Phases of five-dimensional supersymmetric gauge theories

Abstract

Five-dimensional $$ \mathcal{N} $$ N = 1 theories with gauge group U(N), SU(N), USp(2N) and SO(N) are studied at large rank through localization on a large sphere. The phase diagram of theories with fundamental hypermultiplets is universal and characterized by third order phase transitions, with the exception of U(N), that shows both second and third order transitions. The phase diagram of theories with adjoint or (anti-)symmetric hypermultiplets is also determined and found to be universal. Moreover, Wilson loops in fundamental and antisymmetric representations of any rank are analyzed in this limit. Quiver theories are discussed as well. All the results substantiate the ℱ-theorem.

3d defects in 5d: RG flows and defect F-maximization

“…Both are second order, controlled by the real mass parameter, and with critical exponent 1 2 . We note that the defect phase transition in Y N is in a different universality class than the more customary third order ones with finite discontinuity that appear in the planar limit [80,81]. 10 Defect F -theorem: our results for the mass deformed gauge theory defects are consistent with the defect F -theorem [38].…”

Matrix models and holography: Mass deformations of long quiver theories in 5d and 3d

“…In this approach, the Yang-Mills term is subleading in N but dominant in P. The two limits do not commute, and their order of limits is thus relevant (as already pointed out in [109]).…”

“…That is, it is expected to be stationary at the RG fixed points, with its value in the IR lower than its value in the UV. One important open question for 5d SCFTs, is a field theoretic derivation of the 5d F-theorem, see [109,122,129] for evidence in that direction. We have evaluated the sphere free energy for a wide class of 5d SCFTs, in the long quiver limit.…”

“…Recall that we are dealing with balanced quivers, and that the balancing condition reads (see [87,109]…”

“…Turning on massive deformations of large N field theories, there can be phase transitions (typically of third order) when such mass parameters cross a given threshold. It was proven in [109] that balanced linear quivers do not have such phase transitions.…”