Gauge Group SO Research Articles

Grand unification of the sterile neutrino

The simplest way to simultaneously understand all existing indications of neutrino oscillations from solar and atmospheric neutrino deficits and the LSND experiment, seems to be to postulate a sterile neutrino. We present a realistic grand unified model based on the gauge group SO(10)×SO(10) ′ that leads to the desired masses and mixings for the sterile and the known neutrinos needed to understand the above observations while fitting those of the known charged fermions. The model is a grand unified realization of the recently proposed idea that the sterile neutrino is the lightest neutrino of a mirror sector of the universe which has identical matter and gauge content as the standard model. The two SO(10)'s operate on the two sectors in a mirror symmetric way and are connected by a mixed Higgs representations whose net effect is to connect the superheavy right handed neutrinos of the two sectors.

Matrix model for Dirichlet open string

We discuss the open string ending on D p-branes in IKKT framework. First we determine the boundary conditions of Green-Schwarz superstring which are consistent with supersymmetry and κ-symmetry. We point out some subtleties arising from taking the Schild gauge and show that in this gauge the system incorporates the limited dimensional D p-branes ( p=3,7). The matrix regularization for the Dirichlet open string is given by gauge group SO( N). When p=3, the matrix model becomes the dimensional reduction of a 6 dimensional N=1 super Yang-Mills theory.

Supersymmetric gauge theories with classical groups via M theory fivebrane

We study the moduli space of vacua of four-dimensional N = 1and N = 2 supersymmetric gauge theories with the gauge groups Sp(2 N c ), SO(2 N c ) and SO(2 N c + 1) using the M theory fivebrane. Higgs branches of the N = 2 supersymmetric gauge theories are interpreted in terms of the M theory fivebrane and the type IIA s-rule is realized in it. In particular, we construct the fivebrane configuration which corresponds to a special Higgs branch root. This root is analogous to the baryonic branch root in the SU( N c ) theory which remains as a vacuum after the adjoint mass perturbation to break N = 2 to N = 1. Furthermore, we obtain the monopole condensations and the meson vacuum expectation values in the confining phase of N = 1 supersymmetric gauge theories using the fivebrane technique. These are in complete agreement with the field theory results for the vacua in the phase with a single confined photon.

Matrix regularization of an open supermembrane: Towards M-theory five-branes via open supermembranes

We study open supermembranes in 11 dimensional rigid superspace with 6 dimensional topological defects (M-theory five-branes). After rederiving in the Green-Schwarz formalism the boundary conditions for open superstrings in the type IIA theory, we determine the boundary conditions for open supermembranes by imposing kappa symmetry and invariance under a fraction of 11 dimensional supersymmetry. The result seems to imply the self-duality of the three-form field strength on the five-brane world volume. We show that the light-cone gauge formulation is regularized by a dimensional reduction of a 6 dimensional N=1 super Yang-Mills theory with the gauge group SO(N\to\infty). We also analyze the SUSY algebra and BPS states in the light-cone gauge.

Toroidal compactification without vector structure

Many important ideas about string duality that appear in conventional $\T^2$ compactification have analogs for $\T^2$ compactification without vector structure. We analyze some of these issues and show, in particular, how orientifold planes associated with $Sp(n)$ gauge groups can arise from T-duality and how they can be interpreted in F-theory. We also, in an appendix, resolve a longstanding puzzle concerning the computation of $\Tr (-1)^F$ in four-dimensional supersymmetric Yang-Mills theory with gauge group SO(n).

N = 2 supersymmetric gauge theories, branes and orientifolds

Starting with configurations of fourbranes, fivebranes, sixbranes and orientifolds in type 11A string theory we derive via M-theory the curves solving N = 2 supersymmetric gauge theories with gauge groups SO( N) and Sp(2 N). We also obtain new curves describing theories with product gauge groups. A crucial role in the discussion is played by the interaction of the orientifolds with the NS-fivebranes.

Heterotic M(atrix) strings and their interactions

Following a recent proposal of Dijkgraaf, Verlinde and Verlinde, we show that the M(atrix) theory compactified on S 1 Z 2 provides us with a non-perturbative description of the second-quantized light-cone heterotic string. This so-called heterotic M(atrix) string theory is defined by a two-dimensional (8,0) supersymmetric chiral gauge theory with gauge group SO(2 N) in the large N limit. We argue that at the strong coupling fixed point the chiral gauge theory flows to a (8,0) superconformal field theory defined via the SN symmetric product space orbifold. We show that the leading order correction to the strong coupling expansion corresponds to a unique irrelevant operator of scaling dimension three and describes the joining and splitting cubic interactions of the light-cone heterotic string. We also speculate on a M(atrix) description of bosonic strings via dimensional reduction of d = 26 Yang-Mills theory.

Cosmological Einstein–Yang–Mills equations

We use a systematic construction method for invariant connections on homogeneous spaces to find the Einstein–SU(n)–Yang–Mills equations for Friedmann–Robertson–Walker and locally rotationally symmetric homogeneous cosmologies. These connections depend on the choice of a homomorphism from the isotropy group into the gauge group. We consider here the cases of the gauge group SU(n) and SO(n), where these homomorphisms correspond to unitary or orthogonal representations of the isotropy group. For some of the simpler cases the full system of the evolution equations are derived, for others we only determine the number of dynamical variables that remain after some mild fixing of the gauge.

Classification of three-family grand unification in string theory. I. The SO(10) andE6models

We give a classification of three-family SO(10) and E${}_{6}$ grand unification in string theory within the framework of conformal (free) field theory and asymmetric orbifolds. We argue that the construction of such models in heterotic string theory requires certain ${\mathbf{Z}}_{6}$ asymmetric orbifolds that include a ${\mathbf{Z}}_{3}$ outerautomorphism, the latter yielding a level-three current algebra for the grand unification gauge group SO(10) or E${}_{6}$. We then classify all such ${\mathbf{Z}}_{6}$ asymmetric orbifolds that result in models with a non-Abelian hidden sector. All models classified in this paper have only one adjoint (but no other higher representation) Higgs field in the grand unified gauge group. In addition, all of them are completely anomaly-free. There are two types of such three-family models. The first type consists of the unique SO(10) model with SU(2) $\ensuremath{\bigotimes}$ SU(2) $\ensuremath{\bigotimes}$ SU(2) as its hidden sector (which is not asymptotically free at the string scale). This SO(10) model has four left-handed and one right-handed $16$'s. The second type is described by a moduli space containing 17 models (distinguished by their massless spectra). All these models have an SU(2) hidden sector, and five left-handed and two right-handed families in the grand unified gauge group. One of these models is the unique E${}_{6}$ model with an asymptotically free SU(2) hidden sector. The others are SO(10) models, eight of them with an asymptotically free hidden sector at the string scale.

Exploring the moduli space of (0,2) strings

We use an exactly solvable (0,2) supersymmetric conformal field theory with gauge group SO(10) to investigate the superpotential of the corresponding classical string vacuum. We provide evidence that the rational point lies in the Landau-Ginzburg phase of the linear σ-model and calculate exactly all three- and four-point functions of the gauge singlets. These couplings already put severe constraints on the possible flat directions of the superpotential. Finally, we contemplate about the flat direction related to Kähler deformations of the underlying linear σ-model.

An orientifold of Type-IIB theory on K3

A new orientifold of Type-IIB theory on K3 is constructed that has N=1 supersymmetry in six dimensions. The orientifold symmetry consists ofaa |Z 2 involution of K3 combined with orientation reversal on the world-sheet. The closed-string sector in the resulting theory contains nine tensor multiplets and twelve neutral hypermultiplets in addition to the gravity multiplet, and is anomaly free by itself. The open-string sector contains only five-branes and gives rise to maximal gauge groups SO(16) or U(8) × U(8) at different points in the moduli space. Anomalies are canceled by a generalization of the Green-Schwarz mechanism that involves more than one tensor multiplets.

Gauge-Yukawa unification in SO(10) SUSY GUTs

We study supersymmetric unified models with three fermion generations based on the gauge group SO(10) and require gauge-Yukawa unification, i.e. a renormalization group invariant functional relationship among the gauge and Yukawa couplings of the third generation in the symmetric phase. In the case of the minimal model, we find that the predicted values for the top and bottom quark masses are in agreement with the present experimental data for a wide range of supersymmetry breaking scales. We also find that an experimental accuracy of less than 1% for the top quark mass could test the corresponding prediction of the gauge-Yukawa unified model.

A relation between the Kauffman and the HOMFLY polynomials for torus knots

Polynomial invariants corresponding to the fundamental representation of the gauge group SO(N) are computed for arbitrary torus knots in the framework of Chern–Simons gauge theory making use of knot operators. As a result, a formula that relates the Kauffman and the HOMFLY polynomials for torus knots is presented.

Anomaly-free supersymmetric models in six dimensions

The conditions for the cancellation of all gauge, gravitational, and mixed anomalies of N = 1 supersymmetric models in six dimensions are reviewed and illustrated by a number of examples. Of particular interest are models that cannot be realized perturbatively in string theory. An example of this type, which we verify satisfies the anomaly cancellation conditions, is the K3 compactification of the SO(32) theory with small instantons recently proposed by Witten. When the instantons coincide it has gauge group SO(32) × Sp(24). Two new classes of models, for which non-perturbative string constructions are not yet known, are also presented. They have gauge groups SO(2 n + 8) × Sp( n) and SU( n) × SU( n), where n is an arbitrary positive integer.

The vacuum structure of N = 2 super-QCD with classical gauge groups

We determine the vacuum structure of N = 2 supersymmetric QCD with fundamental quarks for gauge groups SO( n) and Sp(2 n), extending prior results for SU( n). The solutions are all given in terms of families of hyperelliptic Riemann surfaces of genus equal to the rank of the gauge group. In the scale-invariant cases, the solutions all have exact S-dualities which act on the couplings by subgroups of PSL(2, Z ) and on the masses by outer automorphisms of the flavor symmetry. They are shown to reproduce the complete pattern of symmetry breaking on the Coulomb branch and predict the correct weak-coupling monodromies. Simple breakings with squark vevs provide further consistency checks involving strong-coupling physics.

Three-Generation Distler-Kachru Models

Distler-Kachru models which yield three generations of chiral fermions with gauge group SO(10) are found. These models have mirror partners.

String GUTs

Standard SUSY-GUTS such as those based on SU(5) or SO(10) lead to predictions for the values of α s and sin 2 ϱ W in amazing agreement with experiment. In this article we investigate how these models may be obtained from string theory, thus bringing them into the only known consistent framework for quantum gravity. String models with matter in standard GUT representations require the realization of affine Lie algebras at higher levels. We start by describing some methods to build level k = 2 symmetric orbifold string models with gauge groups SU(5) or SO(10). We present several examples and identify generic features of the type of models constructed. Chiral fields appropriate to break the symmetry down to the standard model generically appear in the massless spectrum. However, unlike in standard SUSY-GUTs, they often behave as string moduli, i.e., they do not have self-couplings. We also discuss briefly the doublet-triplet Higgs splitting. We find that, in some models, built-in sliding-singlet type of couplings exist.

On the monodromies of N = 2 supersymmetric Yang-Mills theory with gauge group SO(2 n)

We present families of algebraic curves describing the moduli space of N = 2 supersymmetric Yang-Mills theory with gauge group SO(2 n). We test our curves by computing the weak-coupling monodromies and the number of N = 1 vacua.

Duality of Sp(2 Nc) and SO( Nc) supersymmetric gauge theories with adjoint matter

We discuss electric-magnetic duality in two new classes of supersymmetric Yang-Mills theories. The models have gauge group Sp(2 N c ) or SO( N c ) with matter in both the adjoint and defining representations. By perturbing these theories with various superpotentials, we find a variety of new infrared fixed points with dual descriptions. This work is complementary to that of Kutasov and Schwimmer on SU( N c ) and of Intriligator on other models involving Sp(2 N c ) and SO( N c ).

Putting string /string duality to the test

After simultaneous compactification of spacetime and worldvolume on K3, the D = 10 heterotic fivebrane with gauge group SO(32) behaves like a D = 6 heterotic string with gauge group SO(28) × SU(2), but with Kac-Moody levels different from those of the fundamental string. Thus the string/ fivebrane duality conjecture in D = 10 gets replaced by a string/string duality conjecture in D = 6. Since D = 6 strings are better understood than D = 10 fivebranes, this provides a more reliable laboratory in which to test the conjecture. According to string/string duality, the Green-Schwarz factorization of the D = 6 spacetime anomaly polynomial I8 into X 4 X ̃ 44 means that just as X 4 is the σ-model anomaly polynomial of the fundamental string worldsheet so X ̃ 4 should be the corresponding polynomial of the dual string worldsheet. To test this idea we perform a classical dual string calculation of 94 and find agreement with the quantum fundamental string result. This also provides an a posteriori justification for assumptions made in a previous paper on string/fivebrane duality. Finally we speculate on the relevance of string/string duality to the vacuum degeneracy problem.