Gauge Group Structure Research Articles

Gauge group topology of 8D Chaudhuri-Hockney-Lykken vacua

Compactifications of the Chaudhuri-Hockney-Lykken (CHL) string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice ${\mathrm{\ensuremath{\Lambda}}}_{M}$, the so-called Mikhailov lattice. Based on these data, we devise a method to determine the global gauge group structure including all $U(1)$ factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a nontrivial ${\ensuremath{\pi}}_{1}(G)\ensuremath{\equiv}\mathcal{Z}$ for the non-Abelian gauge group $G$ as having gauged a $\mathcal{Z}$ 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly [1] that would obstruct this gauging. We verify this by explicitly computing $\mathcal{Z}$ for all 8D CHL vacua with $\mathrm{rank}(G)=10$. Since our method applies also to ${T}^{2}$ compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a ``parent'' heterotic model.

The global gauge group structure of F-theory compactification with U(1)s

We show that F-theory compactifications with abelian gauge factors generally exhibit a non-trivial global gauge group structure. The geometric origin of this structure lies with the Shioda map of the Mordell-Weil generators. This results in constraints on the mathfrak{u}(1) charges of non-abelian matter consistent with observations made throughout the literature. In particular, we find that F-theory models featuring the Standard Model algebra actually realise the precise gauge group [SU(3) × SU(2) × U(1)]/ℤ6. Furthermore, we explore the relationship between the gauge group structure and geometric (un-)higgsing. In an explicit class of models, we show that, depending on the global group structure, an mathfrak{s}mathfrak{u}(2)oplus mathfrak{u}(1) gauge theory can either unhiggs into an SU(2) × SU(2) or an SU(3) × SU(2) theory. We also study implications of the charge constraints as a criterion for the F-theory ‘swampland’.

Dark matter from the vector of SO(10)

SO(10) grand unified theories can ensure the stability of new particles in terms of the gauge group structure itself, and in this respect are well suited to accommodate dark matter (DM) candidates in the form of new stable massive particles. We introduce new fermions in two vector 10 representations. When SO(10) is broken to the standard model by a minimal 45 + 126 + 10 scalar sector with $SU(3)_C \otimes SU(2)_L \otimes SU(2)_R\otimes U(1)_{B-L}$ as intermediate symmetry group, the resulting lightest new states are two Dirac fermions corresponding to combinations of the neutral members of the $SU(2)_L$ doublets in the 10's, which get splitted in mass by loop corrections involving $W_R$. The resulting lighter mass eigenstate is stable, and has only non-diagonal $Z_{L,R}$ neutral current couplings to the heavier neutral state. Direct detection searches are evaded if the mass splitting is sufficiently large to suppress kinematically inelastic light-to-heavy scatterings. By requiring that this condition is satisfied, we obtain the upper limit $M_{W_R} \lesssim 25$ TeV.

CosPA 2015 and the Standard Model

In this keynote speech, I describe briefly “The Universe”, a journal/newsletter launched by APCosPA Organization, and my lifetime research on the Standard Model of particle physics. In this 21st Century, we should declare that we live in the quantum 4-dimensional Minkowski space-time with the force-fields gauge-group structure [Formula: see text] built-in from the very beginning. This background can see the lepton world, of atomic sizes, and offers us the eyes to see other things. It also can see the quark world, of the Fermi sizes, and this fact makes this entire world much more interesting.

Mordell-Weil torsion and the global structure of gauge groups in F-theory

We study the global structure of the gauge group $G$ of F-theory compactified on an elliptic fibration $Y$. The global properties of $G$ are encoded in the torsion subgroup of the Mordell-Weil group of rational sections of $Y$. Generalising the Shioda map to torsional sections we construct a specific integer divisor class on $Y$ as a fractional linear combination of the resolution divisors associated with the Cartan subalgebra of $G$. This divisor class can be interpreted as an element of the refined coweight lattice of the gauge group. As a result, the spectrum of admissible matter representations is strongly constrained and the gauge group is non-simply connected. We exemplify our results by a detailed analysis of the general elliptic fibration with Mordell-Weil group $\mathbb Z_2$ and $\mathbb Z_3$ as well as a further specialization to $\mathbb Z \oplus \mathbb Z_2$. Our analysis exploits the representation of these fibrations as hypersurfaces in toric geometry.

Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory

The dynamics of charged particles in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy is parametrized using a generalized Courant-Snyder (CS) theory, which extends the original CS theory for one degree of freedom to higher dimensions. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D symplectic rotation, or a $U(2)$ element. The 1D envelope equation, also known as the Ermakov-Milne-Pinney equation in quantum mechanics, is generalized to an envelope matrix equation in higher dimensions. Other components of the original CS theory, such as the transfer matrix, Twiss functions, and CS invariant (also known as the Lewis invariant) all have their counterparts, with remarkably similar expressions, in the generalized theory. The gauge group structure of the generalized theory is analyzed. By fixing the gauge freedom with a desired symmetry, the generalized CS parametrization assumes the form of the modified Iwasawa decomposition, whose importance in phase space optics and phase space quantum mechanics has been recently realized. This gauge fixing also symmetrizes the generalized envelope equation and expresses the theory using only the generalized Twiss function $\ensuremath{\beta}$. The generalized phase advance completely determines the spectral and structural stability properties of a general focusing lattice. For structural stability, the generalized CS theory enables application of the Krein-Moser theory to greatly simplify the stability analysis. The generalized CS theory provides an effective tool to study coupled dynamics and to discover more optimized lattice designs in the larger parameter space of general focusing lattices.

Highlights of supersymmetric hypercharge ±1 triplets

The discovery of a standard model (SM)-like Higgs boson with a relatively heavy mass $m_h$ and hints of di-photon excess has deep implication to supersymmetric standard models (SSMs). We consider the SSM extended with hypercharge $\pm1$ triplets, and investigate two scenarios of it: (A) Triplets significantly couple to the Higgs doublets, which can substantially raise $m_h$ and simultaneously enhance the Higgs to di-photon rate via light chargino loops; (B) Oppositely, these couplings are quite weak and thus $m_h$ can not be raised. But the doubly-charged Higgs bosons, owing to the gauge group structure, naturally interprets why there is an excess rather than a deficient of Higgs to di-photon rate. Additionally, the pseudo Dirac triplet fermion is an inelastic non-thermal dark matter candidate. Light doubly-charged particles, especially the doubly-charged Higgs boson around 100 GeV in scenario B, are predicted. We give a preliminary discussion on their search at the LHC.

On the gauge symmetries of the spinning particle

We reconsider the gauge symmetries of the spinning particle by a direct examination of the Lagrangian using a systematic procedure based on the Noether identities. It proves possible to find a set of local bosonic and fermionic gauge transformations that have a simple gauge group structure, which is a true Lie algebra, both for the massless and massive case. This new fermionic gauge transformation of the “position” and “spin” variables in the action decouples from that of the “einbein” and “gravitino”. It is also possible to redefine the fields so that this simple algebra of commutators of the gauge transformations can be derived directly starting from the Lagrangian written in these new variables. We discuss a possible extension of our analysis of this simple model to more complicated cases.

From surface operators to non-Abelian volume operators in puff field theory

Puff Field Theory is a low energy decoupling regime of string theory that still retains the non-local attributes of the parent theory - while preserving isotropy for its non-local degrees of freedom. It realizes an extended holographic dictionary at strong coupling and dynamical non-local states akin to defects or the surface operators of local gauge theories. In this work, we probe the non-local features of PFT using D3 branes. We find supersymmetric configurations that end on defects endowed with non-Abelian degrees of freedom. These are 2+1 dimensional defects in the 3+1 dimensional PFT that may be viewed as volume operators. We determine their R-charge, vacuum expectation value, energy, and gauge group structure.

On the formulation of D = 11 supergravity and the composite nature of its three-form gauge field

The underlying gauge group structure of the D = 11 Cremmer–Julia–Scherk supergravity becomes manifest when its three-form field A 3 is expressed through a set of one-form gauge fields, B 1 a 1 a 2 , B 1 a 1 ⋯ a 5 , η 1 α , and E a , ψ α . These are associated with the generators of the elements of a family of enlarged supersymmetry algebras E ˜ ( 528 | 32 + 32 ) ( s ) parametrized by a real number s. We study in detail the composite structure of A 3 extending previous results by D’Auria and Fré, stress the equivalence of the above problem to the trivialization of a standard supersymmetry algebra E ( 11 | 32 ) cohomology four-cocycle on the enlarged E ˜ ( 528 | 32 + 32 ) ( s ) superalgebras, and discuss its possible dynamical consequences. To this aim we consider the properties of the first order supergravity action with a composite A 3 field and find the set of extra gauge symmetries that guarantee that the field theoretical degrees of freedom of the theory remain the same as with a fundamental A 3. The extra gauge symmetries are also present in the so–called rheonomic treatment of the first order D = 11 supergravity action when A 3 is composite. Our considerations on the composite structure of A 3 provide one more application of the idea that there exists an extended superspace coordinates/fields correspondence. They also suggest that there is a possible embedding of D = 11 supergravity into a theory defined on the enlarged superspace Σ ˜ ( 528 | 32 + 32 ) ( s ) .

Non-Abelianizable First Class Constraints

We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of gauge group. The sufficient condition is obtained by applying the theorem of implicit function in calculus and studying the local structure of gauge orbits. Since the sufficient condition is necessary for existence of proper gauge fixing conditions, we conclude that in the case of a finite set of non-Abelianizable first class constraints, the Faddeev-Popov determinant is vanishing for any choice of subsidiary constraints. This result is explicitly examined for SO(3) gauge invariant model.

On the underlying gauge group structure of [formula omitted] supergravity

The underlying gauge group structure of D=11 supergravity is revisited. It may be described by a one-parametric family of Lie supergroups Σ˜(s)×⊃SO(1,10), s≠0. The family of superalgebras E˜(s) associated to Σ˜(s) is given by a family of extensions of the M-algebra {Pa,Qα,Zab,Za1⋯a5} by an additional fermionic central charge Qα′. The Chevalley–Eilenberg four-cocycle ω4∼Πα∧Πβ∧Πa∧ΠbΓabαβ on the standard D=11 supersymmetry algebra may be trivialized on E˜(s), and this implies that the three-form field A3 of D=11 supergravity may be expressed as a composite of the Σ˜(s) one-form gauge fields ea, ψα, Bab, Ba1⋯a5 and ηα. Two superalgebras of E˜(s) recover the two earlier D'Auria and Fré decompositions of A3. Another member of E˜(s) allows for a simpler composite structure for A3 that does not involve the Ba1⋯a5 field. Σ˜(s) is a deformation of Σ˜(0), which is singularized by having an enhanced Sp(32) (rather than just SO(1,10)) automorphism symmetry and by being an expansion of OSp(1|32).

Measurements of the QCD colour factors at LEP

A summary of the measurements of the QCD colour factors at LEP is presented. Such measurements provide a test of the gauge group structure underlying the theory of strong interactions. A variety of methods have been applied by the various experiements, and perfect consistency with the expectation of QCD with SU(3) as gauge group is found.

Measurements of the QCD colour factors at LEP and a limit on the light glunio

A summary of the measurements of the QCD colour factors at LEP is presented. Such measurements provide a test of the gauge group structure underlying the theory of strong interactions. A variety of methods have been applied by the various experiments, and perfect consistency with the expectation of QCD with SU(3) as gauge group is found. By translating a colour factor measurement into a determination of the number of active flavours, ALEPH exludes a light gluino for masses below 6.3 GeV/ c 2.

Two-loop neutrino masses and the solar neutrino problem.

The addition of $m$ singlet right-handed neutrinos to the Standard Model leads to radiatively generated mass corrections for the $SU(2)_L $ doublet neutrinos. For those neutrinos which are massless at the tree level after this addition, this implies a small mass generated at the two-loop level via $W^{\pm}$ exchange. We calculate these mass corrections exactly by obtaining an analytic form for the general case of $n$ doublets and $m$ singlets. As a phenomenological application, we consider the $m=1$ case and examine the masses and mixings of the doublet neutrinos which arise as a result of the two-loop correction in the light of experimental data from two sources which may shed light on the question of neutrino masses. These are(a) the neutrino detectors reporting a solar neutrino deficit (and its resolution via Mikheyev-Smirnov-Wolfenstein matter oscillations), and (b) the COBE satellite data on the non-zero angular variations of the cosmic microwave background temperature (and its possible implications for hot dark matter). Within the framework of the extension considered here, which leaves the gauge group structure of the Standard Model intact, we show that it is possible for neutrinos to acquire small masses naturally, with values which are compatible with current theoretical bias and experimental data.

Hidden Sector Structure and Fractionally Charged States in Calabi-Yau Compactified String Model

We investigate the gauge group structure of hidden sector in Calabi-Yau Compactified string model by taking account of the modular invariance condition. The models with phenomenologically favorable observable sector become modular invariant introducing the Wilson line in hidden sector. We also comment on the existence of fractionally charged color neutral states in connection with the proton stability.

Supersymmetric flipped SU(5) revitalized

Abstract We describe a simple N = 1 supersymmetric GUT based on the group SU(5)×U(1) which has the following virtues: the gauge group is broken down to the SU (3) C × SU (2) L × U (1) Y of the standard model using just 10 , 10 Higgs representations, and doublet-triplet mass splitting problem is solved naturally by a very simple missing-partner mechanism. The successful supersymmetric GUT prediction for sin 2 θ w can be maintained, whilst there are no fermion mass relations. The gauge group and representation structure of the model may be obtainable from the superstring.

Superstring-inspired models

We discuss the structure of low-energy groups arising from compactified models based on the heterotic string. Particular regard is paid to the possibility of intermediate scale breaking which may change the low-energy gauge structure and may naturally lead to doublet-triplet splitting and the suppression of proton decay. We present an illustrative example of such a model with a low energy gauge group structure SU 3 c × SU 2 L × SU 2 R × U 1 B−L which may be compatible with low-energy phenomena including limits on neutrino masses and sin 2 θ W. Mechanisms leading to the minimal SU 3 c × SU 2 L × U 1 Y low-energy gauge group are also presented.

A four-dimensional formulation of defect dynamics and some of its consequences

A 4-dimensional formulation of the equations of defect dynamics is given through use of concepts from the exterior calculus. The formulation provides a clear separation of the three basic effects; geometric responses of bodies to loadings, evolution of dislocations, and evolution of disclinations. The theory is shown to admit a 45-fold gauge group and a system of natural gauge conditions whereby the elastic and the plastic parts of the responses may be disentangled. The gauge conditions also lead to both spatial and temporial nonlocality. Self-equilibrating dislocations and disclinations (i.e. those for which there is no plastic distortion or velocity) are shown to exist and conditions for their elimination are given. A complete analogy is established between defect dynamics and co-occupying systems of electromagnetic fields with both electric and magnetic charges and currents. Analogous magnetic charges and currents are shown to vanish only if there are no disclinations present. The gauge group structure and the electrodynamic analogy provide expectations of parallels with Yang-Mills type unified gauge theories. A constitutive theory is obtained through use of the practices of non-equilibrium thermodynamics, one example of which leads to a natural implementation of a yield criteria, an incremental law of plastic distortion, and a proof of Drucker's postulate.

Relations among neutral current couplings to test the SU(2) ⊗ U(1) gauge group structure

We propose a test of the validity of SU(2) ⊗ U(1) as the gauge group of weak and electromagnetic interactions. We find that, among the seven empirical neutral current couplings, there are two restrictions which do not rely on a particular model. The relations are 2( G V + G A) + ( α + β) + 3( γ + δ) = 0 and 2 k − ( α + β) + 3( γ + δ) = 0, where where α, β, γ, δ ( G V, G A) are the couplings measured in neutrino-hadron (electron) scattering and κ is obtained from interference experiments. We also find several inequalities. Comparison with present data is given.