Fermi point in graphene as a monopole in momentum space

We consider the effective field theory of a graphene monolayer with the Coulomb interaction between fermions taken into account. The gauge field in momentum space is introduced. The position of the Fermi point coincides with the position of the corresponding monopole. The procedure of extracting such monopoles during lattice simulations is suggested.     

Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism

We consider noncommutative gauge theory defined by means of Seiberg–Witten maps for an arbitrary semisimple gauge group. We compute the one-loop UV divergent matter contributions to the gauge field effective action to all orders in the noncommutative parameters θ. We do this for Dirac fermions and complex scalars carrying arbitrary representations of the gauge group. We use path-integral methods in the framework of dimensional regularisation and consider arbitrary invertible Seiberg–Witten maps that are linear in the matter fields. Surprisingly, it turns out that the UV divergent parts of the matter contributions are proportional to the noncommutative Yang–Mills action where traces are taken over the representation of the matter fields; this result supports the need to include such traces in the classical action of the gauge sector of the noncommutative theory.     

Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups

Magnetic monopole solutions for an arbitrary compact simple gauge group are considered in the Prasad-Sommerfield limit. For each group and choice of symmetry breaking there is a set of fundamental monopoles with minimal topological charges and possessing no internal degrees of freedom; the number of these is less than or equal to the rank of the gauge group. It is shown that if the unbroken gauge group is abelian, all solutions with higher topological charges belong to p-parameter families, where p is the number of position and group orientation parameters needed to describe a set of non-interacting fundamental monopoles with the given topological charge. It is argued that these solutions, some examples of which are given, should therefore be interpreted as multimonopole configurations. An extension of these results to the case of a non-albelian unbroken gauge symmetry is conjecture and shown to be valid for a number of examples.     

Nahm Transform for Periodic Monopoles¶and ?=2 Super Yang–Mills Theory

We study Bogomolny equations on ℝ²×?¹. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using the Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperk?hler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of ?=2 super Yang–Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius. Received: 20 July 2000 / Accepted: 29 November 2000     

Configurations of SO(3) monopoles with multiple magnetic charge

In this paper we consider configurations of monopoles with multiple magnetic charge in nonabelian gauge theory. Explicit gauge transformations are constructed which eliminate the string singularities for single monopoles of multiple magnetic charge, and for an arbitrary number of monopoles lying along a line. The question of finding nonsingular solutions is discussed.     

Cubic interaction vertex of higher-spin fields with external electromagnetic field

We fulfill the detailed analysis of coupling the charged bosonic higher-spin fields to external constant electromagnetic field in first order in external field strength. Cubic interaction vertex of arbitrary massive and massless bosonic higher-spin fields with external field is found. Construction is based on deformation of free Lagrangian and free gauge transformations by terms linear in electromagnetic field strength. In massive case a formulation with Stueckelberg fields is used. We begin with the most general form of deformations for Lagrangian and gauge transformations, admissible by Lorentz covariance and gauge invariance and containing some number of arbitrary coefficients, and require the gauge invariance of the deformed theory in first order in strength. It yields the equations for the coefficients which are exactly solved. As a result, the complete interacting Lagrangian of arbitrary bosonic higher-spin fields with constant electromagnetic field in first order in electromagnetic strength is obtained. Causality of massive spin-2 and spin-3 fields propagation in the corresponding electromagnetic background is proved.     

Evidence for monopoles in the quantizedSU(2) lattice vacuum: A study at finite temperature

InSU(2) gauge theory colour confinement occurs if the vacuum condenses into a coherent monopole plasma. To verify this picture, the first question to be answered is whether the vacuum supports monopoles at all. Since we expect the monopoles to be dilute and massive in the deconfinement, phase, we begin the search there. The method relies on cooling equilibrium lattice gauge field configurations—which are generated at the appropriate temperature—until the underlying semiclassical solutions emerge. We then pass to the confinement region and ask whether the monopoles condense. Finally, we repeat the procedure for gauge groupSU(3). The results confirm our expectations.     

Heavy fermions in gauge theories: (I). Analysis of a general spinor loop

A general one-loop spinor diagram is analyzed in the coordinate space with an arbitrary number of external scalar, pseudoscalar, vector and axial vector legs. We identify chiral anomalies, and an unambiguous definition of a renormalized spinor loop amplitude in gauge theories is given by studying its symmetry properties. We then study the case when some of fermions carry very large masses compared to external momentum scales. Using a new calculational technique based on Schwinger's proper-time method, we provide the explicit forms of dominant effective local vertices induced by virtual heavy fermions in general spontaneously broken gauge theories. In the sequel to the present paper, these results will be applied to various interesting field theory models.     

Absorption of dilaton partial waves by D3-branes

We calculate the leading term in the low-energy absorption cross section for an arbitrary partial wave of the dilaton field by a stack of many coincident D3-branes. We find that it precisely reproduces the semiclassical absorption cross section of a 3-brane geometry, including all numerical factors. The crucial ingredient in making the correspondence is the identification of the precise operators on the D3-brane world-volume which couple to the dilaton field and all its derivatives. The needed operators are related through T-duality and the IIA/M-theory correspondence to the recently determined M(atrix) theory expressions for multiple moments of the 11D supercurrent. These operators have a characteristic symmetrized trace structure which plays a key combinatorial role in the analysis for the higher partial waves. The results presented here give new evidence for an infinite family of non-renormalization theorems which are believed to exist for two-point functions in N=4 gauge theory in four dimensions.     

Quantenphysikalischer Ursprung der Eichidee

The Quantum Physical Origin of the Gauge Idea To consider quantum physics as an interplay of creation and annihilation processes has the consequence that gauge field theories are not only possible but necessary. Since the complex conjugate phase factors of each pair of fermion creators and annihilators can be arbitrary chosen, quantum field theories must be completely phase invariant. Unfortunately, even globally the Dirac equation for systems of free fermions is not phase invariant. The Dirac matrices are namely transformed, if we multiply the spinor components by different constant phase factors. The Dirac equations before and after the transformation are however physically equivalent. We may therefore say: Systems of free fermions will be completely described, only if we consider the class of all equivalent Dirac equations. Since Dirac's commutation relations are unitarily invariant, the class equivalent Dirac equations is invariant under all transformations of the group U 4. Unitary diagonal matrices yield arbitrary phase transformations. Hence, gauge fields of the group U 4 are compatible with the postulate of general phase invariance. These gauge file are so similar to the QED that we may speak of an “extended quantum electrodynamics”, EQE. Here, we will show that EQE exists. The invariant subgroup U 1 U 4 yields QED. The complementary subgroup SU 4 includes four subgroups SU 3, there subgroups O 4, and six subgroups SU 2. The latter ones may yield three pairs of quarks and three pairs of leptons, where the quarks form a group SU 3. More than two times three pairs of elementary fermions does not exist in in EQE Probably, EQE is different from the United EQD and QCD. However, it should be a promising version of a field theory in elementary particle physics, because it follows from an existing symmetry of the empirically wel founded Dirac theory. EQE is therefore free from hypothesis in the Newtonian sense of the word. Whatever it will finally mean, it cannot be rejected, since phase invariance must be required. The invention of new symmetries and the acception of a bie number of independent spinor components is dispensable or must be postponed at least.     

Torsional Weyl-Dirac Electrodynamics

Issuing from a geometry with nonmetricity and torsion we build up a generalized classical electrodynamics. This geometrically founded theory is coordinate covariant, as well as gauge covariant in the Weyl sense. Photons having arbitrary mass, intrinsic magnetic currents, (magnetic monopoles), and electric currents exist in this framework. The field equations, and the equations of motion of charged (either electrically or magnetically) particles are derived from an action principle. It is shown that the interaction between magnetic monopoles is transmitted by massive photons. On the other hand, the photon is massive only in the presence of magnetic currents. We obtained a static spherically symmetric solution, describing either the Reissner-Nordstrom metric of an electric monopole, or the metric and field of a magnetic monopole. The latter must be massive. In the absence of torsion and in the Einstein gauge one obtains the Einstein-Maxwell theory.     

Radial and Regge excitations in unified,grand unified and subconstituent models

Necessary group theoretic conditions for all elementary gauge bosons and fermions of an arbitrary renormalizable gauge theory to lie on Regge trajectories are reviewed. It is then argued that in properly unified gauge theories all particles of a given spin lie on Regge trajectories. This then implied that a properly unified gauge theory has no local U(1) factor groups, and no massive fermion singlets. A consideration of the general pattern of Regge and radial recurrences to be expected in quantum field theories suggests that the presence or absence of spin $\text{3}\text{2}$ quarks and/or leptons in the TeV region will provide crucial clues to enable one to distinguish between various classes of unified, grand unified, and subconstituent models. The correct interpretation of such excited fermions will require correlation with the Higgs boson mass and possible radial and Regge excitations of the weak vector bosons.     

Inconsistency of QED in the presence of Dirac monopoles

A precise formulation ofU (1) local gauge invariance in QED is presented, which clearly shows that the gauge coupling associated with the unphysical longitudinal photon field is non-observable and actually has an arbitrary value. We then re-examine the Dirac quantization condition and find that its derivation involves solely the unphysical longitudinal coupling. Hence an inconsistency inevitably arises in the presence of Dirac monopoles and this can be considered as a theoretical evidence against their existence. An alternative, independent proof of this conclusion is also presented.     

Exact magnetic monopole solutions in Yang-Mills and unified gauge theories

We study the magnetic monopoles in non-Abelian gauge theories. The exact static, spherically symmetric solutions of the magnetic monopoles in both Yang-Mills and unified gauge theories are obtained. The energyE of the static system is calculable and it is either zero or infinite. The existence of the magnetic monopole solution is a consequence of symmetry rather than dynamics. We propose a new definition of the electromagnetic field tensor, which relates the static solution of gauge fields and the magnetic monopole solution. Experimental implications are discussed.     

Vectorial versus axial Goldstone bosons

The Yukawa interactions of fermions with Goldstone bosons are given in closed form for an arbitrary renormalizable field theory to all orders of perturbation theory or for a general effective Lagrangian. Although the diagonal couplings are always pseudoscalar there is an important difference between spontaneously broken vector and axial-vector global symmetries. Compared to the axial case, the diagonal couplings of “vectorial” Goldstone bosons to charged fermions are suppressed by mixing angles or appear only via radiative corrections involving gauge fields. This general result may be relevant for the problem of flavour symmetry breaking in composite models.     

Z 2 monopoles in the standardSU (2) lattice gauge theory model

The standardSU(2) lattice gauge theory model without fermions may be considered as aZ ₂ model with monopoles and fluctuating coupling constants. At low temperatures β^?1 (=small bare coupling constant) the monopoles are confined.     

Gauge group breaking by Wilson loops

We examine the breaking of gauge symmetries by Wilson loops in the Hosotani-Toms model by determining the background gauge field which minimises the one-loop effective potential for massless Dirac fermions. For anti-periodic fermions, all gauge groups remain unbroken. For periodic fermions, the groups G₂, F₄ and E₈ are broken by quantum corrections due to fermions in any irreducible representation, whereas E₆, E₇ and the classical groups only break if the fermion representation is in the same congruency class as the adjoint.     

On the structure of generalized monopole solutions in gauge theories

A method is presented for constructing generalized 't Hooft monopole solutions in a gauge theory with an arbitrary gauge group. We derive restriction arising from the condition of finite energy. The radial oscillation of the solution is discussed. Using our method we reproduce all the SU(3) solutions known in the literature. Finite energy monopoles possessing magnetic charge in the range g₀?kg₀?(N?1)g₀ are found in SU(N) gauge theories. Different charge quantization conditions are analyzed to understand the structure of our solutions.     

New overlap construction of Weyl fermions on the lattice

In a recent article Hasenfratz and von Allmen have suggested a fixed point action for two flavors of Weyl fermions on the lattice with gauge group SU(2). The block-spin transformation they use maps the chiral and vector symmetries of the underlying vector theory onto two equations of the Ginsparg–Wilson (GW) type. We show that an overlap Dirac operator can be constructed which solves both GW equations simultaneously. We discuss the properties of this overlap operator and its projection onto lattice Weyl fermions which seems to be free of artefacts, in particular the projection operators are independent of the gauge field.