arXiv subjects

Keita Nii

Publications and source records attributed to Keita Nii.

18 recordsLinked to original sources

arXiv2022

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 $n \neq 0$. We argue that the $SU(N)_0$ "ugly-good" duality (which corresponds to the $n \rightarrow \infty$ 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.

hep-th↗

arXiv2020

3d $Spin(N)$ Seiberg dualities

We study low-energy aspects of 3d $\mathcal{N}=2$ $Spin(N)$ gauge theories with matters in vector and (conjugate) spinor representations. Extending the construction of the 4d $\mathcal{N}=1$ $Spin(N)$ Seiberg duality, we find 3d magnetic dual descriptions with tree-level superpotentials slightly different from the 4d ones. We test various consistency checks including RG flows to known 3d dualities and supersymmetry enhancement deformation which leads to a 3d $\mathcal{N}=4$ duality between $SU(2)$ with three hypermultiplets and $U(1)$ with four hypermultiplets.

hep-th↗

arXiv2020

Coulomb branch in 3d $\mathcal{N}=2$ $SU(N)_k$ Chern-Simons gauge theories with chiral matter content

We elaborate on quantum moduli spaces in 3d $\mathcal{N}=2$ $SU(N)_k$ Chern-Simons gauge theories with $F$ fundamental and $\bar{F}$ anti-fundamental matter fields. The quantum flat direction on the Coulomb branch differs so much from the classical one and from the one of the vector-like theories. In many cases, the Coulomb branch is parametrized by the dressed monopoles. As is found from the computation of the superconformal index, these dressed operators at first sight appear to be dressed by massive elementary fields which don't seem to contribute to the low-energy physics. We argue that these dressed fields can be interpreted as a non-abelian monopole dressed (or not dressed) by massless matter fields. Based on this analysis, we will report on the s-confinement phases with non-trivial monopole operators, which is consistent with the duality proposals \cite{Aharony:2014uya, Aharony:2013dha}. Along these studies, we find that the duality reported in \cite{Aharony:2014uya} must be modified when $k=\pm \frac{1}{2}(F-\bar{F})$ in order to have a correct duality map of the baryonic operators.

hep-th↗

arXiv2020

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.

hep-th↗

arXiv2019

"Chiral'' and "Non-chiral'' 3d Seiberg duality

We propose a Seiberg duality for a 3d $\mathcal{N}=2$ $Spin(7)$ gauge theory with $F$ spinor matters. For $F \ge 6$, the theory allows a magnetic dual description with an $SU(F-4)$ gauge group. The matter content on the magnetic side is ``chiral'' and the duality connects ``chiral'' and ``non-chiral'' 3d gauge theories. As a corollary, we can construct a Seiberg duality for a 3d $\mathcal{N}=2$ $G_2$ gauge theory with fundamental matters.

hep-th↗

arXiv2019

Confinement in 3d $\mathcal{N}=2$ exceptional gauge theories

We study the low-energy dynamics in three-dimensional $\mathcal{N}=2$ exceptional gauge theories with matters in a fundamental representation, especially focusing on confinement phases and on a quantum structure of the Coulomb branch in the moduli space of vacua. We argue that the confinement phases of these exceptional gauge theories have a single Coulomb branch. The 3d s-confinement phases for the exceptional gauge groups are associated with quantum-deformed moduli spaces of the corresponding 4d $\mathcal{N}=1$ exceptional gauge theories.

hep-th↗

arXiv2019

On s-confinement in 3d $\mathcal{N}=2$ gauge theories with anti-symmetric tensors

We elaborate on s-confinement phases in three-dimensional $\mathcal{N}=2$ supersymmetric gauge theory, especially focusing on the $SU(N)$ and $USp(2N)$ gauge theories with anti-symmetric tensors and (anti-)fundamental matters. This will elucidate a quantum structure of the Coulomb moduli space of vacua. We stress the importance of so-called dressed Coulomb branch operators for describing these s-confinement phases. The 3d s-confinement phases are highly richer than the 4d ones since there is no chiral anomaly constraint on the matter contents.

hep-th↗

arXiv2019

3d "chiral" Kutasov-Schwimmer duality

We propose a "chiral" version of the Kutasov-Schwimmer duality in a 3d $\mathcal{N}=2$ $SU(N)$ gauge theory with $F$ fundamental matters, $\bar{F}$ anti-fundamental matters and an adjoint matter $X$ with a tree-level superpotential $W= \mathrm{tr} \, X^{k+1}$. The theory exhibits a rich structure of the baryonic and (dressed) Coulomb branch operators. At first sight, the duality seems bad due to the mismatch of the anti-baryonic branch in the moduli space of vacua. The duality well works by realizing that the anti-baryonic operators are identified with some of the dressed Coulomb branch coordinates under the proposed duality. This generalizes the $SU(N)$ ``chiral'' duality with (anti-)fundamental matters, which we previously proposed.

hep-th↗

arXiv2018

Duality and Confinement in 3d $\mathcal{N}=2$ "chiral" $SU(N)$ gauge theories

We study low-energy dynamics of three-dimensional $\mathcal{N}=2$ $SU(N)$ "chiral" gauge theories with $F$ fundamental and $\bar{F}$ anti-fundamental matters without a Chern-Simons term. Compared to a naive semi-classical analysis of the Coulomb branch, its quantum structure is highly richer than expected due to so-called "dressed" Coulomb branch (monopole) operators. We propose dualities and confinement phases for the "chiral" $SU(N)$ theories. The theories with $N>F > \bar{F}$ exhibit spontaneous supersymmetry breaking. The very many Coulomb branch operators generally remain exactly massless and are non-trivially mapped under the dualities. Some dualities lead to a novel duality between $SU(N)$ and $USp(2 \tilde{N})$ theories. For the 3d $\mathcal{N}=2$ $SU(2)$ gauge theory with $2F$ doublets, there are generally $F+2$ "chiral" and "non-chiral" dual descriptions.

hep-th↗

arXiv2018

3d Self-Dualities

We investigate self-dualities in three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. The electric and magnetic theories share the same gauge group. The examples include $SU(2N)$, $SO(7)$ and $SO(8)$ with various matter contents. The duality exchanges the role of the baryon and Coulomb branch operators in some examples. In other examples, the Coulomb branch operator becomes an elementary field on the dual side. These self-dualities in turn teach us a correct quantum structure of the Coulomb moduli space of vacua. Some dualities show symmetry enhancement.

hep-th↗

arXiv2018

Confinement in 3d $\mathcal{N}=2$ $Spin(N)$ gauge theories with vector and spinor matters

We present various confinement phases of three-dimensional $\mathcal{N}=2$ $Spin(N)$ gauge theories with vector and spinor matters. The quantum Coulomb branch of the moduli space of vacua is drastically changed when the rank of the gauge group and the matter contents are changed. In many examples, the Coulomb branch is one- or two-dimensional but its interpretation varies. In some examples, the Coulomb branch becomes three-dimensional and we need to introduce a "dressed" Coulomb branch operator.

hep-th↗

arXiv2018

3d s-confinement for three-index matters

We present s-confinement phases for three-index matters in three-dimensional supersymmetric gauge theories. We find that the 3d $\mathcal{N}=2$ $SU(6)$ and $USp(6)$ gauge theories with three-index anti-symmetric matters show confining phases. The exact superpotentials which describe their low-energy dynamics are derived. We check the validity of our analysis in various ways, including superconformal indices and some deformations.

hep-th↗

arXiv2018

Exact results in 3d $\mathcal{N}=2$ $Spin(7)$ gauge theories with vector and spinor matters

We study three-dimensional $\mathcal{N}=2$ $Spin(7)$ gauge theories with $N_S$ spinorial matters and with $N_f$ vectorial matters. The quantum Coulomb branch on the moduli space of vacua is one- or two-dimensional depending on the matter contents. For particular values of $(N_f,N_S)$, we find s-confinement phases and derive exact superpotentials. The 3d dynamics of $Spin(7)$ is connected to the 4d dynamics via KK-monopoles. Along the Higgs branch of the $Spin(7)$ theories, we obtain 3d $\mathcal{N}=2$ $G_2$ or $SU(4)$ theories and some of them lead to new s-confinement phases. As a check of our analysis we compute superconformal indices for these theories.

hep-th↗

arXiv2017

Low-Energy Dynamics of 3d $\mathcal{N}=2$ $G_2$ Supersymmetric Gauge Theory

We study a three-dimensional $\mathcal{N}=2$ supersymmetric $G_2$ gauge theory with and without fundamental matters. We find that a classical Coulomb branch of the moduli space of vacua is partly lifted by monopole-instantons and the quantum Coulomb moduli space would be described by a complex one-dimensional space. Depending on the number of the matters in a fundamental representation, the low-energy dynamics of the theory shows various phases like s-confinement or quantum merging of the Coulomb and the Higgs branches. We also investigate superconformal indices as an independent check of our analysis.

hep-th↗

arXiv2016

Classical equation of motion and Anomalous dimensions at leading order

Motivated by a recent paper by Rychkov-Tan \cite{Rychkov:2015naa}, we calculate the anomalous dimensions of the composite operators at the leading order in various models including a $ϕ^3$-theory in $(6-ε)$ dimensions. The method presented here relies only on the classical equation of motion and the conformal symmetry. In case that only the leading expressions of the critical exponents are of interest, it is sufficient to reduce the multiplet recombination discussed in \cite{Rychkov:2015naa} to the classical equation of motion. We claim that in many cases the use of the classical equations of motion and the CFT constraint on two- and three-point functions completely determine the leading behavior of the anomalous dimensions at the Wilson-Fisher fixed point without any input of the Feynman diagrammatic calculation. The method developed here is closely related to the one presented in \cite{Rychkov:2015naa} but based on a more perturbative point of view.

hep-th↗

arXiv2016

3d Deconfinement, Product gauge group, Seiberg-Witten and New 3d dualities

We construct a three dimensional deconfinement method which enables us to find new three-dimensional dualities and we apply various techniques developed in four dimensional supersymmetric gauge theories, such as the product gauge groups and Seiberg-Witten curves to the three dimensional $\mathcal{N}=2$ supersymmetric gauge theories. Dual descriptions of three dimensional $\mathcal{N}=2$ supersymmetric gauge theories which involve two-index matters, for example, adjoint, symmetric, and anti-symmetric matters without superpotentials can be obtained. These matters are described in terms of s-confining phases of the supersymmetric gauge theories.

hep-th↗

arXiv2014

ABJ Wilson loops and Seiberg Duality

We study supersymmetric Wilson loops in the ${\cal N} = 6$ supersymmetric $U(N_1)_k\times U(N_2)_{-k}$ Chern-Simons-matter (CSM) theory, the ABJ theory, at finite $N_1$, $N_2$ and $k$. This generalizes our previous study on the ABJ partition function. First computing the Wilson loops in the $U(N_1) \times U(N_2)$ lens space matrix model exactly, we perform an analytic continuation, $N_2$ to $-N_2$, to obtain the Wilson loops in the ABJ theory that is given in terms of a formal series and only valid in perturbation theory. Via a Sommerfeld-Watson type transform, we provide a nonperturbative completion that renders the formal series well-defined at all couplings. This is given by ${\rm min}(N_1,N_2)$-dimensional integrals that generalize the "mirror description" of the partition function of the ABJM theory. Using our results, we find the maps between the Wilson loops in the original and Seiberg dual theories and prove the duality. In our approach we can explicitly see how the perturbative and nonperturbative contributions to the Wilson loops are exchanged under the duality. The duality maps are further supported by a heuristic yet very useful argument based on the brane configuration as well as an alternative derivation based on that of Kapustin and Willett.

hep-th↗

arXiv2014

3d duality with adjoint matter from 4d duality

We study the Seiberg dualities with an adjoint matter for the $U(N)$ and $SU(N)$ gauge groups in three- and four-dimensions with four supercharges. The relation between three- and four-dimensional dualities is investigated. We especially derive the three-dimensional duality from four-dimensional one by the dimensional reduction including the non-perturbative effect of the $\mathbb{S}^1$-compactification. In the $U(N)$ case, we obtain the Kim-Park duality, which is known as a generalization of the Aharony duality including an adjoint matter. In the $SU(N)$ case, we obtain the duality which follows from un-gauging the $U(N)$ Kim-Park duality.

hep-th↗