Adjoint Matter Fields Research Articles

Exact duality and local dynamics in SU(N) lattice gauge theory

We construct exact duality transformations in pure SU(N) Hamiltonian lattice gauge theory in ($2+1$) dimension. This duality is obtained by making a series of iterative canonical transformations on the SU(N) electric vector fields and their conjugate magnetic vector potentials on the four links around every plaquette. The resulting dual description is in terms of the magnetic scalar fields or plaquette flux loops and their conjugate electric scalar potentials. Under SU(N) gauge transformations they both transform like adjoint matter fields. The dual Hamiltonian describes the nonlocal self-interactions of these plaquette flux loops in terms of the electric scalar potentials and with inverted coupling. We show that these nonlocal loop interactions can be made local and converted into minimal couplings by introducing SU(N) auxiliary gauge fields along with new plaquette constraints. The matter fields can be included through minimal coupling. The techniques can be easily generalized to ($3+1$) dimensions.

Monopole deformations of 3d Seiberg-like dualities with adjoint matters

We propose new 3d mathcal{N} = 2 Seiberg-like dualities by considering various monopole superpotential deformations on 3d mathcal{N} = 2 U(Nc) SQCDs with fundamental and adjoint matter fields. We provide nontrivial evidence of these new dualities by comparing the superconformal indices, from which we analyze the change of the moduli space due to the monopole deformation. In addition, we perform the F-maximization to check the relevance of the monopole deformation for some examples, one of which is found to exhibit nontrivial symmetry enhancement in the IR. We prove such enhancement of the global symmetry using the superconformal index.

Asymptotic symmetries of colored gravity in three dimensions

Three-dimensional colored gravity refers to nonabelian isospin extension of Einstein gravity. We investigate the asymptotic symmetry algebra of the SU(N)-colored gravity in (2+1)-dimensional anti-de Sitter spacetime. Formulated by the Chern-Simons theory with SU(N, N) × SU(N, N) gauge group, the theory contains graviton, SU(N) Chern-Simons gauge fields and massless spin-two multiplets in the SU(N) adjoint representation, thus extending diffeomorphism to colored, nonabelian counterpart. We identify the asymptotic symmetry as Poisson algebra of generators associated with the residual global symmetries of the nonabelian diffeomorphism set by appropriately chosen boundary conditions. The resulting asymptotic symmetry algebra is a nonlinear extension of widehat{mathfrak{su}(N)} Kac-Moody algebra, supplemented by additional generators corresponding to the massless spin-two adjoint matter fields.

Deformations of W A,D,E SCFTs

We discuss aspects of theories with superpotentials given by Arnold's $A,D,E$ singularities, particularly the novelties that arise when the fields are matrices. We focus on 4d ${\cal N}=1$ variants of susy QCD, with $U(N_c)$ or $SU(N_c)$ gauge group, $N_f$ fundamental flavors, and adjoint matter fields $X$ and $Y$ appearing in $W_{A,D,E}(X,Y)$ superpotentials. Many of our considerations also apply in other possible contexts for matrix-variable $W_{A,D,E}$. The 4d $W_{A,D,E}$ SQCD-type theories RG flow to superconformal field theories, and there are proposed duals in the literature for the $W_{A_k}$, $W_{D_k}$, and $W_{E_7}$ cases. As we review, the $W_{D_\text{even}}$ and $W_{E_7}$ duals rely on a conjectural, quantum truncation of the chiral ring. We explore these issues by considering various deformations of the $W_{A,D,E}$ superpotentials, and the resulting RG flows and IR theories. Rather than finding supporting evidence for the quantum truncation and $W_{D_\text{even}}$ and $W_{E_7}$ duals, we note some challenging evidence to the contrary.

Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter

In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-$N$ limit. This was done within the tractable setting in which the gauge theory is compactified on a three-sphere whose radius is small compared to the strong length scale. In this paper, we generalize these observations by demonstrating that similar results continue to hold even when massless adjoint matter fields are introduced. These results hold for both thermal and $(-1)^F$-twisted partition functions, and collectively suggest that the spectra of large-$N$ confining gauge theories are organized by the symmetries of two-dimensional conformal field theories.

Spectral sum rules for confining large-N theories

We consider asymptotically-free four-dimensional large-$N$ gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large-$N$ confined-phase spectral sums. The analysis is done in the limit of vanishing 't Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale $\Lambda^{-1}$. Our results motivate us to conjecture some universal spectral sum rules for these large $N$ gauge theories.

The braneology of 3D dualities

In this paper, we study the reduction of four-dimensional Seiberg duality to three dimensions from a brane perspective. We reproduce the nonperturbative dynamics of three-dimensional field theory via a T–duality at a finite radius and the action of Euclidean D–strings. In this way, we also overcome certain issues regarding the brane description of Aharony duality. Moreover, we apply our strategy to more general dualities, such as toric duality for M2–branes and dualities with adjoint matter fields.

Instantons and vortices on noncommutative toric varieties

We elaborate on the quantization of toric varieties by combining techniques from toric geometry, isospectral deformations and noncommutative geometry in braided monoidal categories, and the construction of instantons thereon by combining methods from noncommutative algebraic geometry and a quantized twistor theory. We classify the real structures on a toric noncommutative deformation of the Klein quadric and use this to derive a new noncommutative four-sphere which is the unique deformation compatible with the noncommutative twistor correspondence. We extend the computation of equivariant instanton partition functions to noncommutative gauge theories with both adjoint and fundamental matter fields, finding agreement with the classical results in all instances. We construct moduli spaces of noncommutative vortices from the moduli of invariant instantons, and derive corresponding equivariant partition functions which also agree with those of the classical limit.

Chern-Simons and RG flows: contact with dualities

Contact terms in two point functions of global symmetry currents have recently been proposed as a check of Seiberg-like duality in three dimensional supersymmetric field theories. In this paper we compute the contact terms for various N=2 dual pairs in flat space. We show that the results of this computation agree with the ones obtained from localization. We study dual pairs of gauge theories with (anti-)fundamental matter fields, and some special examples of dual pairs with adjoint and antisymmetric matter fields. We also propose a duality between unitary and symplectic gauge theories.

A 5d/3d duality from relativistic integrable system

We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Omega deformation. In the limit proposed by Nekrasov and Shatashvili, the supersymmetric vacua become isolated and are identified with the eigenstates of a quantum integrable system. The effective twisted superpotentials are the Yang-Yang functional of the relativistic elliptic Calogero-Moser model. We show that they match on-shell by deriving the Bethe ansatz equation from the saddle point of the five-dimensional partition function. We also show that the Chern-Simons terms match and extend our proposal to the elliptic quiver generalizations.

Supersymmetric states in large N Chern-Simons-matter theories

In this paper we study the spectrum of BPS operators/states in N=2 superconformal U(N) Chern-Simons-matter theories with adjoint chiral matter fields, with and without superpotential. The superconformal indices and conjectures on the full supersymmetric spectrum of the theories in the large N limit with up to two adjoint matter fields are presented. Our results suggest that some of these theories may have supergravity duals at strong coupling, while some others may be dual to higher spin theories of gravity at strong coupling. For the N=2 theory with no superpotential, we study the renormalization of R-charge at finite 't Hooft coupling using "Z-minimization". A particularly intriguing result is found in the case of one adjoint matter.

Z-extremization and F-theorem in Chern-Simons matter theories

The three dimensional exact R symmetry of N=2 SCFTs extremizes the partition function localized on a three sphere. Here we verify this statement at weak coupling. We give a detailed analysis for two classes of models. The first one is an SU(N)_k gauge theory at large k with both fundamental and adjoint matter fields, while the second is a flavored version of the ABJ theory, where the CS levels are large but they do not necessarily sum up to zero. We study in both cases superpotential deformations and compute the R charges at different fixed points. When these fixed points are connected by an RG flow we explicitly verify that the free energy decreases at the endpoints of the flow between the fixed points, corroborating the conjecture of an F-theorem in three dimensions.

SUSY adjoint [formula omitted] grand unified model with [formula omitted] flavor symmetry

We construct a supersymmetric (SUSY) SU ( 5 ) model with the flavor symmetry S 4 × Z 3 × Z 4 . Three generations of adjoint matter fields are introduced to generate the neutrino masses via the combined type I and type III see-saw mechanism. The first two generations of the 10-dimensional representation in SU ( 5 ) are assigned to be a doublet of S 4 , the second family 10 is chose as the first component of the doublet, and the first family as the second component. Tri-bimaximal mixing in the neutrino sector is predicted exactly at leading order, charged lepton mixing leads to small deviation from the tri-bimaximal mixing pattern. Subleading contributions introduce corrections of order λ c 2 to all three lepton mixing angles. The model also reproduces a realistic pattern of quark and charged lepton masses and quark mixings. The phenomenological implications of the model are analyzed in detail.

Supersymmetric Gauge Theories with Matter, Toric Geometries and Random Partitions

We derive the relation between the Hilbert space of certain geometries with the BohrSommerfeld quantization and perturbative prepotentials for supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matter fields and one massive adjoint matter field. The gauge theory with one adjoint matter field possesses interesting features. A five-dimensional generalization of Nekrasov’s partition function can be written as a correlation function of two-dimensional chiral bosons and as a partition function of a statistical model of partitions. From a ground state of the statistical model, we reproduce a polyhedron that characterizes the Hilbert space.

On the worldsheet theories of strings dual to free largeNgauge theories

We analyze in detail some properties of the worldsheet of the closed string theories suggested by Gopakumar to be dual to free large N SU(N) gauge theories (with adjoint matter fields). We use Gopakumar's prescription to translate the computation of space-time correlation functions to worldsheet correlation functions for several classes of Feynman diagrams, by explicit computations of Strebel differentials. We compute the worldsheet operator product expansion in several cases and find that it is consistent with general worldsheet conformal field theory expectations. A peculiar property of the construction is that in several cases the resulting worldsheet correlation functions are non-vanishing only on a sub-space of the moduli space (say, for specific relations between vertex positions). Another strange property we find is that for a conformally invariant space-time theory, the mapping to the worldsheet does not preserve the special conformal symmetries, so that the full conformal group is not realized as a global symmetry on the worldsheet (even though it is, by construction, a symmetry of all integrated correlation functions).

Non-perturbative equivalences among large Ncgauge theories with adjoint and bifundamental matter fields

We prove an equivalence, in the large N limit, between certain U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. Lattice regularization is used to provide a non-perturbative definition of these theories; our proof applies in the strong coupling, large mass phase of the theories. Equivalence is demonstrated by constructing and comparing the loop equations for a parent theory and its orbifold projections. Loop equations for both expectation values of single-trace observables, and for connected correlators of such observables, are considered; hence the demonstrated non-perturbative equivalence applies to the large N limits of both string tensions and particle spectra.

On effective superpotentials and Kutasov duality

We derive the effective superpotential for an N=1 SU(N_c) gauge theory with one massless adjoint field and N_f massless fundamental flavors and cubic tree-level superpotential for the adjoint field. This is a generalization of the Affleck-Dine-Seiberg superpotential to gauge theories with one massless adjoint matter field. Using Kutasov's generalization of Seiberg duality, we then find the effective superpotential for a related theory with massive fundamental flavors.

Nonplanar anomalies in noncommutative gauge theories with adjoint matter fields

Using path integral method (Fujikawa's method) we calculate anomalies in noncommutative gauge theories with fermions in the bi-fundamental and adjoint representations. We find that axial and chiral gauge anomalies coming from non-planar contributions are derived in the low noncommutative momentum limit $\widetilde{p}^{\mu}(\equiv \theta^{\mu\nu}p_{\nu}) \to 0$. The adjoint chiral fermion carries no anomaly in the non-planar sector in $D=4k (k=1,2,...,)$ dimensions. It is naturally shown from the path integral method that anomalies in non-planar sector originate in UV/IR mixing.

D-brane probe and closed string tachyons

We consider a D-brane probe in the unstable string background associated with flux branes. The twist in the spacetime metric reponsible for supersymmetry breaking is shown to manifest itself in the mixing of open Wilson lines with the phases of some adjoint matter fields, resulting in a nonlocal and nonsupersymmetric form of Yang-Mills theory as the probe dynamics. This provides a setup where one can study the fate of a large class of unstable closed string theories that includes as a limit type 0 theories and various orbifolds of type II and type 0 theories. We discuss the limit of $\mathbf{C}{/Z}_{n}$ orbifold in some detail and speculate on the couplings with closed string tachyons.

ANOMALY AND NONPLANAR DIAGRAMS IN NONCOMMUTATIVE GAUGE THEORIES

Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For noncommutative QED with fundamental matters, due to UV/IR mixing a finite anomaly emerges from the nonplanar contributions. It involves a generalized ⋆-product of gauge fields.