Two-dimensional gauge theories of the symmetric group S(n) and branched n-coverings of Riemann surfaces in the large-n limit

Branched n-coverings of Riemann surfaces are described by a 2d lattice gauge theory of the symmetric group S(n) defined on a cell discretization of the surface. We study the theory in the large-n limit, and we find a rich phase diagram with first and second order transition lines. The various phases are characterized by different connectivity properties of the covering surface. We point out some interesting connections with the theory of random walks on group manifolds and with random graph theory.Comment: Talk presented at the "Light-cone physics: particles and strings", Trento, Italy, September 200

R-Symmetry and the Topological Twist of N=2 Effective Supergravities of Heterotic Strings

We discuss R-symmetries in locally supersymmetric N=2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R-symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton-axion field has different R-charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang--Mills instantons with triholomorphic hyperinstantons and axion-instantons. For the tree-level classical special manifolds $ST(n)=SU(1,1)/U(1)\times SO(2,n)/(SO(2)$ $\times SO(n))$ R-symmetry with the specified properties is a continuous symmetry, but for the quantum corrected manifolds ${\hat {ST}}(n)$ a discrete R--group of electric--magnetic duality rotations is sufficient and we argue that it exists.Comment: 40 pages, plain LaTeX. Final version to appear on IJMP

Ramond-Ramond (boundary) states

The description of D-branes as boundary states for type II string theories (in the covariant formulation) requires particular care in the R-R sector. Also the vertices for R-R potentials that can couple to D-branes need a careful handling. As an illustration of this, the example of the D0-D8 system is reviewed, where a ``microscopic'' description of the interaction via exchange of R-R potentials becomes possible.Comment: 8 pages, LaTeX, no figures. Talk presented at the 2nd Conference on Quantum aspects of Gauge Theories, Supersymmetry and Unification, Corfu, Greece, 21-26 September 199

Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories

We consider conformal N=2 super Yang-Mills theories with gauge group SU(N) and Nf=2N fundamental hypermultiplets in presence of a circular 1/2-BPS Wilson loop. It is natural to conjecture that the matrix model which describes the expectation value of this system also encodes the one-point functions of chiral scalar operators in presence of the Wilson loop. We obtain evidence of this conjecture by successfully comparing, at finite N and at the two-loop order, the one-point functions computed in field theory with the vacuum expectation values of the corresponding normal-ordered operators in the matrix model. For the part of these expressions with transcendentality zeta(3), we also obtain results in the large-N limit that are exact in the 't Hooft coupling lambda.Comment: 37 pages, 10 figures. v2: typo corrected, 3 references added. Version to appear on JHE

Vector Supersymmetry of 2D Yang-Mills Theory

The vector supersymmetry of the 2D topological BF model is extended to 2D Yang-Mills. The consequences of the corresponding Ward identity on the ultraviolet behavior of the theory are analyzed.Comment: Some references adde

Localization vs holography in 4d4d N=2\mathcal{N}=2 quiver theories

We study 4-dimensional $\mathcal{N}=2$ superconformal quiver gauge theories obtained with an orbifold projection from $\mathcal{N}=4$ SYM, and compute the 2- and 3-point correlation functions among chiral/anti-chiral single-trace scalar operators and the corresponding structure constants. Exploiting localization, we map the computation to an interacting matrix model and obtain expressions for the correlators and the structure constants that are valid for any value of the 't Hooft coupling in the planar limit of the theory. At strong coupling, these expressions simplify and allow us to extract the leading behavior in an analytic way. Finally, using the AdS/CFT correspondence, we compute the structure constants from the dual supergravity theory and obtain results that perfectly match the strong-coupling predictions from localization.Comment: 51 pages, 5 figure

Structure constants in N=2\mathcal{N}=2 superconformal quiver theories at strong coupling and holography

In a four-dimensional $\mathcal{N}=2$ superconformal quiver theory with gauge group $\mathrm{SU}(N)\times\mathrm{SU}(N)$ and bi-fundamental matter, we analytically obtain the exact strong-coupling behavior of the normalized 3-point correlators of single-trace scalar operators in the large-$N$ limit using localization techniques. We then obtain the same strong-coupling behavior from the holographic dual using the AdS/CFT correspondence at the supergravity level. This agreement confirms the validity of the analytic strong-coupling results and of the holographic correspondence in a non-maximally supersymmetric set-up in four dimensions.Comment: 5 pages, 2 figure

HyperK\"ahler quotients and N=4 gauge theories in D=2

We consider certain N=4 supersymmetric gauge theories in D=2 coupled to quaternionic matter multiplets in a minimal way. These theories admit as effective theories sigma-models on non-trivial HyperK\"ahler manifolds obtained as HyperK\"ahler quotients. The example of ALE manifolds is discussed. (Based on a talk given by P. Fr\'e at the F. Gursey Memorial Conference, Istanbul, June 1994).Comment: 22 pages, Latex, no figure

Notes on unoriented D-brane instantons

In the first lecture, we discuss basic aspects of worldsheet and penta-brane instantons as well as (unoriented) D-brane instantons, which is our main focus here, and threshold corrections to BPS-saturated couplings. The second lecture is devoted to non-perturbative superpotentials generated by `gauge' and `exotic' instantons living on D3-branes at orientifold singularities. In the third lecture we discuss the interplay between worldsheet and D-string instantons on $T^4/Z_2$. We focus on a 4-fermi amplitude, give Heterotic and perturbative Type I descriptions, and offer a multi D-string instanton interpretation. We conclude with possible interesting developments.Comment: 31 pages. Based on lectures delivered by M. Bianchi at the Fourth Young Researchers Workshop of the European Superstring Theory Network in Kounnas Bay, Cyprus, September 200

A Nanoporous Silicon Nitride Membrane Using A Two-step Lift-off Pattern Transfer With Thermal Nanoimprint Lithography

Nanoimprint lithography is emerging as a viable contender for fabrication of large-scale arrays of 5500 nm features. A fabrication process for the realization of thin nanoporous membranes using thermal nanoimprint lithography is presented. Suspended silicon nitride membranes were fabricated by low-pressure chemical vapor deposition (LPCVD) in conjunction with a potassium hydroxide-based bulk micromachining process. Nanoscale features were imprinted into a commercially available thermoplastic polymer resist using a prefabricated silicon mold. The pattern was reversed and transferred to a thin aluminum oxide layer by means of a novel two-stage lift-off technique. The patterned aluminum oxide was used as an etch mask in a CHF 3/He-based reactive ion etch process to transfer the pattern to silicon nitride. Highly directional etch profiles with near vertical sidewalls and excellent Si 3N 4/Al 2O 3etch selectivity were observed. One micrometer thick porous membranes with varying dimensions of 250x250 νm 2to 450x450 νm 2and a pore diameter of 400 nm have been engineered and evaluated. Results indicate that the membranes have consistent nanopore dimensions and precisely defined porosity, which makes them ideal as gas exchange interfaces in blood oxygenation systems as well as other applications such as dialysis. © 2012 IOP Publishing Ltd