Presence Of Flux Research Articles

Lectures on gauged supergravity and flux compactifications**Given at the RTN Winter School on Strings, Supergravity and Gauge Theories, CERN, January 2008.

The low-energy effective theories describing string compactifications in the presence of fluxes are the so-called gauged supergravities: deformations of the standard Abelian supergravity theories. The deformation parameters can be identified with the various possible (geometric and non-geometric) flux components. In these lecture notes we review the construction of gauged supergravities in a manifestly duality covariant way and illustrate the construction in several examples.

Quasi-wavelet formulations of turbulence and other random fields with correlated properties

Quasi-wavelets (QWs) are similar to customary wavelets in that they are based on translations and dilations of a parent function; however, their positions and orientations are random. QWs are convenient for representing random fields with a self-similar structure. In this paper, a general, multi-dimensional treatment of QW fields is presented that includes scale-dependence in the number density and amplitude of the QWs. Previous QW formulations are extended to include anisotropy and correlations among several properties of the random fields. These extensions would be difficult (if not impossible) to achieve systematically by Fourier methods. As an example application, it is shown how QW models can be constructed to produce constant turbulent flux layers. Heat flux in buoyantly driven turbulence is modeled as a collection of QWs with predominantly horizontal rotation coupled with dipole scalar perturbations. Predictions for spectra in the presence of fluxes are obtained.

Pegmatite genesis: state of the art

No one universally accepted model of pegmatite genesis has yet emerged that satisfactorily explains all the diverse features of granitic pegmatites. Genesis from residual melts derived from the crystallization of granitic plutons is favoured by most researchers. Incompatible components, fluxes, volatiles and rare elements, are enriched in the residual melts. The presence of fluxes and volatiles, which lower the crystallization temperature, decrease nucleation rates, melt polymerization and viscosity, and increase diffusion rates and solubility, are considered to be critical to the development of large crystals. A number of new concepts have shed light on problems related to pegmatite genesis. Cooling rates calculated from thermal cooling models demonstrate that shallow-level pegmatites cool radically more rapidly than previously believed. Rapid cooling rates for pegmatites represent a quantum shift from the widely held view that the large crystals found in pegmatites are the result of very slow rates of cooling and crystal growth. Experimental and field evidence both suggest that undercooling and disequilibrium crystallization dominate pegmatite crystallization. London’s constitutional zone refining model of pegmatite evolution involves disequilibrium crystallization from an undercooled, flux-bearing granitic melt. The melt is not necessarily flux–rich and the model does not require the presence of an aqueous vapor phase. Experimental studies of volatile- and flux-rich melts and fluid inclusion studies suggest that volatile-rich silicate melts may persist to temperatures well below 500 °C and even down to 350 °C. Studies of melt inclusions and fluid inclusions have led some researchers to suggest that the role of immiscible fluids must be considered in any model regarding pegmatite genesis. Fluid saturation is thought to occur early in the crystallization history of pegmatites. Two types of melt inclusions along with primary fluid inclusions have been found coexisting in pegmatite minerals. Advances by Petr Cerný in pegmatite classification are in wide use and the fractionation trends of Nb, Ta and other HFSE and K, Rb, Cs, Li, Ga and Tl are now well understood. How pegmatitic melts are produced, the types of source rocks involved and how melt generation relates to plate tectonic models are challenging areas for future investigations. Also, the roles of regional zoning, anatexis, and chemical quenching in pegmatite genesis are areas for future pegmatite research.

Topological A-type models with flux

We study deformations of the A-model in the presence of fluxes, by which we mean rank-three tensors with antisymmetrized upper/lower indices, using the AKSZ construction. There are two natural deformations of the A-model in the AKSZ language: 1) the Zucchini model, which can be defined on a generalized complex manifold and reduces to the A-model when the generalized complex structure comes from a symplectic structure, and 2) a topological membrane model, which naturally accommodates fluxes, and reduces to the Zucchini model on the boundary of the membrane when the fluxes are turned off. We show that the fluxes are related to deformations of the Courant bracket which generalize the twist by a closed 3-from H, in the sense that satisfying the AKSZ master equation implies precisely the integrability conditions for an almost generalized complex structure with respect to the deformed Courant bracket. In addition, the master equation imposes conditions on the fluxes that generalize dH = 0. The membrane model can be defined on a large class of U(m)- and U(m) × U(m)-structure manifolds relevant for string theory, including geometries inspired by (1, 1) supersymmetric σ-models with additional supersymmetries due to almost complex (but not necessarily complex) structures in the target space. In addition we show that the model can be defined on three particular half-flat manifolds related to the Iwasawa manifold. When only the closed 3-form flux is turned on it is possible to obtain a topological string model, which we do for the case of a Calabi-Yau. We argue that deformations from the standard A-model are due to the choice of gauge fixing fermion, rather than a flux deformation of the AKSZ action. The particularly interesting cases arise when the fermion depends on auxiliary fields, the simplest possibility being due to the (2, 0)+(0, 2) component of a non-trivial b-field. The model is generically no longer evaluated on holomorphic maps and defines new topological invariants. Deformations due to H-flux can be more radical, completely preventing auxiliary fields from being integrated out.

Inflationary constraints on type IIA string theory

We prove that inflation is forbidden in the most well understood class of semi-realistic type IIA string compactifications: Calabi-Yau compactifications with only standard NS-NS 3-form flux, R-R fluxes, D6-branes and O6-planes at large volume and small string coupling. With these ingredients, the first slow-roll parameter satisfies {epsilon} {ge} 27/13 whenever V > 0, ruling out both inflation (including brane/anti-brane inflation) and de Sitter vacua in this limit. Our proof is based on the dependence of the 4-dimensional potential on the volume and dilaton moduli in the presence of fluxes and branes. We also describe broader classes of IIA models which may include cosmologies with inflation and/or de Sitter vacua. The inclusion of extra ingredients, such as NS 5-branes and geometric or non-geometric NS-NS fluxes, evades the assumptions used in deriving the no-go theorem. We focus on NS 5-branes and outline how such ingredients may prove fruitful for cosmology, but we do not provide an explicit model. We contrast the results of our IIA analysis with the rather different situation in IIB.

Fermion zero modes in the presence of fluxes and a non-perturbative superpotential

We study the effect of background fluxes of general Hodge type on the supersymmetry conditions and on the fermionic zero modes on the world-volume of a Euclidean M5/D3-brane in M-theory/type IIB string theory. Using the naive susy variation of the modulino fields to determine the number of zero modes in the presence of a flux of general Hodge type, an inconsistency appears. This inconsistency is resolved by a modification of the supersymmetry variation of the modulinos, which captures the back-reaction of the non-perturbative effects on the background flux and the geometry.

A D-brane landscape on Calabi-Yau manifolds

We explore the dynamics of magnetized nonsupersymmetric D5-brane configurations on Calabi-Yau orientifolds with fluxes. We show that supergravity D-terms capture supersymmetry breaking effects predicted by more abstract Pi-stability considerations. We also examine superpotential interactions in the presence of fluxes, and investigate the vacuum structure of such configurations. Based on the shape of the potential, we argue that metastable nonsupersymmetric vacua can be in principle obtained by tuning the values of fluxes.

Finite Heisenberg groups in quiver gauge theories

We show by direct construction that a large class of quiver gauge theories admits actions of finite Heisenberg groups. We consider various quiver gauge theories that arise as AdS/CFT duals of orbifolds of C 3 , the conifold and its orbifolds and some orbifolds of the cone over Y p , q . Matching the gauge theory analysis with string theory on the corresponding spaces implies that the operators counting wrapped branes do not commute in the presence of flux.

Fluxes, moduli fixing and MSSM‐like vacua in type IIA string theory

AbstractWe review some of the features of Type IIA compactifications in the presence of fluxes. In particular, the case of T6/(Ω (‐1) σ) orientifolds with RR, NS and metric fluxes is considered. This has revealed to possess remarkable properties such as vacua with all the closed string moduli stabilized, null or negative contributions to the RR tadpoles or supersymmetry on the branes enforced by the closed string background. In this way, Type IIA compactifications with non trivial fluxes seem to constitute a new window into the building of semi‐realistic models in String Theory.

Effect of sample perimeter and temperature on Sn–Zn based lead-free solders

This paper presents studies conducted on Sn–40Pb, Sn–9Zn and Sn–8Zn–3Bi lead-free solders for electronic applications. Differential Scanning Calorimeter (DSC) profile and the microstructure of the solders were discussed. The wettability between different copper perimeter and molten solders with the presence of flux at 250 °C was investigated. The withdrawal force divided by the sample perimeter was used to calculate the surface tension of the molten solders. The wetting properties of the solders were tested at different temperatures using two types of fluxes. The surface tension of Sn–40Pb, Sn–9Zn and Sn–8Zn–3Bi solders was 0.357, 0.481 and 0.4523 N/m, respectively, and these values showed good agreement with reported data. The Cu 6Sn 5 IMC phase was formed between Sn–40Pb solder and Cu substrate. The Sn–9Zn solder exhibits Cu 6Sn 5 and γ-Cu 5Zn 8 phases with Cu substrate while Sn–8Zn–3Bi solder forms a mixture of Cu–Sn + Cu–Zn phase as a first layer from the solder and γ-Cu 5Zn 8 phase as a second layer next to the Cu substrate. For Sn–8Zn–3Bi solder the MHS flux improves the wetting force and contact angle at higher temperatures. Increase in sample perimeter has no effect on contact angle but the addition of Bi to the Sn–Zn system reduces the surface tension and contact angle.

An index for the Dirac operator on D3 branes with background fluxes

We study the problem of instanton generated superpotentials in Calabi-Yau orientifold compactifications directly in type IIB string theory. To this end, we derive the Dirac equation on a Euclidean D3 brane in the presence of background fluxes. We propose an index which governs whether the generation of a superpotential in the effective 4d theory by D3 brane instantons is possible. Applying the formalism to various classes of examples, including the K3 x T^2/Z_2 orientifold, in the absence and presence of fluxes, we show that our results are consistent with conclusions attainable via duality from an M-theory analysis.

Counting fermionic zero modes on M5 with fluxes

We study the Dirac equation on an M5 brane wrapped on a divisor in a Calabi--Yau fourfold in the presence of background flux. We reduce the computation of the normal bundle U(1) anomaly to counting the solutions of a finite--dimensional linear system on cohomology. This system depends on the choice of flux. In an example, we find that the presence of flux changes the anomaly and allows instanton corrections to the superpotential which would otherwise be absent.

Gaugino Condensation and Nonperturbative Superpotentials in Flux Compactifications

There are two known sources of nonperturbative superpotentials for K\"ahler moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux: Euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The first class of effects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the fourfold, is relatively well understood. The second class has been less explored. In this paper, we consider the explicit example of F-theory on $K3 \times K3$ with flux. The fluxes lift the D7 brane matter fields, and stabilize stacks of D7 branes at loci of enhanced gauge symmetry. The resulting theories exhibit gaugino condensation, and generate a nonperturbative superpotential for K\"ahler moduli. We describe how the relevant geometries in general contain cycles of arithmetic genus $\chi \geq 1$ (and how $\chi > 1$ divisors can contribute to the superpotential, in the presence of flux). This second class of effects is likely to be important in finding even larger classes of models where the KKLT mechanism of moduli stabilization can be realized. We also address various claims about the situation for IIB models with a single K\"ahler modulus.

Tm 3+ activated lanthanum phosphate: a blue PDP phosphor

Plasma display panels (PDPs) are gaining attention due to their high performance and scalability as a medium for large format TVs. The performance and life of a PDP strongly depends upon the nature of phosphors. Currently, Eu 2+ activated barium magnesium aluminate (BAM) is being used as a blue component. Because of its low life, efforts are being made to explore new blue emitting phosphors. One of the alternatives to BAM is Tm 3+ activated lanthanum phosphate (LPTM) phosphor. LPTM phosphor samples are prepared by a solid-state as well as sol–gel process in presence of flux. The phosphor of the present investigation, having uniform and spherical shape particles in the range of 0.1–2 μm, is appropriate for thin phosphor screens required for PDP applications. It exhibits a narrow band emission in the blue region, peaking at 452 nm and also a number of narrow bands in the UV region when excited by 147 and 173 nm radiation from a xenon gas mixture. Various possible transitions responsible for UV and visible emission from Tm 3+ ion are presented. These phosphors also exhibit good color saturation and better stability when excited with VUV radiation. To achieve higher brightness, they are blended with other UV excited blue emitting phosphors such as BAM. Results related to morphology, excitation, after glow decay, emission and degradation of these phosphors in the powder form as well as in plasma display panels are presented and discussed.

A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states

We propose a general and compact scheme for the computation of the periods and amplitudes of the chiral persistent currents, magnetizations and magnetic susceptibilities in mesoscopic fractional quantum Hall disk samples threaded by Aharonov–Bohm magnetic field. This universal approach uses the effective conformal field theory for the edge states in the quantum Hall effect to derive explicit formulas for the corresponding partition functions in presence of flux. We point out the crucial role of a special invariance condition for the partition function, following from the Bloch–Byers–Yang theorem, which represents the Laughlin spectral flow. As an example we apply this procedure to the Z k parafermion Hall states and show that they have universal non-Fermi liquid behavior without anomalous oscillations. For the analysis of the high-temperature asymptotics of the persistent currents in the parafermion states we derive the modular S-matrices constructed from the S matrices for the u ( 1 ) sector and that for the neutral parafermion sector which is realized as a diagonal affine coset.

Brane worlds in 5D and warped compactifications in IIB

In computing potentials for moduli in, for instance, type IIB string theory in the presence of fluxes and branes a factorisable ansatz for the ten-dimensional metric is usually made. We investigate the validity of this ansatz by examining the cosmology of a brane world in a five-dimensional bulk and find that it contradicts the results obtained by using a factorisable ansatz. We explicitly identify the problem with the latter in the IIB case. These arguments support our previous work on this question.

Non-perturbative RR Potentials in the c=1 Matrix Model

We use the \hat c=1 matrix model to compute the potential energy V(C) for (the zero mode of) the RR scalar in two-dimensional type 0B string theory. The potential is induced by turning on a background RR flux, which in the matrix model corresponds to unequal Fermi levels for the two types of fermions. Perturbatively, this leads to a linear runaway potential, but non-perturbative effects stabilize the potential, and we find the exact expression V(C)=\frac{1}{2\pi}\int da\arccos [\cos(C)/\sqrt{1+e^{-2\pi a}}]. We also compute the finite-temperature partition function of the 0B theory in the presence of flux. The perturbative expansion is T-dual to the analogous result in type 0A theory, but non-perturbative effects (which depend on C) do not respect naive R\to 1/R duality. The model can also be used to study scattering amplitudes in background RR fluxes.

String-density wave and Gossamer superconductivity in high- Tc cuprates

We investigate a string-density wave state in the underdoped region of high- T c cuprates theoretically based on the two-dimensional Hubbard model. There is a tendency towards a formation of stripes in the low-doping region due to the lattice distortion and strong Coulomb interaction. The tilt of CuO octahedra induces transfer integrals between p x, y -orbitals and Cu t 2g-orbitals, which brings about the spin-orbit interaction for the d electrons in the CuO plane. The spin-orbit interaction induces a flux state with time-reversal symmetry breaking; then the striped state with a flux, which is a generalization of d-density wave, is stabilized from the under to lightly doped region. This state shows a pseudogap behavior due to a modification of the electron dispersion relation in the presence of flux. It is shown that the spin-orbit interaction stabilizes the diagonal-striped state in the lightly doped region.

Soft supersymmetry breaking in Calabi–Yau orientifolds with D-branes and fluxes

In this paper we compute the N=1 effective low energy action for a stack of N space–time filling D3-branes in generic type IIB Calabi–Yau orientifolds with non-trivial background fluxes by reducing the Dirac–Born–Infeld and Chern–Simons actions. Specifically, we determine the Kähler potential for the excitations of the D-brane including their couplings to all bulk moduli fields. In the effective theory, N=1 supergravity is spontaneously broken by the presence of fluxes and we compute the induced soft supersymmetry breaking terms. We find an interesting structure in the resulting soft terms with generically universal soft scalar masses.

N = 4 supergravity for type IIB on T6/ℤ2 in presence of fluxes

We report on the construction of four-dimensional gauged supergravity models that can be interpreted as type IIB orientifold compactification in the presence of 3-form fluxes and D3-branes. We mainly address our attention to the symplectic embedding of the U-duality group of the theory and the consequent choice of the gauge group, whose four-dimensional Killing vectors are the remnants of the ten-dimensional fluxes. We briefly discuss the structure of the scalar potential arising from the gauging and the properties of the Killing vectors in order to preserve some amount of supersymmetry.