Contributor info: Dr Cyril Closset

Cyril Closset, Osama Khlaif

SciPost Phys. 15, 085 (2023) · published 8 September 2023 | Toggle abstract · pdf

We consider unitary SQCD, a three-dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-matter theory consisting of one $U(N_c)_{k, k+l N_c}$ vector multiplet coupled to $n_f$ fundamental and $n_a$ antifundamental chiral multiplets, where $k$ and $l$ parameterise generic CS levels for $U(N_c)=(SU(N_c)\times U(1))/\mathbb{Z}_{N_c}$. We study the moduli space of vacua of this theory with $n_a=0$, for generic values of the parameters $N_c, k, l, n_f$ and with a non-zero Fayet-Ilopoulos parameter turned on. We uncover a rich pattern of vacua including Higgs, topological and hybrid phases. This allows us to derive a closed-form formula for the flavoured Witten index of unitary SQCD for any $n_f\neq n_a$, generalising previously known results for either $l=0$ or $n_f=n_a$. Finally, we analyse the vacuum structure of recently proposed infrared-dual gauge theories and we match vacua across the dualities, thus providing intricate new checks of those dualities. Incidentally, we also discuss a seemingly new level/rank duality for pure CS theories with $U(N)\times U(N')$ gauge group.

Cyril Closset, Horia Magureanu

SciPost Phys. 12, 065 (2022) · published 17 February 2022 | Toggle abstract · pdf

The simplest non-trivial 5d superconformal field theories (SCFT) are the famous rank-one theories with $E_n$ flavour symmetry. We study their $U$-plane, which is the one-dimensional Coulomb branch of the theory on $\mathbb{R}^4 \times S^1$. The total space of the Seiberg-Witten (SW) geometry -- the $E_n$ SW curve fibered over the $U$-plane -- is described as a rational elliptic surface with a singular fiber of type $I_{9-n}$ at infinity. A classification of all possible Coulomb branch configurations, for the $E_n$ theories and their 4d descendants, is given by Persson's classification of rational elliptic surfaces. We show that the global form of the flavour symmetry group is encoded in the Mordell-Weil group of the SW elliptic fibration. We study in detail many special points in parameters space, such as points where the flavour symmetry enhances, and/or where Argyres-Douglas and Minahan-Nemeschansky theories appear. In a number of important instances, including in the massless limit, the $U$-plane is a modular curve, and we use modularity to investigate aspects of the low-energy physics, such as the spectrum of light particles at strong coupling and the associated BPS quivers. We also study the gravitational couplings on the $U$-plane, matching the infrared expectation for the couplings $A(U)$ and $B(U)$ to the UV computation using the Nekrasov partition function.

Cyril Closset, Michele Del Zotto, Vivek Saxena

SciPost Phys. 6, 052 (2019) · published 1 May 2019 | Toggle abstract · pdf

We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities $\mathbf{X}$ and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to $\mathbf{X}$. Focussing on the case of toric CY singularities, we analyze the "gauge-theory phases" of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type $A_{M-1}$ fibered over a real line, and the map between the K\"ahler parameters of $\mathbf{X}$ and the Coulomb branch parameters of the field theory (masses and VEVs) can be read off systematically. Different type IIA "reductions" give rise to different gauge theory phases, whose existence depends on the particular (partial) resolutions of the isolated singularity $\mathbf{X}$. We also comment on the case of non-isolated toric singularities. Incidentally, we propose a slightly modified expression for the Coulomb-branch prepotential of 5d $\mathcal{N}=1$ gauge theories.