João P. Nunes

Evaluation of glueball masses from supergravity

In the framework of the conjectured duality relation between large {ital N} gauge theory and supergravity the spectra of masses in large {ital N} gauge theory can be determined by solving certain eigenvalue problems in supergravity. In this paper we study the eigenmass problem given by Witten as a possible approximation for masses in QCD without supersymmetry. We place a particular emphasis on the treatment of the horizon and related boundary conditions. We construct exact expressions for the analytic expansions of the wave functions both at the horizon and at infinity and show that requiring smoothness at the horizon and normalizability gives a well defined eigenvalue problem. We show, for example, that there are no smooth solutions with a vanishing derivative at the horizon. The mass eigenvalues up to m{sup 2}=1000 corresponding to smooth normalizable wave functions are presented. We comment on the relation of our work with the results found in a recent paper by C. Cs{acute a}ki {ital et al.}, hep-th/9806021, which addresses the same problem. {copyright} {ital 1998} {ital The American Physical Society}

The superior effect of nature based solutions in land management for enhancing ecosystem services

The rehabilitation and restoration of land is a key strategy to recover services -goods and resources- ecosystems offer to the humankind. This paper reviews key examples to understand the superior effect of nature based solutions to enhance the sustainability of catchment systems by promoting desirable soil and landscape functions. The use of concepts such as connectivity and the theory of system thinking framework allowed to review coastal and river management as a guide to evaluate other strategies to achieve sustainability. In land management NBSs are not mainstream management. Through a set of case studies: organic farming in Spain; rewilding in Slovenia; land restoration in Iceland, sediment trapping in Ethiopia and wetland construction in Sweden, we show the potential of Nature based solutions (NBSs) as a cost-effective long term solution for hydrological risks and land degradation. NBSs can be divided into two main groups of strategies: soil solutions and landscape solutions. Soil solutions aim to enhance the soil health and soil functions through which local eco-system services will be maintained or restored. Landscape solutions mainly focus on the concept of connectivity. Making the landscape less connected, facilitating less rainfall to be transformed into runoff and therefore reducing flood risk, increasing soil moisture and reducing droughts and soil erosion we can achieve the sustainability. The enhanced eco-system services directly feed into the realization of the Sustainable Development Goals of the United Nations.

Synthesis of Chiral Cyclopentenones

The cyclopentenone unit is a very powerful synthon for the synthesis of a variety of bioactive target molecules. This is due to the broad diversity of chemical modifications available for the enone structural motif. In particular, chiral cyclopentenones are important precursors in the asymmetric synthesis of target chiral molecules. This Review provides an overview of reported methods for enantioselective and asymmetric syntheses of cyclopentenones, including chemical and enzymatic resolution, asymmetric synthesis via Pauson-Khand reaction, Nazarov cyclization and organocatalyzed reactions, asymmetric functionalization of the existing cyclopentenone unit, and functionalization of chiral building blocks.

Coherent state transforms and vector bundles on elliptic curves

Abstract We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k , rank n and genus one non-abelian theta functions with the unitarity of the CST transform being preserved. Furthermore, the shift in the level k → k + n appears in a natural way in this finite-dimensional framework.

A NEW DERIVATION OF THE PICARD-FUCHS EQUATIONS FOR EFFECTIVE N = 2 SUPER YANG-MILLS THEORIES

Abstract A new method to obtain the Picard-Fuchs equations of effective, N = 2 supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding N = 2 theory.

A NOTE ON THE PICARD–FUCHS EQUATIONS FOR N=2 SEIBERG–WITTEN THEORIES

A concise presentation of the PF equations for N= 2 Seiberg–Witten theories for the classical groups of rank r with Nf massless hypermultiplets in the fundamental representation is provided. For Nf=0 all r PF equations can be given in a generic form. For certain cases with Nf≠0, not all equations are generic. However, in all cases there are at least r-2 generic PF equations. For these cases the classical part of the equations is generic, while the quantum part can be formulated using a method described in a previous paper by the authors, which is well suited to symbolic computer calculations.

BF THEORIES AND GROUP-LEVEL DUALITY

It is known that the partition function and correlators of the two-dimensional topological field theory GK(N)/GK(N) on the Riemann surface Σg,s is given by Verlinde numbers, dim Vg,s,K, and that the large K limit of dim Vg,s,K gives Volμs, the volume of the moduli space of flat connections of gauge group G(N) on Σg,s, up to a power of K. Given this relationship, we complete the computation of VolμMs using only algebraic results from conformal field theory. The group-level duality of GK(N) is used to show that if G(N) is a classical group, then limN→∞GK(N)/GK(N) is a BF theory with gauge group G(K). Therefore this limit computes Volμs, the volume of the moduli space of flat connections of gauge group G(K).

On the Picard-Fuchs equations for massive N=2 Seiberg-Witten theories

Abstract A new method to obtain the Picard-Fuchs equations of effective, N = 2 supersymmetric gauge theories with massive matter hypermultiplets in the fundamental representation is presented. It generalises a previously described method to derive the Picard-Fuchs equations of both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. The techniques developed are well suited to symbolic computer calculations.

Field Strength Correlators for Two-Dimensional Yang–Mills Theories Over Riemann Surfaces

The path integral computation of field strength correlation functions for two-dimensional Yang–Mills theories over Riemann surfaces is studied. The calculation is carried out by Abelianization, which leads to correlators that are topological. They are nontrivial as a result of the topological obstructions to the Abelianization. It is shown in the large N limit on the sphere that the correlators undergo second order phase transitions at the critical point. Our results are applied to a computation of contractible Wilson loops.

Extending coherent state transforms to Clifford analysis

We introduce two extensions of the Segal-Bargmann coherent state transform from