Let's Twist Again: General Metrics of G(2) Holonomy from Gauged Supergravity

We construct all complete metrics of cohomogeneity one G(2) holonomy with S^3 x S^3 principal orbits from gauged supergravity. Our approach rests on a generalization of the twisting procedure used in this framework. It corresponds to a non-trivial embedding of the special Lagrangian three-cycle wrapped by the D6-branes in the lower dimensional supergravity. There are constraints that neatly reduce the general ansatz to a six functions one. Within this approach, the Hitchin system and the flop transformation are nicely realized in eight dimensional gauged supergravity.Comment: 31 pages, latex; v2: minor changes, references adde

Supersymmetric Electroweak Cosmic Strings

We study the connection between $N=2$ supersymmetry and a topological bound in a two-Higgs-doublet system with an $SU(2)\times U(1)_Y\times U(1)_{Y^{\prime}}$ gauge group. We derive the Bogomol'nyi equations from supersymmetry considerations showing that they hold provided certain conditions on the coupling constants, which are a consequence of the huge symmetry of the theory, are satisfied. Their solutions, which can be interpreted as electroweak cosmic strings breaking one half of the supersymmetries of the theory, are studied. Certain interesting limiting cases of our model which have recently been considered in the literature are finally analyzed.Comment: 20 pages, RevTe

Spin Susceptibility of Noncentrosymmetric Heavy-fermion Superconductor CeIrSi3 under Pressure: 29Si-Knight Shift Study on Single Crystal

We report 29Si-NMR study on a single crystal of the heavy-fermion superconductor CeIrSi3 without an inversion symmetry along the c-axis. The 29Si-Knight shift measurements under pressure have revealed that the spin susceptibility for the ab-plane decreases slightly below Tc, whereas along the c-axis it does not change at all. The result can be accounted for by the spin susceptibility in the superconducting state being dominated by the strong antisymmetric (Rashba-type) spin-orbit interaction that originates from the absence of an inversion center along the c-axis and it being much larger than superconducting condensation energy. This is the first observation which exhibits an anisotropy of the spin susceptibility below Tc in the noncentrosymmetric superconductor dominated by strong Rashba-type spin-orbit interaction.Comment: 4 pages, 4 figures, Accepted for publication in Phys. Rev. Let

Self-dual solitons in N=2 supersymmetric semilocal Chern-Simons theory

We embed the semilocal Chern-Simons-Higgs theory into an N=2 supersymmetric system. We construct the corresponding conserved supercharges and derive the Bogomol'nyi equations of the model from supersymmetry considerations. We show that these equations hold provided certain conditions on the coupling constants as well as on the Higgs potential of the system, which are a consequence of the huge symmetry of the theory, are satisfied. They admit string-like solutions which break one half of the supersymmetries --BPS Chern-Simons semilocal cosmic strings-- whose magnetic flux is concentrated at the center of the vortex. We study such solutions and show that their stability is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops.Comment: 12 pages, LaTeX, no figures, to appear in Modern Physics Letters

A classification of second order equations via nonlocal transformations.

Thesis (M.Sc.)-University of Natal, Durban, 2000.The study of second order ordinary differential equations is vital given their proliferation in mechanics. The group theoretic approach devised by Lie is one of the most successful techniques available for solving these equations. However, many second order equations cannot be reduced to quadratures due to the lack of a sufficient number of point symmetries. We observe that increasing the order will result in a third order differential equation which, when reduced via an alternate symmetry, may result in a solvable second order equation. Thus the original second order equation can be solved. In this dissertation we will attempt to classify second order differential equations that can be solved in this manner. We also provide the nonlocal transformations between the original second order equations and the new solvable second order equations. Our starting point is third order differential equations. Here we concentrate on those invariant under two- and three-dimensional Lie algebras

Quantum transport in noncentrosymmetric superconductors and thermodynamics of ferromagnetic superconductors

We consider a general Hamiltonian describing coexistence of itinerant ferromagnetism, spin-orbit coupling and mixed spin-singlet/triplet superconducting pairing in the context of mean-field theory. The Hamiltonian is diagonalized and exact eigenvalues are obtained, thus allowing us to write down the coupled gap equations for the different order parameters. Our results may then be applied to any model describing coexistence of any combination of these three phenomena. As a specific application of our results, we consider tunneling between a normal metal and a noncentrosymmetric superconductor with mixed singlet and triplet gaps. The conductance spectrum reveals information about these gaps in addition to how the influence of spin-orbit coupling is manifested. We also consider the coexistence of itinerant ferromagnetism and triplet superconductivity as a model for recently discovered ferromagnetic superconductors. The coupled gap equations are solved self-consistently, and we study the conditions necessary to obtain the coexistent regime of ferromagnetism and superconductivity. Analytical expressions are presented for the order parameters, and we provide an analysis of the free energy to identify the preferred system state. Moreover, we make specific predictions concerning the heat capacity for a ferromagnetic superconductor. In particular, we report a nonuniversal relative jump in the specific heat, depending on the magnetization of the system, at the uppermost superconducting phase transition. [Shortened abstract due to arXiv submission.]Comment: 19 pages, 15 figures (high quality figures available in published version). Accepted for publication in Phys. Rev.

Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories

We study the electric flux tubes that undertake color confinement in N=2 supersymmetric Yang-Mills theories softly broken down to N=1 by perturbing with the first two Casimir operators. The relevant Abelian Higgs model is not the standard one due to the presence of an off-diagonal coupling among different magnetic U(1) factors. We perform a preliminary study of this model at a qualitative level. BPS vortices are explicitely obtained for particular values of the soft breaking parameters. Generically however, even in the ultrastrong scaling limit, vortices are not critical but live in a "hybrid" type II phase. Also, ratios among string tensions are seen to follow no simple pattern. We examine the situation at the half Higgsed vacua and find evidence for solutions with the behaviour of superconducting strings. In some cases they are solutions to BPS equations.Comment: 15 pages, 1 figure, revtex; v2: typos corrected, final versio

Wrapped branes with fluxes in 8d gauged supergravity

We study the gravity dual of several wrapped D-brane configurations in presence of 4-form RR fluxes partially piercing the unwrapped directions. We present a systematic approach to obtain these solutions from those without fluxes. We use D=8 gauged supergravity as a starting point to build up these solutions. The configurations include (smeared) M2-branes at the tip of a G_2 cone on S^3 x S^3, D2-D6 branes with the latter wrapping a special Lagrangian 3-cycle of the complex deformed conifold and an holomorphic sphere in its cotangent bundle T^*S^2, D3-branes at the tip of the generalized resolved conifold, and others obtained by means of T duality and KK reduction. We elaborate on the corresponding N=1 and N=2 field theories in 2+1 dimensions.Comment: 32 pages, LateX, v2: minor changes, reference added, v3: section 3.5.2 improve

Helical vortex phase in the non-centrosymmetric CePt_3Si

We consider the role of magnetic fields on the broken inversion superconductor CePt_3Si. We show that upper critical field for a field along the c-axis exhibits a much weaker paramagnetic effect than for a field applied perpendicular to the c-axis. The in-plane paramagnetic effect is strongly reduced by the appearance of helical structure in the order parameter. We find that to get good agreement between theory and recent experimental measurements of H_{c2}, this helical structure is required. We propose a Josephson junction experiment that can be used to detect this helical order. In particular, we predict that Josephson current will exhibit a magnetic interference pattern for a magnetic field applied perpendicular to the junction normal. We also discuss unusual magnetic effects associated with the helical order.Comment: 5 pages, 2 figures, Accepted as Phys Rev. Lette