Original Gauge Research Articles

New regulators for quantum field theories with compactified extra dimensions. II. Ultraviolet finiteness and effective field theory implementation

In the previous article, we proposed two new regulators for quantum field theories in spacetimes with compactified extra dimensions. Unlike most other regulators that have been used in the extra-dimension literature, these regulators are specifically designed to respect the original higher-dimensional Lorentz and gauge symmetries that exist prior to compactification, and not merely the four-dimensional symmetries which remain afterward. In this paper, we use these regulators in order to develop a method for extracting ultraviolet-finite results from one-loop calculations. This method also allows us to derive Wilsonian effective field theories for Kaluza-Klein modes at different energy scales. Our method operates by ensuring that divergent corrections to parameters describing the physics of the excited Kaluza-Klein modes are absorbed into the corresponding parameters for zero modes, thereby eliminating the need to introduce independent counterterms for parameters characterizing different Kaluza-Klein modes. Our effective field theories can therefore simplify calculations involving Kaluza-Klein modes, and be compared directly to potential experimental results emerging from collider data.

New regulators for quantum field theories with compactified extra dimensions. I. Fundamentals

In this paper, we propose two new regulators for quantum field theories in spacetimes with compactified extra dimensions. We refer to these regulators as the 'extended hard cutoff' and 'extended dimensional regularization'. Although based on traditional four-dimensional regulators, the key new feature of these higher-dimensional regulators is that they are specifically designed to handle mixed spacetimes in which some dimensions are infinitely large and others are compactified. Moreover, unlike most other regulators which have been used in the extra-dimension literature, these regulators are designed to respect the original higher-dimensional Lorentz and gauge symmetries that exist prior to compactification, and not merely the four-dimensional symmetries which remain afterward. This distinction is particularly relevant for calculations of the physics of the excited Kaluza-Klein modes themselves, and not merely their radiative effects on zero modes. By respecting the full higher-dimensional symmetries, our regulators avoid the introduction of spurious terms which would not have been easy to disentangle from the physical effects of compactification. As part of our work, we also derive a number of ancillary results. For example, we demonstrate that in a gauge-invariant theory, analogues of the Ward-Takahashi identity hold not only for the usual zero-mode (four-dimensional) photons, but for all excitedmore » Kaluza-Klein photons as well.« less

P-Adic analysis and the transfinite E8 exceptional Lie symmetry group unification

In P-Adic analysis like in a fractal Cantorian space there is no absolute scale. P-Adic analysis with its prime numbers base is the mathematical quarks of the exceptional E8 and E-infinity. The P-Adic space permits the use of Weyl original spacetime gauge theory which is the rationale behind E-infinity.

Residual stresses in aluminum castings

Abstract The majority of manufacturing processes induce residual stresses in the surface of the component produced. These residual stresses can be either beneficial or in some cases detrimental to the performance of the component in question. This investigation involves the use of a previously described new low-cost method to determine the superficial residual stresses in a casting of A356 aluminum alloy. The technique concerned involves the measurement of the change in spacing of previously applied pairs of micro-hardness indentations which occurs upon stress relief. In the case of a compressive residual stress, this spacing will increase after stress relief. In estimating the strain concerned it should be noted that the equivalent ‘original gage length’ will be the relaxed spacing measurement. This strain multiplied by the modulus of elasticity will indicate the corresponding stress for a uniaxial stress state. The special 3 bar test frames that were employed had their residual stresses measured using both a cutting and a thermal stress relief technique. From the results it can be seen that the use of cutting is probably applicable to the more localized stresses that occur in the vicinity of the cutting zone. However, the stresses that remain in the frame redistribute themselves to maintain equilibrium, and are not measurable until the cut frame is stress relieved thermally. It was noted that the levels of strain measured were unusually high. This may be related to the occasional spontaneous failure of the castings on removal from their molds. The current paper describes the results of on-going research in this area.

A vibrational circular dichroism implementation within a Slater-type-orbital based density functional framework and its application to hexa- and hepta-helicenes

We describe the implementation of the rotational strengths for vibrational circular dichroism (VCD) in the Slater-type orbital based Amsterdam Density Functional (ADF) package. We show that our implementation, which makes use of analytical derivative techniques and London atomic orbitals, yields origin independent rotational strengths. The basis set dependence in the particular case of Slater-type basis functions is also discussed. It turns out that the triple zeta STO basis sets with one set of polarization functions (TZP) are adequate for VCD calculations. The origin- dependence of the atomic axial tensors is checked by a distributed origin gauge implementation. The distributed and common origin gauge implementations yield virtually identical atomic axial tensors with the Slater-type basis sets employed here, proving that our implementation yields origin independent rotational strengths. We verify the implementation for a set of benchmark molecules, for which the dependence of the VCD spectra on the particular choice of the exchange–correlation functional is studied. The pure functionals BP86 and OLYP show a particularly good performance. Then, we apply this approach to study the VCD spectra of hexa- and hepta- helicenes. In particular we focus on relationships between the sign of the rotational strengths of the two helicenes.

Gapless bosonic excitation without symmetry breaking: An algebraic spin liquid with soft gravitons

A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the graviton, although they have a soft $\omega\sim k^2$ dispersion relation. There are three branches of gapless excitations in this phase, one of which is gapless scalar trace mode, the other two have the same polarization and gauge symmetries as the gravitons. The dynamics of this novel phase is described by a new set of Maxwell's equations. The defects carrying gauge charges can drive the system into the superfluid order when the defects are condensed; also the topological defects are coupled to the dual gauge field in the same manner as the charge defects couple to the original gauge field, after the condensation of the topological defects, the system is driven into the Mott Insulator phase. In the 2 dimensional case, the gapless soft graviton as well as the algebraic liquid phase are destroyed by the vertex operators in the dual theory, and the stripe order is most likely to take place close to the 2 dimensional quantum critical point at which the vertex operators are tuned to zero.

Analysis of the Influence of the Specimen Shape on the Zone of Homogeneous Stress in Tensile Test

Abstract Results of the analysis of the influence of the specimen shape and grip-end length on the homogeneous strain in original gauge length are presented in the paper. All the results were obtained for the 316L austenitic stainless steel and for different cross-sections of the sheet specimens. The calculations were performed using program Abaqus/Explicit based on the finite element model (FEM) for the deformation process. Correlation between the strain distribution in the sample and such parameters as transition radius and grip-end length is presented in the paper.

On SUSY standard-like models from orbifolds ofD= 6 Gepner orientifolds

As a further elaboration of the proposal of Ref. [1] we address the construction of Standard-like models from configurations of stacks of orientifold planes and D-branes on an internal space with the structure ${(Gepner model)^{c=6} \times T^2}/Z_N$. As a first step, the construction of D=6 Type II B orientifolds on Gepner points, in the diagonal invariant case and for both, odd and even, affine levels is discussed. We build up the explicit expressions for B-type boundary states and crosscaps and obtain the amplitudes among them. From such amplitudes we read the corresponding spectra and the tadpole cancellation equations. Further compactification on a T^2 torus, by simultaneously orbifolding the Gepner and the torus internal sectors, is performed. The embedding of the orbifold action in the brane sector breaks the original gauge groups and leads to N=1 supersymmetric chiral spectra. Whenever even orbifold action on the torus is considered, new branes, with worldvolume transverse to torus coordinates, must be included. The detailed rules for obtaining the D=4 model spectra and tadpole equations are shown. As an illustration we present a 3 generations Left-Right symmetric model that can be further broken to a MSSM model.

Formula omitted] symmetry and dual gauge algebra of M-theory on a twisted seven-torus

We consider M-theory compactified on a twisted 7-torus with fluxes when all the seven antisymmetric tensor fields in four dimensions have been dualized into scalars and thus the E 7 ( 7 ) symmetry is recovered. We find that the Scherk–Schwarz and flux gaugings define a “dual” gauge algebra, subalgbra of E 7 ( 7 ) , where some of the generators are associated with vector fields which are dual to part of the original vector fields (deriving from the 3-form). In particular they are dual to those vector fields which have been “eaten” by the antisymmetric tensors in the original theory by the (anti-)Higgs mechanism. The dual gauge algebra coincides with the original gauge structure when the quotient with respect to these dual (broken) gauge generators is taken. The particular example of the S–S twist corresponding to a “flat group” is considered.

A simulation method for the calculation of chemical potentials in small, inhomogeneous, and dense systems

We present a modification of the gauge cell Monte Carlo simulation method [A. V. Neimark and A. Vishnyakov, Phys. Rev. E 62, 4611 (2000)] designed for chemical potential calculations in small confined inhomogeneous systems. To measure the chemical potential, the system under study is set in chemical equilibrium with the gauge cell, which represents a finite volume reservoir of ideal particles. The system and the gauge cell are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of density fluctuations in the system. The chemical potential is rigorously calculated from the equilibrium distribution of particles between the system cell and the gauge cell and does not depend on the gauge cell size. This scheme, which we call a mesoscopic canonical ensemble, bridges the gap between the canonical and the grand canonical ensembles, which are known to be inconsistent for small systems. The ideal gas gauge cell method is illustrated with Monte Carlo simulations of Lennard-Jones fluid confined to spherical pores of different sizes. Special attention is paid to the case of extreme confinement of several molecular diameters in cross section where the inconsistency between the canonical ensemble and the grand canonical ensemble is most pronounced. For sufficiently large systems, the chemical potential can be reliably determined from the mean density in the gauge cell as it was implied in the original gauge cell method. The method is applied to study the transition from supercritical adsorption to subcritical capillary condensation, which is observed in nanoporous materials as the pore size increases.

Supersymmetric large- N reduced model with multiple matter

We showed in [ hep-th/0303210] that the Dijkgraaf–Vafa theory can be regarded as large- N reduction in the case of N=1 supersymmetric U( N) gauge theories, with single adjoint matter. We generalize this to gauge theories with gauge groups being the products of some unitary groups coupled to bifundamental or fundamental matter. We show that some large- N reduced models of these theories are supermatrix models, whose free energy is equivalent to the prepotentials of the original gauge theories. The supermatrix model in our approach should be taken in the Veneziano limit N c , N f →∞ with N f / N c fixed.

EFFECTIVE 't HOOFT–POLYAKOV MONOPOLES FROM PURE SU(3) GAUGE THEORY

The well-known topological monopoles originally investigated by 't Hooft and Polyakov are known to arise in classical Yang–Mills–Higgs theory. With a pure gauge theory, it is known that the classical Yang–Mills field equation do not have such finite energy configurations. Here we argue that such configurations may arise in a semi-quantized Yang–Mills theory, where the original gauge group, SU(3), is reduced to a smaller gauge group, SU(2), and with some combination of the coset fields of the SU(3) to SU(2) reduction acting as effective scalar fields. The procedure is called semi-quantized since some of the original gauge fields are treated as quantum degrees of freedom, while others are postulated to be effectively described as classical degrees of freedom. Some speculation is offer on a possible connection between these monopole configurations and the confinement problem, and the nucleon spin puzzle.

Group-theoretical aspects of orbifold and conifold GUTs

Motivated by the simplicity and direct phenomenological applicability of field-theoretic orbifold constructions in the context of grand unification, we set out to survey the immensely rich group-theoretical possibilities open to this type of model building. In particular, we show how every maximal-rank, regular subgroup of a simple Lie group can be obtained by orbifolding and determine under which conditions rank reduction is possible. We investigate how standard model matter can arise from the higher-dimensional SUSY gauge multiplet. New model building options arise if, giving up the global orbifold construction, generic conical singularities and generic gauge twists associated with these singularities are considered. Viewed from the purely field-theoretic perspective, such models, which one might call conifold GUTs, require only a very mild relaxation of the constraints of orbifold model building. Our most interesting concrete examples include the breaking of E 7 to SU(5) and of E 8 to SU(4)×SU(2)×SU(2) (with extra factor groups), where three generations of standard model matter come from the gauge sector and the families are interrelated either by SU(3) R-symmetry or by an SU(3) flavour subgroup of the original gauge group.

Dijkgraaf–Vafa theory as large- N reduction

We construct a large- N twisted reduced model of the four-dimensional super-Yang–Mills theory coupled to one adjoint matter. We first consider a non-commutative version of the four-dimensional superspace, and then give the mapping rule between matrices and functions on this space explicitly. The supersymmetry is realized as a part of the internal U(∞) gauge symmetry in this reduced model. Our reduced model can be compared with the Dijkgraaf–Vafa theory that claims the low-energy glueball superpotential of the original gauge theory is governed by a simple one-matrix model. We show that their claim can be regarded as the large- N reduction in the sense that the one-matrix model they proposed can be identified with our reduced model. The map between matrices and functions enables us to make direct identities between the free energies and correlators of the gauge theory and the matrix model. As a by-product, we can give a natural explanation for the unconventional treatment of the one-matrix model in the Dijkgraaf–Vafa theory where eigenvalues lie around the top of the potential.

Calculation of NMR chemical shifts for taxol and α‐pinene within the generalized gradient approximation

AbstractSimulations of the nuclear magnetic shielding within the generalized gradient approximation (GGA) for α‐pinene and taxol were carried out to assess the performance of the method for bigger molecules. The localized orbital/local origin gauge (LORG) formalism and the modified “0.05” Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) proposed recently by Wilson and others was used. A modest dependence of the results on the basis set size was observed. For the current implementation, the uncoupled calculations were up to 47 times faster than the usual coupled‐perturbed (CP)–gauge‐invariant atomic orbital (GIAO) method and provided similar accuracy. Reproducing both the absolute as the relative chemical shifts the GGA/LORG procedure can thus be used as a faster alternative to the coupled techniques. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Longitudinal gluons and Nambu-Goldstone bosons in a two-flavor color superconductor

In a two-flavor color superconductor, the SU(3)_c gauge symmetry is spontaneously broken by diquark condensation. The Nambu-Goldstone excitations of the diquark condensate mix with the gluons associated with the broken generators of the original gauge group. It is shown how one can decouple these modes with a particular choice of 't Hooft gauge. We then explicitly compute the spectral density for transverse and longitudinal gluons of adjoint color 8. The Nambu-Goldstone excitations give rise to a singularity in the real part of the longitudinal gluon self-energy. This leads to a vanishing gluon spectral density for energies and momenta located on the dispersion branch of the Nambu-Goldstone excitations.

Orientiworld

We propose a consistent string theory framework for embedding brane world scenarios with infinite-volume extra dimensions. In this framework the Standard Model fields are localized on D3-branes sitting on top of an orientifold 3-plane. The transverse 6-dimensional space is a non-compact orbifold or a more general conifold. The 4-dimensional gravity on D3-branes is reproduced due to the 4-dimensional Einstein-Hilbert term induced at the quantum level. The orientifold 3-plane plays a crucial role, in particular, without it the D3-brane world-volume theories would be conformal due to the tadpole cancellation. We point out that in some cases the 4-dimensional Planck scale is controlled by the size of certain relevant (as opposed to marginal) orbifold blow-ups. We can then have a scenario with the desirable 4-dimensional Planck scale, the string scale of order TeV, and the cross-over to 10-dimensional gravity around the present Hubble size. We discuss some general features as well as concrete models in this ``Orientiworld'' framework, including those with D7-branes. We point out that the D7-brane gauge symmetry at the quantum level becomes part of the 4-dimensional gauge symmetry. We present an N=1 supersymmetric model with 3 chiral generations of quarks and leptons, where the original gauge group (which contains an SU(6) subgroup) can be Higgsed to obtain a Pati-Salam model with 3 chiral generations, the Pati-Salam Higgs fields required to break the gauge group further to that of the Standard Model, as well as the desired electroweak Higgs doublets. The superpotential in this model is such that we have precisely one heavy (top-like) generation.

Renormalizable Abelian-Projected Effective Gauge Theory Derived from Quantum Chromodynamics

We show that an effective Abelian gauge theory can be obtained as a renormalizable theory from QCD in the maximal Abelian gauge. The derivation improves in a systematic manner the previous version that was obtained by one of the authors and was referred to as the Abelian-projected effective gauge theory. This result supports the view that we can construct an effective Abelian gauge theory from QCD without losing characteristic features of the original non-Abelian gauge theory. In fact, it is shown that the effective coupling constant in the resulting renormalizable theory has a renormalization-scale dependence governed by the $\beta$-function that is exactly the same as that of the original Yang-Mills theory, irrespective of the choice of gauge fixing parameters of the maximal Abelian gauge and the parameters used for identifying the dual variables. Moreover, we evaluate the anomalous dimensions of the fields and parameters in the resultant theory. By choosing the renormalized parameters appropriately, we can switch the theory into an electric or a magnetic theory.

Computations of the Raman optical activity via the sum‐over‐states expansions

A computationally convenient and reasonably accurate scheme of computation of the Raman Optical Activity (ROA) is presented and tested on model examples. Electromagnetic tensors were obtained using the sum-over-states (SOS) methodology, while their nuclear derivatives were estimated through numerical differentiation. An origin dependence of the results was overcome by a distributed origin gauge transformation. Becke-3LYP functional and corresponding Kohn–Sham orbitals are used for the excited states. The method was compared to a benchmark coupled-perturbed (CP) calculation on formamide and a standard ROA spectral simulation and experiment for α-pinene. Spectra of four standard peptide conformations (α-helix, 310-helix, coil, and β-sheet) were simulated with smaller fragments and compared to previous experimental observations. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 426–435, 2001

YANG–MILLS DUALITY AND THE GENERATION PUZZLE

The fermion generation puzzle has survived into this century as one of the great mysteries in particle physics. We consider here a possible solution within the Standard Model framework based on a non-Abelian generalization of electric–magnetic duality. First, by constructing in loop space a non-Abelian generalization of the Abelian dual transform (Hodge *), one finds that a "magnetic" symmetry exists also in classical Yang–Mills theory dual to the original ("electric") gauge symmetry. Secondly, from a result of 't Hooft's, one obtains that for confined color SU(3), the dual symmetry [Formula: see text] is spontaneously broken and can play the role of the "horizontal symmetry" for generations. Thirdly, such an identification not only offers an explanation why there should be three and apparently only three generations of fermions with the remarkable mass and mixing patterns seen in experiment, but allows even a calculation of the relevant parameters giving very sensible results. Other testible predictions follow ranging from rare hadron decays to cosmic ray air showers.