a soft SUSY breaking deformation [45]. It would be nice to perform a similar analysis on the X 1,N theory subject to the deformations studied in [47] and to see also if, as happens for the E 1 theory in this context [46], soft supersymmetry breaking deformations lead to instabilities on the Higgs branch of these theories. This is at the moment still work in progress.…”

“…Tuning the i-th effective coupling t i to zero makes the i-th and the (i + 1)-th brane coincide, leading to a preserved SU (2) which rotates the corresponding elements of the VEV matrix. Finally, we can consider the supersymmetric deformation analyzed in [47] where all branes with even (resp. odd) labels are forced to lie on the same line and are separated from the group of odd (resp.…”

“…The large N regime of X 1,N was studied in [47]. In particular, both a supersymmetric and a SUSY breaking deformation of the fixed point were analyzed in the large N limit of the web, unveiling the existence of a second order phase transition in the phase diagram of the theory for specific values of mass parameters.…”

Free energy on the sphere for non-abelian gauge theories

“…The CFT capturing this phase transition would therefore be a UV completion of YM, and provide an example of a non-supersymmetric interacting CFT in d > 4. This scenario was further explored in [26], that showed that actually the phase transition should be viewed as separating the YM phase from a phase with spontaneous breaking of the instantonic JHEP04(2023)099 U (1), and in [48] where a certain generalization of the theory admitting a large N limit was argued to have a second order transition in that limit.…”