Product Gauge Groups Research Articles

META-STABLE BRANE CONFIGURATIONS BY DUALIZING THE TWO GAUGE GROUPS

We consider the [Formula: see text] supersymmetric gauge theories with product gauge groups. The two kinds of D6-branes in the electric theory are both displaced and rotated respectively where these deformations are interpreted as the mass terms and quartic terms for the two kinds of flavors. Then we apply the Seiberg dual to the whole gauge group factors by moving the branes and obtain the corresponding dual gauge theories. By analyzing the magnetic superpotentials consisting of an interaction term between a magnetic meson field and dual matters as well as the above deformations for each gauge group, we present the type IIA nonsupersymmetric meta-stable brane configurations.

MORE ON META-STABLE BRANE CONFIGURATIONS BY DUALIZING THE MULTIPLE GAUGE GROUPS

We reexamine the [Formula: see text] supersymmetric gauge theories with product gauge groups by adding the mass terms and the quartic terms for the flavors: two-gauge group theory with fundamentals, bifundamentals and adjoints, three-gauge group theory with fundamentals and bifundamentals, and their orientifold 4-plane generalizations. By moving the branes appropriately, we obtain the corresponding dual gauge theories. By analyzing the dual superpotentials, we present the type IIA nonsupersymmetric meta-stable brane configurations.

Topological interactions in warped extra dimensions

Topological interactions will be generated in theories with compact extra dimensions where fermionic chiral zero modes have different localizations. This is the case in many warped extra dimension models where the right-handed top quark is typically localized away from the left-handed one. Using deconstruction techniques, we study the topological interactions in these models. These interactions appear as trilinear and quadrilinear gauge boson couplings in low energy effective theories with three or more sites, as well as in the continuum limit. We derive the form of these interactions for various cases, including examples of Abelian, non-Abelian and product gauge groups of phenomenological interest. The topological interactions provide a window into the more fundamental aspects of these theories and could result in unique signatures at the Large Hadron Collider, some of which we explore.

META-STABLE BRANE CONFIGURATIONS WITH MULTIPLE NS5-BRANES

Starting from an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group and the bifundamentals, we apply Seiberg dual to each gauge group, obtain the [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the gauge singlets. Then we describe the intersecting brane configurations, where there are NS-branes and D4-branes (and anti-D4-branes), of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We also discuss the case where the orientifold 4-planes are added into the above brane configuration. Next, by adding an orientifold 6-plane, we apply to an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group (where a single symplectic or orthogonal gauge group is present) and the bifundamentals. Finally, we describe the other cases where the orientifold 6-plane intersects with NS-brane.

META-STABLE BRANE CONFIGURATIONS OF TRIPLE PRODUCT GAUGE GROUPS

From an [Formula: see text] supersymmetric electric gauge theory with the gauge group [Formula: see text] with fundamentals for each gauge group and the bifundamentals, we apply Seiberg dual to each gauge group and obtain the [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the additional gauge singlets. By analyzing the F-term equations of the dual magnetic superpotentials, we describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We apply also to the case for [Formula: see text] supersymmetric electric gauge theory with the gauge group [Formula: see text] with flavors for each gauge group and the bifundamentals. Finally, we describe the meta-stable brane configurations of multiple product gauge groups.

GAUGE-HIGGS UNIFICATION MODELS WITH COSET SPACE DIMENSIONAL REDUCTION SCHEME

We investigate the gauge-Higgs unification models within the scheme of the coset space dimensional reduction, beginning with two types of set up; fourteen-dimensional gauge theory with simple gauge groups and ten-dimensional gauge theory with direct product gauge groups. We found some phenomenologically acceptable models through an exhaustive search for the candidates of the coset spaces, the gauge group in higher dimension, and fermion representation.

Toward a proof of Montonen-Olive duality via multiple M2-branes

We derive 4-dimensional N=4 U(N) supersymmetric Yang-Mills theory from a 3-dimensional Chern-Simons-matter theory with product gauge group U(N)^{2n}. The latter describes M2-branes probing an orbifold where a torus emerges in a scaling limit. It is expected that the SL(2, Z) duality of the 4-dimensional Yang-Mills theory will be shown in M-theory point of view since it is trivially realized as modular transformations of the torus. Indeed, starting from one single Chern-Simons-matter theory, we find infinitely many equivalent 4-dimensional theories differing up to T-transformation of the SL(2, Z) redefinition of the gauge coupling tau=theta/2pi + 4pi i/g^2 and a parity transformation in 4 dimensions. Although S-transformation can not be shown in our work, it is important that a part of the SL(2, Z) transformation is realized via the M2-brane action. Thus we think our work can be a step toward a proof of Montonen-Olive duality via M2-branes.

Meta-stable brane configuration of product gauge groups

Starting from the gauge theory with fundamental and bifundamental flavors, we apply the Seiberg dual to the first gauge group and obtain the dual gauge theory with dual matters including the gauge singlets. By analyzing the F-term equations of the superpotential, we describe the intersecting type IIA brane configuration for the meta-stable nonsupersymmetric vacua of this gauge theory. By introducing an orientifold 6-plane, we generalize to the case for gauge theory with fundamental and bifundamental flavors. Finally, the gauge theory with matters is also described very briefly.

Partial breaking of [formula omitted] supersymmetry and of gauge symmetry in the [formula omitted] gauge model

We explore vacua of the U ( N ) gauge model with N = 2 supersymmetry recently constructed in hep-th/0409060. In addition to the vacuum previously found with unbroken U ( N ) gauge symmetry in which N = 2 supersymmetry is partially broken to N = 1 , we find cases in which the gauge symmetry is broken to a product gauge group ∏ i = 1 n U ( N i ) . The N = 1 vacua are selected by the requirement of a positive definite Kähler metric. We obtain the masses of the supermultiplets appearing on the N = 1 vacua.

G2holonomy, mirror symmetry and phases ofN= 1 SYM

We study the phase structure of four-dimensional N=1 super Yang-Mills theories realized on D6-branes wrapping the RP^3 of a Z_2 orbifold of the deformed conifold. The non-trivial fundamental group of RP^3 allows for the gauge group to be broken to various product groups by Z_2 Wilson lines. We study the classical moduli space of theories in various pictures related by dualities including an M-theory lift. The quantum moduli space is analyzed in a dual IIB theory, where a complex curve contained in the target space plays a key role. We find that the quantum moduli space is made up of several branches, characterized by the presence or absence of a low energy U(1) gauge symmetry, which are connected at points of monopole condensation. The resulting picture of the quantum moduli space shows how the various gauge theories with different product gauge groups are connected to one another.

Supertwistor Orbifolds: Gauge Theory Amplitudes and Topological Strings

Witten established correspondence between multiparton amplitudes in four-dimensional maximally supersymmetric gauge theory and topological string theory on supertwistor space $CP^{3|4}$. We extend Witten's correspondence to gauge theories with lower supersymmetries, product gauge groups, and fermions and scalars in complex representations. Such gauge theories arise in high-energy limit of the Standard Model of strong and electroweak interactions. We construct such theories by orbifolding prescription. Much like gauge and string theories, such prescription is applicable equally well to topological string theories on supertwistor space. We work out several examples of orbifolds of $CP^{3|4}$ that are dual to N=2, 1, 0 quiver gauge theories. We study gauged sigma model describing topological B-model on the superorbifolds, and explore mirror pairs with particular attention to the parity symmetry. We check the orbifold construction by studying multiparton amplitudes in these theories with particular attention to those involving fermions in bifundamental representations and interactions involving U(1) subgroups.

Instantons on Quivers and Orientifolds

We compute the prepotential for gauge theories descending from ${\cal N}=4$ SYM via quiver projections and mass deformations. This accounts for gauge theories with product gauge groups and bifundamental matter. The case of massive orientifold gauge theories with gauge group SO/Sp is also described. In the case with no gravitational corrections the results are shown to be in agreement with Seiberg-Witten analysis and previous results in the literature.

Phases of [formula omitted] supersymmetric gauge theories with flavors

We explore the phases of N=1 supersymmetric U( N) gauge theories with fundamental matter that arise as deformations of N=2 SQCD by the addition of a superpotential for the adjoint chiral multiplet. As the parameters in the superpotential are varied, the vacua of this theory sweep out various branches, which in some cases have multiple semiclassical limits. In such limits, we recover the vacua of various product gauge group theories, with flavors charged under some group factors. We describe in detail the structure of the vacua in both classical and quantum regimes, and develop general techniques such as an addition and a multiplication map which relate vacua of different gauge theories. We also consider possible indices characterizing different branches and potential relationships with matrix models.

Prepotential and instanton corrections in Script N = 2 supersymmetric SU(N1) × SU(N2) Yang Mills theories

In this paper we analyse the non-hyperelliptic Seiberg-Witten curves derived from M-theory that encode the low energy solution of N=2 supersymmetric theories with product gauge groups. We consider the case of a SU(N_1)xSU(N_2) gauge theory with a hypermultiplet in the bifundamental representation together with matter in the fundamental representations of SU(N_1) and SU(N_2). By means of the Riemann bilinear relations that hold on the Riemann surface defined by the Seiberg--Witten curve, we compute the logarithmic derivative of the prepotential with respect to the quantum scales of both gauge groups. As an application we develop a method to compute recursively the instanton corrections to the prepotential in a straightforward way. We present explicit formulas for up to third order on both quantum scales. Furthermore, we extend those results to SU(N) gauge theories with a matter hypermultiplet in the symmetric and antisymmetric representation. We also present some non-trivial checks of our results.

One loop renormalizability of spontaneously broken gauge theory with a product of gauge groups on noncommutative spacetime: the U(1) × U(1) case

A generalization of the standard electroweak model to noncommutative spacetime would involve a product gauge group which is spontaneously broken. Gauge interactions in terms of physical gauge bosons are canonical with respect to massless gauge bosons as required by the exact gauge symmetry, but not so with respect to massive ones; and furthermore they are generally asymmetric in the two sets of gauge bosons. On noncommutative spacetime this already occurs for the simplest model of U(1) x U(1). We examine whether the above feature in gauge interactions can be perturbatively maintained in this model. We show by a complete one loop analysis that all ultraviolet divergences are removable with a few renormalization constants in a way consistent with the above structure.

Localized fermions and anomaly inflow via deconstruction

We study fermion localization in gauge theory space. We consider four-dimensional product gauge groups in which light chiral fermions transform under different gauge factors of the product group. This construction provides a suppression of higher dimensional operators. For example, it can be used to suppress dangerous proton decay operators. The anomalies associated with the light chiral fermions are compensated by Wess-Zumino terms, which in the continuum limit reproduce the five-dimensional Chern-Simons term.

Grand-unification scale generation through anomalous U(1) breaking

We discuss the anomalous U(1) gauge symmetry as a mechanism of generating the grand-unification scale. We conclude that unification to a simple group cannot be realized unless some parameters are ``tuned'', and that models with product gauge groups are preferred. We consider the ``R-invariant natural unification'' model with gauge groups SU(5)_{GUT} \times U(3)_H. In this model the doublet-triplet splitting problem is solved and the unwanted GUT relation m_s = m_\mu is avoided maintaining m_b = m_\tau. Moreover, R-invariance suppresses the dangerous proton decays induced by dimension four and five operators.

Branes, geometry and N = 1 duality with product gauge groups of SO and Sp

We study N = 1 dualities in four-dimensional supersymmetric gauge theories as the world volume theory of D4 branes with one compact direction in type IIA string theory. We generalize the previous work for SO( N c1 ) × Sp( N c2 ) with the superpotential W = Tr X 4 to the case of W = Tr X 4( k+1) in terms of brane configuration. We conjecture that the new dualities for the product gauge groups of SO( N c1 ) × Sp( N c2 ) × SO( N c3 ), SO( N c1 ) × Sp( N c2 ) × SO( N c3 ) × Sp( N c4 ) and higher multiple product gauge groups can be obtained by reversing the ordering of NS5 branes and D6 branes while preserving the linking numbers. We also describe the above dualities in terms of wrapping D6 branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. The theory with adjoint matter can be regarded as taking multiple copies of NS5 brane in the configuration of brane or geometric approaches.

Duality between simple-group gauge theories and some applications

In this paper we investigate N=1 supersymmetric gauge theories with a product gauge group. By using smoothly confining dynamics, we can find new dualities which include higher-rank tensor fields, and in which the dual gauge group is simple, not a product. Some of them are dualities between chiral and non-chiral gauge theories. We also discuss some applications to dynamical supersymmetry breaking phenomena and new confining theories with a tree-level superpotential.

Three-dimensional gauge theories and ADE monopoles

We study three-dimensional N=4 gauge theories with product gauge groups constructed from ADE Dynkin diagrams. One-loop corrections to the metric on the Coulomb branch are shown to coincide with the metric on the moduli space of well-separated ADE monopoles. We propose that this correspondence is exact.