Adjoint SU Research Articles

Adjoint SU(5) GUT model with modular S4 symmetry

We study the textures of SM fermion mass matrices and their mixings in a supersymmetric adjoint SU(5) Grand Unified Theory with modular S4 being the horizontal symmetry. The Yukawa entries of both quarks and leptons are expressed by modular forms with lower weights. Neutrino sector has an adjoint SU(5) representation 24 as matter superfield, which is a triplet of S4. The effective light neutrino masses is generated through Type-III and Type-I seesaw mechanism. The only common complex parameter in both charged fermion and neutrino sectors is modulus τ . Down-type quarks and charged leptons have the same joint effective operators with adjoint scalar in them, and their mass discrepancy in the same generation depends on Clebsch-Gordan factor. Especially for the first two generations the respective Clebsch-Gordan factors made the double Yukawa ratio \U0001d4b4d\U0001d4b4μ/\U0001d4b4e\U0001d4b4s = 12, in excellent agreement with the experimental result. We reproduce proper CKM mixing parameters and all nine Yukawa eigenvalues of quarks and charged leptons. Neutrino masses and MNS parameters are also produced properly with normal ordering is preferred.

On rational R-matrices with adjoint SU(n) symmetry**Dedicated to the memory of Petr Petrovich Kulish.

Using the representation theory of Yangians we construct the rational R-matrix which takes values in the adjoint representation of SU(n). From this we derive an integrable SU(n) spin chain with lattice spins transforming under the adjoint representation. However, the resulting Hamiltonian is found to be non-Hermitian.

Higgs criticality in a two-dimensional metal

We analyze a candidate theory for the strange metal near optimal hole-doping in the cuprate superconductors. The theory contains a quantum phase transition between metals with large and small Fermi surfaces of spinless fermions carrying the electromagnetic charge of the electron, but the transition does not directly involve any broken global symmetries. The two metals have emergent SU(2) and U(1) gauge fields respectively, and the transition is driven by the condensation of a real Higgs field, carrying a finite lattice momentum and an adjoint SU(2) gauge charge. This Higgs field measures the local antiferromagnetic correlations in a "rotating reference frame". We propose a global phase diagram around this Higgs transition, and describe its relationship to a variety of recent experiments on the cuprate superconductors.

Dynamical generation of the weak and Dark Matter scales from strong interactions

Assuming that mass scales arise in nature only via dimensional transmutation, we extend the dimension-less Standard Model by adding vector-like fermions charged under a new strong gauge interaction. Their non-perturbative dynamics generates a mass scale that is transmitted to the elementary Higgs boson by electro-weak gauge interactions. In its minimal version the model has the same number of parameters as the Standard Model, predicts that the electro-weak symmetry gets broken, predicts new-physics in the multi-TeV region and is compatible with all existing bounds, provides two Dark Matter candidates stable thanks to accidental symmetries: a composite scalar in the adjoint of SU(2)_L and a composite singlet fermion; their thermal relic abundance is predicted to be comparable to the measured cosmological DM abundance. Some models of this type allow for extra Yukawa couplings; DM candidates remain even if explicit masses are added.

The minimal adjoint-SU(5) × Z 4 GUT model

An extension of the adjoint SU(5) model with a flavour symmetry based on the Z_4 group is investigated. The Z_4 symmetry is introduced with the aim of leading the up- and down-quark mass matrices to the Nearest-Neighbour-Interaction form. As a consequence of the discrete symmetry embedded in the SU(5) gauge group, the charged lepton mass matrix also gets the same form. Within this model, light neutrinos get their masses through type-I, type-III and one-loop radiative seesaw mechanisms, implemented, respectively, via a singlet, a triplet and an octet from the adjoint fermionic 24 fields. It is demonstrated that the neutrino phenomenology forces the introduction of at least three 24 fermionic multiplets. The symmetry SU(5)xZ_4 allows only two viable zero textures for the effective neutrino mass matrix. It is showed that one texture is only compatible with normal hierarchy and the other with inverted hierarchy in the light neutrino mass spectrum. Finally, it is also demonstrated that Z_4 freezes out the possibility of proton decay through exchange of colour Higgs triplets at tree-level.

The Adjoint SU(5) constrained by a Z4 flavour symmetry

We study the neutrino mass spectrum in the context of the adjoint SU(5) model constrained by a Z4 flavour symmetry that imposes the nearest-neighbour interaction form on both up- and down-quark mass matrices. We show that at least three adjoint fermionic fields are required in order to reproduce the light neutrino mass spectrum.

A Global SU(5) F-theory model with Wilson line breaking

We engineer compact SU(5) Grand Unified Theories in F-theory in which GUT-breaking is achieved by a discrete Wilson line. Because the internal gauge field is flat, these models avoid the high scale threshold corrections associated with hypercharge flux. Along the way, we exemplify the `local-to-global' approach in F-theory model building and demonstrate how the Tate divisor formalism can be used to address several challenges of extending local models to global ones. These include in particular the construction of G-fluxes that extend non-inherited bundles and the engineering of U(1) symmetries. We go beyond chirality computations and determine the precise (charged) massless spectrum, finding exactly three families of quarks and leptons but excessive doublet and/or triplet pairs in the Higgs sector (depending on the example) and vector-like exotics descending from the adjoint of SU(5)_{GUT}. Understanding why vector-like pairs persist in the Higgs sector without an obvious symmetry to protect them may shed light on new solutions to the mu problem in F-theory GUTs.

Equivariant reduction ofU(4)gauge theory overSF2×SF2and the emergent vortices

We consider a U(4) Yang-Mills theory on M x S_F^2 x S_F^2 where M is an arbitrary Riemannian manifold and S_F^2 x S_F^2 is the product of two fuzzy spheres spontaneously generated from a SU(\cal {N}) Yang-Mills theory on M which is suitably coupled to six scalars in the adjoint of SU({\cal N}). We determine the SU(2) x SU(2)-equivariant U(4) gauge fields and perform the dimensional reduction of the theory over S_F^2 x S_F^2. The emergent model is a U(1)^4 gauge theory coupled to four complex and eight real scalar fields. We study this theory on R_2 and find that, in certain limits, it admits vortex type solutions with U(1)^3 gauge symmetry and discuss some of their properties.

Separability of two-qubit state in terms of local invariants

The separability condition for the two-qubit mixed state is formulated in terms of a system of inequalities in invariants of the adjoint SU(2) ⊗ SU(2) action on the space of density matrices, i.e., positive semidefinite 4 × 4 Hermitian matrices.

New solution for neutrino masses and leptogenesis in adjoint SU(5)

We investigate baryogenesis via leptogenesis and generation of neutrino masses and mixings through the Type I plus Type III seesaw plus an one-loop mechanism in the context of Renormalizable Adjoint SU(5) theory. One light neutrino remains massless, because the contributions of three heavy Majorana fermions \rho_0, \rho_3 and \rho_8 to the neutrino mass matrix are not linearly independent. However none of these heavy fermions is decoupled from the generation of neutrino masses. This opens a new range in parameter space for successful leptogenesis, in particular, allows for inverted hierarchy of the neutrino masses.

Fermionic operator mixing in holographic p-wave superfluids

We use gauge-gravity duality to compute spectral functions of fermionic operators in a strongly-coupled defect field theory in p-wave superfluid states. The field theory is (3+1)-dimensional N=4 supersymmetric SU(Nc) Yang-Mills theory, in the 't Hooft limit and with large coupling, coupled to two massless flavors of (2+1)-dimensional N=4 supersymmetric matter. We show that a sufficiently large chemical potential for a U(1) subgroup of the global SU(2) isospin symmetry triggers a phase transition to a p-wave superfluid state, and in that state we compute spectral functions for the fermionic superpartners of mesons valued in the adjoint of SU(2) isospin. In the spectral functions we see the breaking of rotational symmetry and the emergence of a Fermi surface comprised of isolated points as we cool the system through the superfluid phase transition. The dual gravitational description is two coincident probe D5-branes in AdS5 x S5 with non-trivial worldvolume SU(2) gauge fields. We extract spectral functions from solutions of the linearized equations of motion for the D5-branes' worldvolume fermions, which couple to one another through the worldvolume gauge field. We develop an efficient method to compute retarded Green's functions from a system of coupled bulk fermions. We also perform the holographic renormalization of free bulk fermions in any asymptotically Euclidean AdS space.

ON THE ROLE OF LOW-ENERGY CP VIOLATION IN LEPTOGENESIS

The link between low-energy CP violation and leptogenesis became more accessible with the understanding of flavor effects. However, a definite well-motivated model where such a link occurs was still lacking. Adjoint SU(5) is a simple grand unified theory where neutrino masses are generated through the Type I and Type III seesaw mechanisms, and the lepton asymmetry is generated by the fermionic triplet responsible for the Type III seesaw. We focus exclusively on the case of inverted hierarchy for neutrinos, and we show that successful flavored leptogenesis in this theory strongly points towards low-energy CP violation. Moreover, since the range of allowed masses for the triplet is very restricted, we find that the discovery at the LHC of new states present in the theory, together with proton decay and unification of gauge couplings, can conspire to provide a hint in favor of leptogenesis.

α-SYMMETRIES, COLORED DIMENSIONS AND GAUGE–STRING CORRESPONDENCE

We propose a scenario of gauge–string correspondence by relating the SU(3) color group to hidden space–time isometries originating from extra dimensions. These isometries (α-symmetries) are the special symmetries of RNS superstring theories under global nonlinear space–time transformations. The vertex operators for the octet of gluons are constructed by the procedure of "photon painting," that is, with the SU(3) subgroup of the α-symmetry generators acting on a regular open string photon, so the corresponding open string excitations are in the adjoint of SU(3). Remarkably, the operator algebra of these massless gluon vertices is closed and possesses the full zigzag symmetry, crucial for the isomorphism between open strings and QCD. As a result, the scattering amplitudes of the constructed open string vertex operators have a field-theoretic rather than a stringy structure, including the absence of standard tower of massive intermediate states. Our model also suggests that the total number of underlying hidden dimensions is three, with each extra dimension carrying its appropriate SU(3) color and anticolor.

Grand unification and light color-octet scalars at the LHC

We study the properties and production mechanisms of color-octet scalars at the Large Hadron Collider. We focus on the single production of both charged and neutral members of an (8,2){sub 1/2} doublet through bottom-quark initial states. These channels provide a window to the underlying Yukawa structure of the scalar sector. Color-octet scalars naturally appear in grand unified theories based on the SU(5) gauge symmetry. In the context of adjoint SU(5) these fields are expected to be light to satisfy constraints coming from unification and proton decay, and may have TeV-scale masses. One combination of their couplings is defined by the relation between the down-quark and charged-lepton Yukawa couplings. Observation of these states at the LHC gives an upper bound on the proton lifetime if they truly arise from this grand unified theory. We demonstrate that TeV-mass scalars can be observed over background at the LHC using boosted top-quark final states, and study how well the scalar Yukawa parameters can be measured.

Universality, vortices, and confinement: Modified SO(3) lattice gauge theory at nonzero temperature

We investigate the adjoint SU(2) lattice gauge theory in $3+1$ dimensions with the Wilson plaquette action modified by a ${Z}_{2}$ monopole suppression term. For the zero-twist sector we report on indications for the existence of a finite temperature transition decoupled from the unphysical bulk transitions.

SU(2) reduction of six-dimensional (1,0) supergravity

We obtain a gauged supergravity theory in three dimensions with eight real supersymmetries by means of a Scherk–Schwarz reduction of pure N=(1,0) supergravity in six dimensions on the SU(2) group manifold. The SU(2) Yang–Mills fields in the model propagate, since they have an ordinary kinetic term in addition to Chern–Simons couplings. The other propagating degrees of freedom consist of a dilaton, five scalars which parameterise the coset SL(3, R)/ SO(3), three vector fields in the adjoint of SU(2), and twelve spin- 1 2 fermions. The model admits an AdS 3 vacuum solution. We also show how a charged black hole solution can be obtained, by performing a dimensional reduction of the rotating self-dual string of six-dimensional (1,0) supergravity.

Chiral symmetry breaking in the AdS/CFT correspondence

We study the SU(3)-invariant relevant deformation of D=4 N=4 SU(N) gauge theory at large N using the AdS/CFT correspondence. At low energies, we obtain a nonsupersymmetric gauge theory with three left-handed quarks in the adjoint of SU(N). In terms of the five dimensional gauged supergravity, there is an unstable critical point in the scalar potential for fluctuations of some fields in a nontrivial representation of the symmetry group SU(3). On the field theory side, this corresponds to dynamical breaking of the SU(3) chiral symmetry down to SO(3). We compute the condensate of the quark bilinear and the two-point correlation function of the spontaneously broken currents from supergravity and find a nonzero `pion' decay constant, f_pi.

Z2 monopoles, vortices and the universality of the SU(2) deconfinement transition

We investigate the effect of Z 2 magnetic monopoles and vortices on the finite temperature deconfinement phase transition in the fundamental - adjoint SU(2) lattice gauge theory. In the limit of complete suppression of the Z 2 monopoles, the mixed action for the SU(2) theory in its Villain form is shown to be self-dual under the exchange of the fundamental and adjoint couplings. By further suppressing the Z 2 vortices we show that the extended model reduces to the Wilson action with a modified coupling. The universality of the SU(2) deconfinement phase transition with the Ising model is therefore expected to remain intact in the entire plane of the fundamental-adjoint couplings in the continuum limit. The self-duality arguments related to the suppression of Z 2 monopoles are also applicable to the Villain form of mixed action for the SU( N) theory with Z N magnetic monopoles.

Abelian dominance and adjoint sources in lattice QCD.

Certain properties of maximal abelian projection are derived which suggest that the fundamental and adjoint SU(2) string tensions are reproduced by singly and doubly charged abelian Wilson loops, respectively. Thus, abelian dominance, which has been observed for color sources (quarks) in the fundamental representation, can be extended to higher representations. Numerical evidence in support of this conjecture also for adjoint quarks is presented. The difference between maximal abelian and local projections is elucidated and the role of non-Wilson-like terms in the effective abelian action is discussed.

Study of confinement in the adjoint SU(2)-Higgs model by means of the Fredenhagen and Marcu criterion

We report on numerical results of a simulation of the standard adjoint SU(2)-Higgs model with clear evidence for charge confinement in the Higgs and confined phases. We report also on some numerical results on the accuracy of the icosahedron in describing the full SU(2) gauge group.