On the Witten index of 3d $\mathcal{N}=2$ unitary SQCD with general CS levels

Abstract

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 $n_f\ne n_a$, 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 $U(N)\times U(N^{\prime })$ gauge group.

arXiv comment37 pages+appendix; v2: corrected typos and references; v3: small clarifications after feedback from SciPost referees

References in corpus (32)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Phases of $N=2$ Theories In Two Dimensions
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Level/rank Duality and Chern-Simons-Matter Theories
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Seiberg Duality in Chern-Simons Theory
• A topologically twisted index for three-dimensional supersymmetric theories
• IR Duality in d=3 N=2 Supersymmetric USp(2N_c) and U(N_c) Gauge Theories
• Comments on 3d Seiberg-like dualities
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Comments on twisted indices in 3d supersymmetric gauge theories
• Aspects of 3d N=2 Chern-Simons-Matter Theories
• Supersymmetric Index Of Three-Dimensional Gauge Theory
• Branes and Supersymmetry Breaking in Three Dimensional Gauge Theories
• Supersymmetric partition functions and the three-dimensional A-twist
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• Dynamics of N=2 Supersymmetric Chern-Simons Theories
• Mirror Symmetry and Toric Geometry in Three-Dimensional Gauge Theories
• Supersymmetric Index and s-rule for Type IIB Branes
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Supersymmetric partition functions on Riemann surfaces
• Non-Abelian 3d Bosonization and Quantum Hall States
• Type IIB construction of flavoured ABJ(M) and fractional M2 branes
• Living on the walls of super-QCD
• Twisted Hilbert Spaces of 3d Supersymmetric Gauge Theories
• Quantum K theory of symplectic Grassmannians
• Wilson loop algebras and quantum K-theory for Grassmannians
• Twisted indices, Bethe ideals and 3d $\mathcal{N}=2$ infrared dualities
• Generalized Giveon-Kutasov duality
• 3d $\mathcal{N}=2$ dualities for $SU(N_c)\times U(1)$ Chern-Simons gauge theories
• Witten index in N=1 and N=2 SYMCS theories with matter
• Mildly Flavoring domain walls in SU(N) SQCD: baryons and monopole superpotentials

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• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories
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• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials