Product Gauge Groups Research Articles

A survey of family unification models with bifundamental matter

Extensions of the Standard Model have been attempted from the bottom up and from the top down, yet there remains a largely unexplored middle ground. In this paper, using the Mathematica package LieART, we exhaustively enumerate embeddings of the Standard Model within the class of theories with bifundamental fermions in product gauge group SU(a)×SU(b)×SU(c) with no more generators than E6, while achieving SM family unification rather than replication. We incorporate simple phenomenological constraints and find 151 unique models, including 9 that have only vector-like particle content beyond-the-Standard Model (BSM) particles, which we conjecture belong to 5 infinite families of such models. We describe the potentially most viable models: namely, the 9 with strictly vector-like BSM content along with the 29 models we found with no more than 30 additional BSM chiral particles. These include models with fractional electric charge color singlets, and hence magnetic monopoles with multiple Dirac charge. This latter collection of models predicts chiral particles with masses near the electroweak scale accessible to current and future collider experiments.

Confinement on the moose lattice

In this work we present a new class of mathcal{N} = 1 supersymmetric confining gauge theories, with strikingly simple infrared theories that descend from intricate interconnected networks of product gauge groups. A diagram of the gauge groups and the charged matter content of the ultraviolet theory has the structure of a triangular lattice, with SU(N) or SU(3N) gauge groups at each of the vertices, connected by bifundamental chiral superfields. This structure admits a U(1)R conserving superpotential with marginal (trilinear) operators. With the introduction of this superpotential, the SU(3N) and SU(N) gauge groups confine: in the far infrared limit of the supersymmetric theory, the relevant degrees of freedom are gauge invariant “mesons” and “baryons.” In this paper we show how the properties of the infrared degrees of freedom depend on the topology and shape of the moose/quiver “lattice” of the original gauge theory. Between the local structure of the moose lattice at higher energies, and the boundary dependence that emerges in the infrared, the 4d moose lattice theory reproduces features of a 6d spacetime with two compact dimensions. We investigate various deformations of the theory, and propose some phenomenological applications for BSM models.

Superconformal index for [formula omitted][formula omitted] Chern-Simons quiver gauge theories

We compute superconformal indices for N=3ADEˆ Chern-Simons quiver gauge theories with a product gauge group ∏iU(N)i, using the method of supersymmetric localization. We also perform a large N analysis of the index. This index includes contribution from non zero magnetic flux sector. The fact that these theories have a weakly coupled UV completion in terms of N=3 supersymmetric Chern-Simons Yang-Mills theories enables us to apply the localization technique. Such theories have dual M-theory description on AdS4×M7, where M7 is a tri-Sasaki Einstein manifold.

Magnetic impurities, integrable vortices and the Toda equation

The five integrable vortex equations, recently studied by Manton, are generalized to include magnetic impurities of the Tong-Wong type. Under certain conditions these generalizations remain integrable. We further set up a gauge theory with a product gauge group, two complex scalar fields and a general charge matrix. The second species of vortices, when frozen, are interpreted as the magnetic impurity for all five vortex equations. We then give a geometric compatibility condition, which enables us to remove the constant term in all the equations. This is similar to the reduction from the Taubes equation to the Liouville equation. We further find a family of charge matrices that turn the five vortex equations into either the Toda equation or the Toda equation with the opposite sign. We find exact analytic solutions in all cases and the solution with the opposite sign appears to be new.

Magnetic lattices for orthosymplectic quivers

For any gauge theory, there may be a subgroup of the gauge group which acts trivially on the matter content. While many physical observables are not sensitive to this fact, the choice of the precise gauge group becomes crucial when the magnetic lattice of the theory is considered. This question is addressed in the context of Coulomb branches for 3d mathcal{N} = 4 quiver gauge theories, which are moduli spaces of dressed monopole operators. We compute the Coulomb branch Hilbert series of many unitary-orthosymplectic quivers for different choices of gauge groups, including diagonal quotients of the product gauge group of individual factors, where the quotient is by a trivially acting subgroup. Choosing different such diagonal groups results in distinct Coulomb branches, related as orbifolds. Examples include nilpotent orbit closures of the exceptional E-type algebras and magnetic quivers that arise from brane physics. This includes Higgs branches of theories with 8 supercharges in dimensions 4, 5, and 6. A crucial ingredient in the calculation of exact refined Hilbert series is the alternative construction of unframed magnetic quivers from resolved Slodowy slices, whose Hilbert series can be derived from Hall-Littlewood polynomials.

SUSY breaking in monopole quivers

We study 3d monopole quivers, theories with product gauge groups interacting through monopole superpotentials and we observe that they are a natural setup for the study of the spontaneous breaking of 3d mathcal{N} = 2 supersymmetry. We give evidence of this statement by studying various examples of increasing complexity, considering quivers that are mirror dual to Wess-Zumino models. These Wess-Zumino models, in opportune regimes of parameters, break supersymmetry in perturbatively controllable (meta)stable vacua.

A high quality composite axion

The strong CP problem is a compelling motivation for physics beyond the Standard Model. The most popular solutions invoke a global U(1)PQ symmetry, but are challenged by quantum gravitational corrections which are thought to be incompatible with global symmetries, arguing that realistic theories contain additional structure. We explore a construction in which the U(1)PQ symmetry is protected to arbitrary order by virtue of a supersymmetric, confining SU(N)L × SU(N) × SU(N)R × U(1)X product gauge group, achieving left|overline{uptheta}right| < 10−11 for an SU(5) model with fa ≲ 3 × 1011 GeV. This construction leads to low energy predictions such as a U(1)X gauge symmetry, and for X = B − L engineers a naturally mathcal{O} (TeV) value for the μ parameter of the MSSM.

Towards exotic matter and discrete non-abelian symmetries in F-theory

We present a prescription in F-theory for realizing matter in “exotic” representations of product gauge groups. For 6D vacua, bifundamental hypermultiplets are engineered by starting at a singular point in moduli space which includes 6D superconformal field theories coupled to gravity. A deformation in Higgs branch moduli space takes us to a weakly coupled gauge theory description. In the corresponding elliptically fibered Calabi-Yau threefold, the minimal Weierstrass model parameters (f, g, Δ) vanish at collisions of the discriminant at least to order (4, 6, 12), but with sufficiently high order of tangency to ensure the existence of T-brane deformations to a weakly coupled gauge theory with exotic bifundamentals. We present explicit examples including bifundamental hypermultiplets of {mathfrak{e}}_7times mathfrak{s}{mathfrak{u}}_2 and {mathfrak{e}}_6times mathfrak{s}{mathfrak{u}}_3 , each of which have dual heterotic orbifold descriptions. Geometrically, these matter fields are delocalized across multiple points of an F-theory geometry. Symmetry breaking with such representations can be used to produce high dimension representations of simple gauge groups such as the four-index symmetric representation of mathfrak{s}{mathfrak{u}}_2 and the three-index symmetric representation of mathfrak{s}{mathfrak{u}}_3 , and after further higgsing can yield discrete non-abelian symmetries.

Bosonizing three-dimensional quiver gauge theories

We start with the recently conjectured 3d bosonization dualities and gauge global symmetries to generate an infinite sequence of new dualities. These equate theories with non-Abelian product gauge groups and bifundamental matter. We uncover examples of Bose/Bose and Fermi/Fermi dualities, as well as a sequence of dualities between theories with scalar matter in two-index representations. Our conjectures are consistent with level/rank duality in massive phases.

Product group confinement in SUSY gauge theories

We propose a new set of s-confining theories with product gauge groups and no tree-level superpotential, based on a model with one antisymmetric matter field and four flavors of quarks. For each product group we find a set of gauge-invariant operators which satisfy the ’t Hooft anomaly matching conditions, and we identify the dynamically generated superpotential which reproduces the classical constraints between operators. Several of these product gauge theories confine without breaking chiral symmetry, even in cases where the classical moduli space is quantum-modified. These results may be useful for composite model building, particularly in cases where small operators of the form left(Qoverline{Q}right) are absent, or for theories with multiple natural energy scales, and may provide new ways to break supersymmetry dynamically.

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.

Gluon condensates from the Hamiltonian formalism

We derive recently obtained relations connecting the logarithmic gauge coupling derivative of the hadron mass and the cosmological constant to the matter and vacuum gluon condensates, within a Hamiltonian framework. The key idea is a canonical transformation which brings the relevant part of the Hamiltonian into a suitable form. We have checked that the transformation is free from rescaling anomalies. The Hamiltonian framework allows one to extend these connections to the case of direct product gauge groups relevant to the Standard Model for example. Furthermore, we illustrate the relations within the Schwinger model and super Yang–Mills theory (Seiberg–Witten theory).

Naturalness and the weak gravity conjecture.

The weak gravity conjecture (WGC) is an ultraviolet consistency condition asserting that an Abelian force requires a state of charge q and mass m with q>m/m_{Pl}. We generalize the WGC to product gauge groups and study its tension with the naturalness principle for a charged scalar coupled to gravity. Reconciling naturalness with the WGC either requires a Higgs phase or a low cutoff at Λ∼qm_{Pl}. If neither applies, one can construct simple models that forbid a natural electroweak scale and whose observation would rule out the naturalness principle.

A twistor string for the ABJ(M) theory

We construct an open string theory whose single-trace part of the tree-level S-matrix reproduces the S-matrix of the ABJ(M) theory with a unitary gauge group. We also demonstrate that the multi-trace part of the string theory tree-level S-matrix — which has no counterpart in the pure $ \mathcal{N} $ = 6 super-Chern-Simons theory — is due to conformal supergravity interactions and identify certain Lagrangian interaction terms. Our construction suggests that there exists a higher dimensional theory which can be dimensionally-reduced, in a certain sense, to the ABJ(M) theory. It also suggests a generalization of this theory to product gauge groups with more than two factors.

Vortices and impurities

Abstract We describe the BPS dynamics of vortices in the presence of impurities. We argue that a moduli space of solitons survives the addition of both electric and magnetic impurities. However, dynamics on the moduli space is altered. In the case of electric impurities, the metric remains unchanged but the dynamics is accompanied by a connection term, acting as an effective magnetic field over the moduli space. We give an expression for this connection and compute the vortex-impurity bound states in simple cases. In contrast, magnetic impurities distort the metric on the moduli space. We show that magnetic impurities can be viewed as vortices associated to a second, frozen, gauge group. We provide a D-brane description of the dynamics of vortices in product gauge groups and show how one can take the limit such that a subset of the vortices freeze.

Existence of non-Abelian vortices with product gauge groups

In this paper we establish several sharp existence and uniqueness theorems for some non-Abelian vortex models arising in supersymmetric gauge field theories. We prove these results by studying a family of systems of elliptic equations with exponential nonlinear terms in both doubly periodic-domain and planar cases. In the doubly periodic-domain case we obtain some necessary and sufficient conditions, each explicitly expressed in terms of a single inequality interestingly relating the vortex numbers, to coupling parameters and size of the domain, for the existence of solutions to these systems. In the planar case we establish the existence results for any vortex numbers and coupling parameters. Sharp decay estimates for the planar solutions are also obtained. Furthermore, the solutions are unique, which give rise to the quantized integrals in all cases.

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic toSU(3)c×SU(2)L×U(1)Y

In the Standard Model (SM) the hypercharges of quarks and leptons are not determined by the gauge group itself. In a recent paper [C. Hattori et al., Phys. Rev. D 83, 015009 (2011)] it is shown that if the direct product gauge group ${G}_{\mathrm{SM}}$ is slightly modified to the semidirect product group ${G}_{\mathrm{SM}}^{\ensuremath{'}}$, hypercharges are restricted to quantized values as $n/6$ $\mathrm{mod}\text{ }\mathbb{Z}(n=0,1,3,4)$. In this brief paper, we examine all of the compact Lie groups locally isomorphic to ${G}_{\mathrm{SM}}$ and show that ${G}_{\mathrm{SM}}^{\ensuremath{'}}$ (or its isomorphisms) is the unique possibility that yields the correct hypercharge quantization.

Heterotic T-folds with a small number of neutral moduli

We discuss non-geometric supersymmetric heterotic string models in D=4, in the framework of the free fermionic construction. We perform a systematic scan of models with four a priori left-right asymmetric Z_2 projections and shifts. We analyze some 2^{20} models, identifying 18 inequivalent classes and addressing variants generated by discrete torsions. They do not contain geometrical or trivial neutral moduli, apart from the dilaton. However, we show the existence of flat directions in the form of exactly marginal deformations and identify patterns of symmetry breaking where product gauge groups, realized at level one, are broken to their diagonal at higher level. We also describe an "inverse Gepner map" from Heterotic to Type II models that could be used, in certain non geometric settings, to define "effective" topological invariants.

Gravitational and Yang-Mills instantons in holographic RG flows

We study various holographic RG flow solutions involving warped asymptotically locally Euclidean (ALE) spaces of $A_{N-1}$ type. A two-dimensional RG flow from a UV (2,0) CFT to a (4,0) CFT in the IR is found in the context of (1,0) six dimensional supergravity, interpolating between $AdS_3\times S^3/\mathbb{Z}_N$ and $AdS_3\times S^3$ geometries. We also find solutions involving non trivial gauge fields in the form of SU(2) Yang-Mills instantons on ALE spaces. Both flows are of vev type, driven by a vacuum expectation value of a marginal operator. RG flows in four dimensional field theories are studied in the type IIB and type I$'$ context. In type IIB theory, the flow interpolates between $AdS_5\times S^5/\mathbb{Z}_N$ and $AdS_5\times S^5$ geometries. The field theory interpretation is that of an N=2 $SU(n)^N$ quiver gauge theory flowing to N=4 SU(n) gauge theory. In type I$'$ theory the solution describes an RG flow from N=2 quiver gauge theory with a product gauge group to N=2 gauge theory in the IR, with gauge group $USp(n)$. The corresponding geometries are $AdS_5\times S^5/(\mathbb{Z}_N\times \mathbb{Z}_2)$ and $AdS_5\times S^5/\mathbb{Z}_2$, respectively. We also explore more general RG flows, in which both the UV and IR CFTs are N=2 quiver gauge theories and the corresponding geometries are $AdS_5\times S^5/(\mathbb{Z}_N\times \mathbb{Z}_2)$ and $AdS_5\times S^5/(\mathbb{Z}_M\times \mathbb{Z}_2)$. Finally, we discuss the matching between the geometric and field theoretic pictures of the flows.

Semidirect product gauge group[SU(3)c×SU(2)L]⋊U(1)Yand quantization of hypercharge

In the Standard Model the hypercharges of quarks and leptons are not determined by the gauge group $SU(3)_{\rm c} \times SU(2)_{\rm L} \times U(1)_{\rm Y}$ alone. We show that, if we choose the semidirect product group $[SU(3)_{\rm c} \times SU(2)_{\rm L}] \rtimes U(1)_{\rm Y}$ as its gauge group, the hyperchages are settled to be $n/6 \mod {\mathbb{Z}}\;(n = 0,1,3,4) $. In addition, the conditions for gauge-anomaly cancellation give strong constraints. As a result, the ratios of the hypercharges are uniquely determined and the gravitational anomaly is automatically canceled. The standard charge assignment to quarks and leptons can be properly reproduced. For exotic matter fields their hypercharges are also discussed.