Rigid SU Research Articles

Effect of different types of shoes on balance among soccer players.

in soccer, balance ability is important to reduce non-contact injuries. The effect of footwear on balance is poorly understood in this sport. Soccer boots and futsal trainers need to guarantee a good grip on compliant surfaces. Running shoes are designed to reduce friction on rigid su rfaces. The purpose of the present study was to investigate these types of shoes on balance ability. twenty-four healthy male volunteers were recruited from amateur soccer teams. They were ask to perform the BESS (Balance Error Scoring System) test to measure the number of instability episodes in 6 conditions: double-leg, single-leg, and tandem stances on firm and foam surfaces. Anova with factor (several shoes) and Bonferroni were used to compare the means of two subtotal scores (firm and foam surface) and the final total score (BESS). the three shoe models led to greater stability than when the subject was barefoot (p=0.001). Only on the firm surface the soccer boots were statistically better than futsal trainers (p=0.009). the lack of stability while barefoot could be explained by the fact that with shoes there is a greater surface area, which produces a sensory filter that leads to posture modifications to improve stability. The greater stability, that was found in the three types of footwear, could be guaranteed by the design to reduce friction (for running shoes) and by the presence of studs (for soccer boots and futsal trainers).

Supersymmetric AdS vacua and separation of scales

Abstract The moduli space of the supersymmetric massive IIA AdS4 × S 2(B4) vacua, where S 2(B4) is a two-sphere bundle over a four-dimensional Kähler-Einstein base B4, includes three independent parameters which can be thought of as corresponding to the sizes of AdS4, B4 and the S 2 fiber. It might therefore be expected that these vacua do not suffer from the absence of scale separation. We show that the independence of the geometric moduli survives flux quantization. However, we uncover an attractor behavior whereby all sizes flow to equality in some neighborhood of spacetime independently of the initial conditions set by the parameters of the solution. This is further confirmed by the study of the ratio of internal to external scalar curvatures. We also show that the asymptotic Kaluza-Klein spectrum of a ten-dimensional massive scalar is governed by a scale of the order of the AdS4 radius. Furthermore we point out that the curvature ratio in supersymmetric IIA AdS4 vacua with rigid SU(3) structure is of order one, indicating the absence of scale separation in this large class of vacua.

Physical renormalization condition for the quark-mixing matrix

We investigate the renormalization of the quark-mixing matrix in the Electroweak Standard Model. The corresponding counterterms are gauge independent as can be shown using an extended BRS symmetry. Using rigid SU(2)L symmetry, we prove that the ultraviolet-divergent parts of the invariant counterterms are related to the field renormalization constants of the quark fields. We point out that for a general class of renormalization schemes rigid SU(2)L symmetry cannot be preserved in its classical form, but is renormalized by finite counterterms. Finally, we discuss a genuine physical renormalization condition for the quark-mixing matrix that is gauge independent and does not destroy the symmetry between quark generations.

New gauged N = 8, D = 4 supergravities

New gaugings of four-dimensional N = 8 supergravity are constructed, including one which has a Minkowski space vacuum that preserves N = 2 supersymmetry and in which the gauge group is broken to SU(3) × U(1)2. Previous gaugings used the form of the ungauged action which is invariant under a rigid symmetry and promoted a 28-dimensional subgroup (SO(8), SO(p, 8 − p) or the non-semi-simple contraction CSO(p, q, 8 − p − q)) to a local gauge group. Here, a dual form of the ungauged action is used which is invariant under SU*(8) instead of and new theories are obtained by gauging 28-dimensional subgroups of SU*(8). The gauge groups are non-semi-simple and are different real forms of the CSO(2p, 8 − 2p) groups, denoted as CSO*(2p, 8 − 2p), and the new theories have a rigid SU(2) symmetry. The five-dimensional gauged N = 8 supergravities are dimensionally reduced to D = 4. The D = 5, SO(p, 6 − p) gauge theories reduce, after a duality transformation, to the D = 4, CSO(p, 6 − p, 2) gauging while the SO*(6) gauge theory reduces to the D = 4, CSO*(6, 2) gauge theory. The new theories are related to the old ones via an analytic continuation. The non-semi-simple gaugings can be dualized to forms with different gauge groups.

Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations

Using the formulation of the immersion of a two-dimensional surface into the three-dimensional Euclidean space proposed recently, a mapping from each symmetry of integrable equations to surfaces in R3 can be established. We show that among these surfaces the sphere plays a unique role. Indeed, under the rigid SU(2) rotations all integrable equations are mapped to a sphere. Furthermore we prove that all compact surfaces generated by the infinitely many generalized symmetries of the sine-Gordon equation are homeomorphic to a sphere. We also find some new Weingarten surfaces arising from the deformations of the modified Kurteweg–de Vries and of the nonlinear Schrödinger equations. Surfaces can also be associated with the motion of curves. We study curve motions on a sphere and we identify a new integrable equation characterizing such a motion for a particular choice of the curve velocity.

A search for non-perturbative dualities of local N = 2 Yang - Mills theories from Calabi - Yau 3-folds

The generalization of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi - Yau 3-fold. Duality symmetries of this manifold are connected with the analogous dualities associated with the dynamical Riemann surface of the rigid theory. N = 2 rigid gauge theories are reviewed in a framework ready for comparison with the local case. As a byproduct we give in general the full duality group (quantum monodromy) for an arbitrary rigid SU(r+1) gauge theory, extending previous explicit constructions for the r = 1,2 cases. In the coupling to gravity, R-symmetry and monodromy groups of the dynamical Riemann surface, whose structure we discuss in detail, are embedded into the symplectic duality group associated with the moduli space of the dynamical Calabi - Yau 3-fold.

Exact monodromy group of N = 2 heterotic superstring

We describe an N = 2 heterotic superstring model of rank 3 which is dual to the type II string compactified on a Calabi-Yau manifold with Betti numbers b 1,1 = 2 and b 1,2 = 86. We show that the exact duality symmetry found from the type II realization contains the perturbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid SU(2) super-Yang-Mills theory. Moreover, it contains a non-perturbative monodromy which is stringy in origin and corresponds roughly to an exchange of the string coupling with the compactification radius.

Harmonic Space and Quaternionic Manifolds

We find a principle of harmonic analyticity underlying the quaternionic (quaternion-Kähler) geometry and solve the differential constraints which define this geometry. To this end the original 4 n-dimensional quaternionic manifold is extended to a bi-harmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group rotating the complex structures. Then the constraints can be rewritten as integrability conditions for the existence of an analytic subspace in the bi-harmonic space and solved in terms of two unconstrained potentials on the analytic subspace. Geometrically, the potentials have the meaning of vielbeins associated with the harmonic coordinates. We also establish a one-to-one correspondence between the quaternionic spaces and off-shell N = 2 supersymmetric sigma-models coupled to N = 2 supergravity. The general N = 2 sigma-model Lagrangian when written in the harmonic superspace is composed of the quaternionic potentials. Coordinates of the analytic subspace are identified with superfields describing N = 2 matter hypermultiplets and a compensating hypermultiplet of N = 2 supergravity. As an illustration we present the potentials for the symmetric quaternionic spaces.

Gauged seven-dimensional supergravity

We construct Yang-Mills theory and simple supergravity in seven dimensions. We gauge the rigid SU(2) symmetry of the latter. The potential for the scalar field φ is of the form exp(φ) and has no extremum. Possible improvement due to a “topological mass term” is discussed.

Extended conformal supergravity

Abstract We present the complete structure of extended conformal supergravity for N ⩽4. The relation with the graded algebra SU(2, 2| N ) and with the multiplet of currents is discussed. The N = 4 superconformal theory has a formulation with local SU(4)×U(1) and rigid SU(1, 1) invariance. We give the linearized invariant actions for all N . For N = 2 we exhibit the complete non-linear lagrangian.