Giveon-Kutasov Duality Research Articles

Twisted indices, Bethe ideals and 3d mathcal{N} = 2 infrared dualities

We study the topologically twisted index of 3d mathcal{N} = 2 supersymmetric gauge theories with unitary gauge groups. We implement a Gröbner basis algorithm for computing the Σg× S1 index explicitly and exactly in terms of the associated Bethe ideal, which is defined as the algebraic ideal associated with the Bethe equations of the corresponding 3d A-model. We then revisit recently discovered infrared dualities for unitary SQCD with gauge group U(Nc)k,k+lNc with l ≠ 0, namely the Nii duality that generalises the Giveon-Kutasov duality, the Amariti-Rota duality that generalises the Aharony duality, and their further generalisations in the case of arbitrary numbers of fundamental and antifundamental chiral multiplets. In particular, we determine all the flavour Chern-Simons contact terms needed to make these dualities work. This allows us to check that the twisted indices of dual theories match exactly. We also initiate the study of the Witten index of unitary SQCD with l ≠ 0.

3d mathcal{N} = 3 generalized Giveon-Kutasov duality

We generalize the Giveon-Kutasov duality for the 3d mathcal{N} = 3 U(N)k,k+nN Chern-Simons matter gauge theory with F fundamental hypermultiplets by introducing SU(N) and U(1) Chern-Simons levels differently. We study the supersymmetric partition functions and the superconformal indices of the duality, which supports the validity of the duality proposal. From the duality, we can map out the low-energy phases: for example, confinement appears for F + k − N = −n = 1 or N = 2F = k = −n = 2. For F + k − N < 0, supersymmetry is spontaneously broken, which is in accord with the fact that the partition function vanishes. In some cases, the theory shows supersymmetry enhancement to 3d mathcal{N} = 4. For k = 0, we comment on the magnetic description dual to the so-called “ugly” theory, where the usual decoupled sector is still interacting with others for n ≠ 0. We argue that the SU(N)0 “ugly-good” duality (which corresponds to the n → ∞ limit in our setup) is closely related to the S-duality of the 4d mathcal{N} = 2 SU(N) superconformal gauge theory with 2N fundamental hypermultiplets. By reducing the number of flavors via real masses, we suggest possible ways to flow to the “bad” theories.

Generalized Giveon-Kutasov duality

We generalize the Giveon-Kutasov duality by adding possible Chern-Simons interactions for the U(N) gauge group. Some of the generalized dualities are known in the literature and many others are new to the best of our knowledge. The dualities are connected to the non-supersymmetric bosonization duality via mass deformations. For N = 1, there are an infinite number of magnetic-dual theories.

Tests of Seiberg-like dualities in three dimensions

We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for mathcal{N} = 3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a generalization of the latter. Our analysis also confirms previously known results concerning decoupled free sectors in mathcal{N} = 4 gauge theories realized by monopole operators.

Supersymmetric U(N) Chern–Simons-Matter Theory and Phase Transitions

We study ${\mathcal{N}}=2$ supersymmetric $U(N)$ Chern-Simons with $N_{f}$ fundamental and $N_{f}$ antifundamental chiral multiplets of mass $m$ in the complete parameter space spanned by $(g,\,m,\,N,\,N_{f})$, where $g$ denotes the coupling constant. In particular, we analyze the matrix model description of its partition function, both at finite $N$ using the method of orthogonal polynomials together with Mordell integrals and, at large $N$ with fixed $g$, using the theory of Toeplitz determinants. We show for the massless case that there is an explicit realization of the Giveon-Kutasov duality. For finite $N$, with $N>N_{f}$, three regimes that exactly correspond to the known three large $N$ phases of theory are identified and characterized.

Chern Simons duality with a fundamental boson and fermion

We compute the thermal free energy for all renormalizable Chern Simon theories coupled to a single fundamental bosonic and fermionic field in the 't Hooft large N limit. We use our results to conjecture a strong weak coupling duality invariance for this class of theories. Our conjectured duality reduces to Giveon Kutasov duality when restricted to {\cal N}=2 supersymmetric theories and to an earlier conjectured bosonization duality in an appropriate decoupling limit. Consequently the bosonization duality may be regarded as a deformation of Giveon Kutasov duality, suggesting that it is true even at large but finite N.

Flows between dualities for 3d Chern-Simons theories

We study Seiberg-like dualities for 3d N=2 theories with flavors in fundamental and adjoint representations. The recent results of Intriligator and Seiberg provide a derivation of an Aharony duality from a Giveon-Kutasov duality. We extend their result to the case of more general theories involving various masses for fundamental quarks and adjoint fields. By fine tuning the vev of a scalar field and using various identifications between gauge groups and their singlet duals, we derive several examples of Aharony dualities. For theories with an adjoint field, we discuss the connection between the Aharony dualities proposed by Kim and Park for theories with multiple Coulomb branches and Giveon-Kutasov-Niarchos dualities.

Aspects of 3d $ \mathcal{N}=2 $ Chern-Simons-Matter theories

We comment on various aspects of the the dynamics of 3d N=2 Chern-Simons gauge theories and their possible phases. Depending on the matter content, real masses and FI parameters, there can be non-compact Higgs or Coulomb branches, compact Higgs or Coulomb branches, and isolated vacua. We compute the Witten index of the theories, and show that it does not change when the system undergoes a phase transition. We study aspects of monopole operators and solitons in these theories, and clarify subtleties in the soliton collective coordinate quantization. We show that solitons are compatible with a mirror symmetry exchange of Higgs and Coulomb branches, with BPS solitons on one branch related to the modulus of the other. Among other results, we show how to derive Aharony duality from Giveon-Kutasov duality.