Superconductivity in Supersymmetric Theories

The study of superconductivity has been undertaken through the breaking of supersymmetric gauge theories which automatically incorporate the condensation of monopoles and dyons leading to confining and superconducting phases. Constructing the effective Lagrangian near a singularity in moduli space for N=2 supersymmetric theory with SU(2) gauge group, it has been shown that when a mass term is added to this Lagrangian, the N=2 Supersymmetry is reduced to N=1 supersymmetry yielding the dyonic condensation which leads to confinement and superconductivity as the consequence of generalized Meissner effect. In the Coulomb phase of N=2 SU(3) Yang–Mills theory the gauge symmetry has been broken down to SU(2)×U(l) and it has been shown that on perturbing it by suitable tree-level superpotential this supersymmetry theory breaks to N=1 SU(2) Yang-Mills theory described by Higgs field in confining phase incorporating superconductivity.     

Superconductivity in Supersymmetric Theory in Restricted Chromodynamics

The study of superconductivity, dual superconductivity and color superconductivity has been undertaken through the breaking of super symmetric gauge theory in restricted chromo dynamics (RCD) which automatically incorporates the condensation of monopoles and dyons leading to confining and superconducting phases. Dyonic supermultiplets in N=1 super symmetry have been obtained quantum mechanically in RCD and it has been shown that dyon appears in RCD theory only through restricted part of the generalized potential and it is only this part of this potential which is responsible for quark confinement and the resulting superconductivity through the mechanism of dyonic condensation.     

Heavy quark and gluino potentials to two loops

The static potentials for systems of a heavy quark and anti-quark, two gluinos and a quark and a gluino are computed for all possible color configurations of a SU(Nc) gauge group.     

Quark chiral condensate from the overlap quark propagator

From the overlap lattice quark propagator calculated in the Landau gauge,we determine the quark chiral condensate by fitting operator product expansion formulas to the lattice data.The quark propagators are computed on domain wall fermion configurations generated by the RBC-UKQCD Collaborations with N_f = 2 + 1flavors.Three ensembles with different light sea quark masses are used at one lattice spacing 1/a = 1.75(4) Ge V.We obtain ψψ (2 GeV)MS =(-304(15)(20) MeV)~3in the SU(2) chiral limit.     

Lattice study of dense matter with two colors and four flavors

We present results from a simulation of SU(2) lattice gauge theory with N _f = 4 flavors of Wilson fermion and non-zero quark chemical potential μ, using the same 12³×24 lattice, bare gauge coupling, and pion mass in cut-off units as a previous study (S. Hands, S. Kim, J.I. Skullerud, Phys. Rev. D 81, 091502(R) (2010)) with N _f = 2 . The string tension for N _f = 4 is found to be considerably smaller implying smoother gauge field configurations. Thermodynamic observables and order parameters for superfluidity and color deconfinement are studied, and comparisons drawn between the two theories. Results for quark density and pressure as functions of μ are qualitatively similar for N _f = 2 and N _f = 4 ; in both cases there is evidence for a phase in which baryonic matter is simultaneously degenerate and confined. Results for the stress-energy tensor, however, suggest that while N _f = 2 has a regime where dilute matter is non-relativistic and weakly interacting, N _f = 4 matter is relativistic and strongly interacting for all values of μ above onset.     

Quantum Wall Crossing in $${{\mathcal N}=2}$$ Gauge Theories

We study refined and motivic wall-crossing formulas in N=2{{\mathcal N}=2} supersymmetric gauge theories with SU(2) gauge group and N _f < 4 matter hypermultiplets in the fundamental representation. Such gauge theories provide an excellent testing ground for the conjecture that “refined = motivic.”     

Quark masses and flavor-mixing angles in a six-quark model of quantum flavordynamics

The Cabibbo-like flavor-mixing angles are related to quark masses through spontaneous symmetry breaking in an illustrative model of quantum flavordynamics based on the SU_2L x SU_2R x U₁ flavor gauge group and on six quark flavors. Theoretical and experimental consequences of the scheme are discussed.     

Ternary Z2 × Z3 Graded Algebras and Ternary Dirac Equation

The wave equation generalizing the Dirac operator to the Z₃-graded case is introduced, whose diagonalization leads to a sixth-order equation. It intertwines not only quark and anti-quark state as well as the u and d quarks, but also the three colors, and is therefore invariant under the product group Z₂ × Z₂ × Z₃. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry and of the SU(2) × U(1) that arise automatically in this model, leading to the full bosonic gauge sector of the Standard Model.

     

Light quarks and instantons

Instantons and anti-instantons can profoundly influence the structure of a non-Abelian gauge theory involving N flavors of massless quarks. Interactions of the quarks with these pseudoparticles can spontaneously generate a quark mass, break the theory's SU(N) × SU(N) chiral symmetry and bind quark-antiquark pairs to form N² ? 1 Goldstone bosons. If the spontaneously generated quark mass is small, multipseudoparticle configurations can be treated in a dilute gas approximation.     

Quantum ’t Hooft Loops of SYM $${{\mathcal N}=4}$$ as Instantons of YM2 in Dual Groups SU(N) and SU(N)/ZN

A relation between circular 1/2 BPS ’t Hooft operators in 4d N=4{{\mathcal N}=4} SYM and instantonic solutions in 2D Yang-Mills theory (YM₂) has recently been conjectured. Localization indeed predicts that those ’t Hooft operators in a theory with gauge group G are captured by instanton contributions to the partition function of YM₂, belonging to representations of the dual group ^L G. This conjecture has been tested in the case G = U(N) =  ^L G and for fundamental representations. In this paper, we examine this conjecture for the case of the groups G = SU(N) and ^L G = SU(N)/Z _N and loops in different representations. Peculiarities when groups are not self-dual and representations not “minimal” are pointed out.     

Heavy Quark Hadron Mass Scale

Without the spin interactions the hadron masses within a multiplet are degenerate. The light quark hadron degenerate multiplet mass spectrum is extended from the 3 quark ground state multiplets at J^P = 0⁻, ½⁺, 1⁻ to include the excited states which follow the spinorial decomposition of SU(2) × SU(2). The mass scales for the 4, 5, 6,… quark hadrons are obtained from the degenerate multiplet mass m₀/M = n²/α with n = 4, 5, 6,… The 4, 5, 6,… quark hadron degenerate multiplet masses follow by splitting of the heavy quark mass scales according to the spinorial decomposition of SU(2) × SU(2).     

A reanalysis of finite temperature <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory

We revise the SU(N _c ), N _c =3,4,6, lattice data on pure gauge theories at finite temperature by means of a quasi-particle approach. In particular, we focus on the relation between the effective mass of the quasi-particle and the order of the deconfinement transition, the scaling of the interaction measure with N²_c -1N^{2}_{c} -1, the role of gluon condensate, and the screening mass.     

The Donaldson–Witten Function for Gauge Groups of Rank Larger Than One

We study correlation functions in topologically twisted , d=4 supersymmetric Yang–Mills theory for gauge groups of rank larger than one on compact four-manifolds X. We find that the topological invariance of the generator of correlation functions of BRST invariant observables is not spoiled by noncompactness of field space. We show how to express the correlators on simply connected manifolds of b _2,+(X)>0 in terms of Seiberg–Witten invariants and the classical cohomology ring of X. For manifolds X of simple type and gauge group SU(N) we give explicit expressions of the correlators as a sum over =1 vacua. We describe two applications of our expressions, one to superconformal field theory and one to large N expansions of SU(N) , d=4 supersymmetric Yang–Mills theory. Received: 30 March 1998 / Accepted: 17 April 1998     

Radiative quark masses constrained by the gauge group only

We discuss the possibility of obtaining the observed pattern of quark masses and mixings as a consequence of radiative corrections, gauge invariance and particle content of the theory. We do not allow any kind of additional symmetry, such as family and discrete symmetries. A model based on the gauge groupSU(3)×SU(2) _L ×SU(2) _R ×U(1) _B?L is considered. It turns out that the correct values of quark masses can be reasonably reproduced. The typical strength of the flavour changing couplings of theZ ⁰-boson is however at least one order of magnitude above the experimental upper bounds. A comparison is made with a model in which an additional discrete symmetry is present. In this case flavour changing phenomena can be kept under control.     

Cabibbo angle and quark masses in a four-quark model of quantum flavordynamics

The Cabibbo angle is related through spontaneous symmetry breaking to the masses of the light quarks in an illustrative model of quantum flavordynamics based on the SU_2L × SU_2R × U₁ flavor gauge group and on four quark flavors. The agreement with experiment is quite good.     

Quaternion Octonion Reformulation of Grand Unified Theories

In this paper, Grand Unified theories are discussed in terms of quaternions and octonions by using the relation between quaternion basis elements with Pauli matrices and Octonions with Gell Mann λ matrices. Connection between the unitary groups of GUTs and the normed division algebra has been established to re-describe the SU(5) gauge group. We have thus described the SU(5) gauge group and its subgroup SU(3) _C ×SU(2) _L ×U(1) by using quaternion and octonion basis elements. As such the connection between U(1) gauge group and complex number, SU(2) gauge group and quaternions and SU(3) and octonions is established. It is concluded that the division algebra approach to the theory of unification of fundamental interactions as the case of GUTs leads to the consequences towards the new understanding of these theories which incorporate the existence of magnetic monopole and dyon.     

Analysis of the Nonet Scalar Mesons as Tetraquark States with New QCD Sum Rules

In this article, we take the scalar diquarks as point particles and describe them as basic quantum fields, then introduce the SU(3) color gauge interaction and new vacuum condensates to study the nonet scalar mesons as tetraquark states with the QCD sum rules. Comparing with the conventional quark currents, the diquark currents have the outstanding advantage to satisfy the two criteria of the QCD sum rules more easily.     

Quark matter in QC<Subscript>2</Subscript>D

Results are presented from a numerical study of lattice QCD with gauge group SU(2) and two flavors of Wilson fermion at non-zero quark chemical potential μ ≫ T. Studies of the equation of state, the superfluid condensate, and the Polyakov line all suggest that in addition to the low-density phase of Bose-condensed diquark baryons, there is a deconfined phase at higher quark density in which quarks form a degenerate system, whose Fermi surface is only mildly disrupted by Cooper pair condensation.     

Toward finite quantum field theories

The properties that make theN=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule _s=0,1/2(–1)^2s+1(2s+1)M _s ² =0. FiniteN=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting ofN=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finiteN=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that anN=1 finiteSU (5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments.