On the Witten index of 3d N=2 unitary SQCD with general CS levels

Cyril Closset; Osama Khlaif

doi:10.21468/SciPostPhys.15.3.085

On the Witten index of 3d N=2 unitary SQCD with general CS levels

Cyril Closset, Osama Khlaif

Mathematics

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Abstract

We consider unitary SQCD, a three-dimensional N=2 supersymmetric Chern-Simons-matter theory consisting of one U(N_c)_k,k+lNc 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)×U(1))/ℤ_Nc. 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≠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)×U(N′) gauge group.

Original language	English
Article number	085
Number of pages	40
Journal	SciPost Physics
Volume	15
Issue number	3
DOIs	https://doi.org/10.21468/SciPostPhys.15.3.085
Publication status	Published - 8 Sept 2023

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title = "On the Witten index of 3d N=2 unitary SQCD with general CS levels",

abstract = "We consider unitary SQCD, a three-dimensional N=2 supersymmetric Chern-Simons-matter theory consisting of one U(Nc)k,k+lNc vector multiplet coupled to nf fundamental and na antifundamental chiral multiplets, where k and l parameterise generic CS levels for U(Nc)=(SU(Nc)×U(1))/ℤNc. We study the moduli space of vacua of this theory with na=0, for generic values of the parameters Nc,k,l,nf 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 nf≠na, generalising previously known results for either l=0 or nf=na. 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)×U(N′) gauge group.",

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N2 - We consider unitary SQCD, a three-dimensional N=2 supersymmetric Chern-Simons-matter theory consisting of one U(Nc)k,k+lNc vector multiplet coupled to nf fundamental and na antifundamental chiral multiplets, where k and l parameterise generic CS levels for U(Nc)=(SU(Nc)×U(1))/ℤNc. We study the moduli space of vacua of this theory with na=0, for generic values of the parameters Nc,k,l,nf 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 nf≠na, generalising previously known results for either l=0 or nf=na. 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)×U(N′) gauge group.

AB - We consider unitary SQCD, a three-dimensional N=2 supersymmetric Chern-Simons-matter theory consisting of one U(Nc)k,k+lNc vector multiplet coupled to nf fundamental and na antifundamental chiral multiplets, where k and l parameterise generic CS levels for U(Nc)=(SU(Nc)×U(1))/ℤNc. We study the moduli space of vacua of this theory with na=0, for generic values of the parameters Nc,k,l,nf 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 nf≠na, generalising previously known results for either l=0 or nf=na. 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)×U(N′) gauge group.

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JF - SciPost Physics

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On the Witten index of 3d N=2 unitary SQCD with general CS levels

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