Phase structure of $\mathcal{N}=2^{\ast }$ SYM on ellipsoids

Abstract

We analyse the phase structure of an $\mathcal{N}=2$ massive deformation of $\mathcal{N}=4$ SYM theory on an four-dimensional ellipsoid using recent results on supersymmetric localisation. Besides the 't~Hooft coupling $\lambda$, the relevant parameters appearing in the theory and discriminating between the different phases are the hypermultiplet mass $M$ and the deformation (or squashing) parameter $Q$. The master field approximation of the matrix model associated to the analytically continued theory in the regime $Q\sim 2M$ and on the compact space, is exactly solvable and does not display any phase transition, similarly to $\mathcal{N}=2$ $SU(N)$ SYM with $2N$ massive hypermultiplets. In the strong coupling limit, equivalent in our settings to the decompactification of the four-dimensional ellipsoid, we find evidence that the theory undergoes an infinite number of phase transitions starting at finite coupling and accumulating at $\lambda =\infty$. Quite interestingly, the threshold points at which transitions occur can be pushed towards the weak coupling region by letting $Q$ approach $2M$.

41 pages

References in corpus (5)

• Wilson loops: From four-dimensional SYM to two-dimensional YM
• Super-Rényi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals
• N=2* Super-Yang-Mills Theory at Strong Coupling
• Supersymmetric $U(N)$ Chern-Simons-matter theory and phase transitions
• Phases of planar 5-dimensional supersymmetric Chern-Simons theory

Cited by in corpus (1)

• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories