Gauge/string duality in confining theories

This is the content of a set of lectures given at the “XIII Jorge André Swieca Summer School on Particles and Fields”, Campos do Jordão, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non‐Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D–branes at singularities and wrapping D–branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non‐perturbative phenomena in non‐Abelian gauge theories as seen from supergravity.     

Electronic Structures of Highly Symmetrical Compounds of f Elements. 34 [1] Synthesis and Spectroscopic Characterization of Biscyclohexylisocyanide Adducts derived from the Tris(bis(trimethylsilyl)amido)lanthanide(III) Moiety as well as Crystal,Molecular, and Electronic Structure of the Corresponding Neodymium Compound

The reaction of tris(bis(trimethylsilyl)amido)lanthanide(III) (Ln(btmsa)₃) with two equiv. of cyclohexylisocyanide gives good yields of complexes of composition Ln(btmsa)₃(CNC₆H₁₁)₂ (Ln = Y( 1 ), La( 2 ), Ce( 3 ), Pr( 4 ), Nd( 5 ), Sm( 6 ), Eu( 7 ), Tb( 8 ), Dy( 9 ), Ho( 10 ), Tm( 11 ) and Yb( 12 )). Complex 5 crystallizes in the monoclinic space group C2/c with a = 25.689(8) Å, b = 12.165(2) Å, c = 17.895(15) Å, β = 122.47 (2)°, V = 4718.07 ų, Z = 4 and R = 0.0342. The structure of compound 5 shows the five‐coordinate Nd³⁺ ion in a nearly exact trigonal bipyramidal environment with two CNC₆H₁₁ molecules in the axial and the three btmsa ligands in the equatorial positions. The linear dichroism spectrum of a single crystal of complex 5 was measured at room temperature, and the absorption spectrum of powdered material at low temperatures. From the spectra obtained a truncated crystal field (CF) splitting pattern is derived, and simulated by fitting the parameters of a phenomenological Hamiltonian. For 80 assignments a reduced r.m.s. deviation of 20.7 cm^—1 is achieved. Making use of the calculated wavefunctions and eigenvalues the experimentally determined temperature dependence of μ²_eff could be reproduced by adopting an orbital reduction factor k = 0.991, and on the basis of the CF parameters used the experimentally oriented non‐relativistic molecular orbital scheme of compound 5 is set up.     

Lie-algebra expansions, Chern–Simons theories and the Einstein–Hilbert Lagrangian

Starting from gravity as a Chern–Simons action for the AdS algebra in five dimensions, it is possible to modify the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein–Hilbert action plus non-minimally coupled matter. The modified system is gauge invariant under the Poincaré group enlarged by an Abelian ideal. Although the resulting action naively looks like general relativity plus corrections due to matter sources, it is shown that the non-minimal couplings produce a radical departure from GR. Indeed, the dynamics is not continuously connected to the one obtained from Einstein–Hilbert action. In a matter-free configuration and in the torsionless sector, the field equations are too strong a restriction on the geometry as the metric must satisfy both the Einstein and pure Gauss–Bonnet equations. In particular, the five-dimensional Schwarzschild geometry fails to be a solution; however, configurations corresponding to a brane-world with positive cosmological constant on the worldsheet are admissible when one of the matter fields is switched on. These results can be extended to higher odd dimensions.     

Resurgent Transseries and the Holomorphic Anomaly

The gauge theoretic large N expansion yields an asymptotic series which requires a nonperturbative completion to be well defined. Recently, within the context of random matrix models, it was shown how to build resurgent transseries solutions encoding the full nonperturbative information beyond the ’t Hooft genus expansion. On the other hand, via large N duality, random matrix models may be holographically described by B-model closed topological strings in local Calabi–Yau geometries. This raises the question of constructing the corresponding holographically dual resurgent transseries, tantamount to nonperturbative topological string theory. This paper addresses this point by showing how to construct resurgent transseries solutions to the holomorphic anomaly equations. These solutions are built upon (generalized) multi-instanton sectors, where the instanton actions are holomorphic. The asymptotic expansions around the multi-instanton sectors have both holomorphic and anti-holomorphic dependence, may allow for resonance, and their structure is completely fixed by the holomorphic anomaly equations in terms of specific polynomials multiplied by exponential factors and up to the holomorphic ambiguities—which generalizes the known perturbative structure to the full transseries. In particular, the anti-holomorphic dependence has a somewhat universal character. Furthermore, in the non-perturbative sectors, holomorphic ambiguities may be fixed at conifold points. This construction shows the nonperturbative integrability of the holomorphic anomaly equations and sets the ground to start addressing large-order analysis and resurgent nonperturbative completions within closed topological string theory.     

Measuring T₂ and T₁, and imaging T₂ without spin echoes

During adiabatic excitation, the nuclear magnetization in the transverse plane is subject to T(2) (spin-spin) relaxation, depending on the pulse length τ. Here, this property is exploited in a method of measuring T(2) using the ratio of NMR signals acquired with short and long-duration self-refocusing adiabatic pulses, without spin-echoes. This Dual-τ method is implemented with B(1)-insensitive rotation (BIR-4) pulses. It is validated theoretically with Bloch equation simulations independent of flip-angle, and experimentally in phantoms. Dual-τT(2) measurements are most accurate at short T(2) where results agree with standard spin-echo measures to within 10% for T(2) ≤ 100 ms. Dual-τ MRI performed with a long 0° BIR-4 pre-pulse provides quantitative T(2) imaging of phantoms and the human foot while preserving desired contrast and functional properties of the rest of the MRI sequence. A single 0° BIR-4 pre-pulse can provide T(2) contrast-weighted MRI and serve as a "T(2)-prep" sequence with a lower B(1) requirement than prior approaches. Finally, a Tri-τ experiment is introduced in which both τ and flip-angle are varied, enabling measurement of T(2), T(1) and signal intensity in just three acquisitions if flip-angles are well-characterized. These new methods can potentially save time and simplify relaxation measurements and/or contrast-weighted NMR and MRI.     

Near stabilization of the Ce moment upon dilution in (Ce,La)Al3

Susceptibility measurements taken for 1.5 ≤ T ≤ 17 K on the system Ce_xLa_1?xAl₃ indicate that the Ce moment is nearly stabilized on dilution. Evidence for this is the fact that the fractional occupancy of the 4f¹ configuration and the spin correlation time both increase as x → 0. Crystalline electric fields influence the susceptibility of these valence fluctuation systems.     

Organic vapor excitation by electron beam pumping of rare-gas—Organic vapor mixtures

Broad-band fluorescence at 4000 Å has been observed from gas phase mixtures of the dyes POPOP and α-NPO in Xe and Ar. The photon yields have been measured at 3 atm total pressure and are found to reach the following maximum values: α-NPO/Xe: 2%, α-NPO/Ar: 5%, POPOP/Xe: 9%, POPOP/Ar: 20%.