119513982
Super Yang-Mills, matrix models and geometric transitions
Super Yang-Mills, modeles de matrices et transitions geometriques. J'expose deux applications de la relation entre les theories de jauge supersymetriques N = 1 a quatre dimensions, les modeles de matrices jauges a zero dimension, et les transitions geometriques en theorie des cordes. La premiere traite du spectre des parois ou branes BPS. Il est demontre qu'un etat de type D-brane, dont la tension en couplage faible est proportionnelle a N ∼ 1/g s , et un etat de type soliton de corde fermee, dont la tension en couplage faible est proportionnelle a N 2 ∼ 1/g 2 s , peuvent etre continument deformes l'un en l'autre. Ceci est un aspect de la theorie plus generale des espaces quantiques de parametres N = 1. La deuxieme est une nouvelle methode, purement geometrique, pour calculer exactement la somme sur les diagrammes planaires en zero dimension. C'est un exemple de dualite entre cordes ouvertes et cordes fermees.
17019473
Nonperturbative double scaling limits
Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path)-integrals by gauge theory or nonlinear σ model (path)-integrals. We explain how this solves one of the most fundamental limitations of the classic approach: we automatically obtain nonperturbative definitions in non-Borel summable cases. This is exemplified in the simplest possible examples involving O(N) symmetric nonlinear σ models with N-dimensional target spaces, for which we construct (multi)critical metrics. The nonperturbative definitions of the double scaled, manifestly positive, partition functions rely on remarkable identities involving (path)-integrals.
17626338
Spectral asymmetry and supersymmetry
Fractional charges, and in particular the spectral asymmetry eta of certain Dirac operators, can appear in the central charge of supersymmetric field theories. This yields unexpected analyticity constraints on eta from which classic results can be recovered in an elegant way. The method could also be applied in the context of string theory.
15472365
Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
We study the physics of $\mathcal{N}=1$ super Yang-Mills theory with the gauge group $\mathrm{U}(N)$ and one adjoint Higgs field, by using the recently derived exact effective superpotentials. Interesting phenomena occur for some special values of the Higgs potential couplings. We find critical points with massless glueballs and/or massless monopoles, confinement without a mass gap, and tensionless domain walls. We describe the transitions between regimes with different patterns of gauge symmetry breaking, or, in the matrix model language, between solutions with a different number of cuts. The standard large N expansion is singular near the critical points, with domain wall tensions scaling as a fractional power of N. We argue that the critical points are four-dimensional analogues of the Kazakov critical points that are commonly found in low dimensional matrix integrals. We define a double scaling limit that yields the exact tension of BPS two-branes in the resulting $\mathcal{N}=1,$ four-dimensional noncritical string theory. D-brane states can be deformed continuously into closed string solitonic states, and vice versa, along paths that go over regions where the string coupling is strong.
119685691
Gravitational actions in two dimensions and the Mabuchi functional
Abstract The Mabuchi energy is an interesting geometric functional on the space of Kahler metrics that plays a crucial role in the study of the geometry of Kahler manifolds. We show that this functional, as well as other related geometric actions, contribute to the effective gravitational action when a massive scalar field is coupled to gravity in two dimensions in a small mass expansion. This yields new theories of two-dimensional quantum gravity generalizing the standard Liouville models.
16340483
The strong coupling spectrum of the Seiberg-Witten theory
Abstract We carefully study the global structure of the solution of the N = 2 supersymmetric pure Yang-Mills theory with gauge group SU(2) obtained by Seiberg and Witten. We exploit itsZsymmetry and describe the curve in moduli space where BPS states can become unstable, separating the strong-coupling from the weak-coupling region. This allows us to obtain the spectrum of stable BPS states in the strong-coupling region: we prove that only the two particles responsible for the singularities of the solution (the magnetic monopole and the dyon of unit electric charge) are present in this region. Our method also permits us to very easily obtain the weak-coupling spectrum, without using semiclassical methods. We discuss how the BPS states disintegrate when crossing the border from the weak- to the strong-coupling region.
119050628
Cosmic ray recipes
Cosmic rays represent one of the most fascinating research themes in modern astronomy and physics. After almost a century since their discovery, a huge amount of scientific literature has been written on this topic and it is not always easy to extract from it the necessary information for somebody who approaches the subject for the first time. This has been the main motivation for preparing this article, which is a concise and self-contained review for whoever is interested in studying cosmic rays. The priority has been given here to well established facts, which are not at risk to get obsolete in a few years due to the fast progress of the research in this field. Also many data are presented, which are useful to characterize the doses of ionizing radiation delivered to organisms living on the Earth due to cosmic rays. The technical terms which are often encountered in the scientific literature are explained in a separate appendix.
18013930
On a bosonization approach to disordered systems
In [1] a new bosonization procedure has been illustrated, which allows us to express a fermionic Gaussian system in terms of commuting variables by introducing an extra dimension. The Fermi–Bose duality principle established in this way also has many potential applications outside the context of gauge field theories in which it has been developed. In this work we present an application to the problem of averaging the correlation functions with respect to random potentials in disordered systems and similar problems.
121963535
Bosonization techniques on algebraic curves and conformal field theories
The bosonization of b‐c systems is studied with conformal weight λ on Riemann surfaces in which the moduli space is parametrized by the branch points (algebraic curves). Besides being interesting in itself, the problem is related to perturbative string theories and to nonfree conformal field theories on the complex plane with the insertion of certain spin fields called the twist fields. The method of λ‐differentials is proposed, which allows a complete treatment of the b‐c systems on algebraic curves with local Abelian monodromy group. It can be nevertheless applied also to more general algebraic curves allowing the computation of the Green’s functions and shedding some light about the structure of the twist fields in the general case. The connections between our formalism and the solutions of the Riemann monodromy problem, used to find out the conformal blocks of conformal field theories, are pointed out.
121629019
A path integral approach to the dynamics of random chains
In this work the dynamics of a freely jointed random chain with small masses attached to the joints is studied from a microscopic point of view. The chain is treated using a stringy approach, in which a statistical sum is performed over all two dimensional trajectories spanned by the chain during its fluctuations. In the limit in which the chain becomes a continuous curve, the probability function for such a system coincides with the partition function of a generalized nonlinear sigma model. The cases of open or closed chains in two and three dimensions are discussed. In three dimensions it is possible also to introduce some rigidity at the joints, allowing the segments of the chain to take only particular angles with respect to a given direction.
118955749
MULTIVALUED FIELDS ON THE COMPLEX PLANE AND BRAID GROUP STATISTICS
In this paper we study a class of theories of free particles on the complex plane satisfying a non-Abelian statistics. This kind of particles are generalizations of the anyons and are sometimes called plectons. The peculiarity of these theories is that they are associated to free conformal field theories defined on Riemann surfaces with a discrete and non-Abelian group of authomorphisms Dm. More explicitly, the plectons appear here as “induced vertex operators” that simulate, on the complex plane, the nontrivial topology of the Riemann surface. In order to express the local exchange algebra of the particles, one is led to introduce an R matrix satisfying a multiparameter generalization of the usual Yang-Baxter equations. It is interesting that analogous generalizations have already been investigated in connection with integrable models, in which the spectral parameter takes its values on a Riemann surface that is in many respects similar to the Riemann surfaces we are studying here. The explicit form of the R matrices mentioned above can be also used to define a multiparameter version of the quantum complex hyperplane.