15116130
Galois symmetries in super Yang-Mills theories
Classifying the phases of gauge theories is hindered by the lack of local order parameters. In particular, the standard Wilson's and 't Hooft's non-local order parameters are known to be insufficient to explain the existence of the plethora of phases that are found in supersymmetric gauge theories. Motivated by these observations, we reanalyze the concept of gauge symmetry breaking using Galois theory. Unlike the ordinary classical notion of unbroken gauge group, the Galois symmetry makes sense in the full quantum theory and must be a phase invariant. The algebraic structure underlying the space of vacua of supersymmetric gauge theories, that we have developed recently, is precisely designed to allow a rigorous mathematical implementation of these ideas.
119318242
Partial Gauge Fixing and Equivariant Cohomology
Given a gauge theory with gauge group G, it is sometimes useful to find an equivalent formulation in terms of a nontrivial gauge subgroup H⊂G. This amounts to fixing the gauge partially from G down to H. We study this problem systematically, both from the algebraic and from the path integral points of view. We find that the usual BRST cohomology must be replaced by an equivariant version and that the ghost Lagrangian must always include quartic ghost terms, even at tree level. Both the Cartan and Weil models for equivariant cohomology play a role and find natural interpretations within the physics framework. Applications include the construction of D-brane models of emergent space, the 't Hooft Abelian projection scenario in quantum chromodynamics and the formulation of the low-energy effective theories of grand unified models. © 2014 American Physical Society.
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.
1817006
Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD
We explicitly determine the global structure of the SL(2, Z) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.
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.
14411174
Consistency conditions in the chiral ring of super-Yang Mills theories
Abstract Starting from the generalized Konishi anomaly equations at the non-perturbative level, we demonstrate that the algebraic consistency of the quantum chiral ring of the N = 1 super-Yang–Mills theory with gauge group U ( N ) , one adjoint chiral superfield X and N f ⩽ 2 N flavours of quarks implies that the periods of the meromorphic one-form Tr d z z − X must be quantized. This shows in particular that identities in the open string description of the theory, that follow from the fact that gauge invariant observables are expressed in terms of gauge variant building blocks, are mapped onto non-trivial dynamical equations in the closed string description.
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.
116932271
Applications of a generalization of the nonlinear sigma model with O(d) group of symmetry to the dynamics of a constrained chain
Subject of this work are the applications of a field theoretical model, called here generalized nonlinear sigma model or simply GNLSM,to the dynamics of a chain subjected to constraints. Chains with similar properties and constraints have been discussed in a seminal paper of Edwards and Goodyear using an approach based on the Langevin equation. The GNLSM has been proposed in a previous publication in order to describe the dynamics of a two dimensional chain. In this paper the model is extended to d dimensions and a bending energy term is added to its action. As an application, two observables are computed in the case of a very stiff chain. The first observable is the dynamical form factor of a ring shaped chain. The second observable is a straightforward generalization to dynamics of the static form factor. This observable is relevant in order to estimate the average distance between two arbitrary points of the chain. Finally, a variant of the GNLNM is presented, in which the topological conditions which constrain the motion of two linked chains are imposed with the help of the Gauss linking invariant.
119503591
Free and Interacting 2-D Maxwell Field Theory on Conformally Flat Space Times
The free Maxwell field theory is quantized in the Lorentz gauge on a two dimensional manifold $M$ with conformally flat background metric. It is shown that in this gauge the theory is equivalent, at least at the classical level, to a biharmonic version of the bosonic string theory. This equivalence is exploited in order to construct in details the propagator of the Maxwell field theory on $M$. The expectation values of the Wilson loops are computed. A trivial result is obtained confirming in the Lorentz gauge previous calculations. Finally the interacting case is briefly discussed taking the Schwinger model as an example. The two and three point functions of the Schwinger model are explicitly derived at the lowest order on a Riemann surface.
16793358
FIELD THEORIES ON THE POINCARÉ DISK
The massive scalar field theory and the chiral Schwinger model are quantized on a Poincare disk of radius ρ. The amplitudes are derived in terms of Legendre functions. The behavior at long distances and near the boundary of some of the relevant correlation functions is studied. The exact computation of the chiral determinant appearing in the Schwinger model is obtained exploiting perturbation theory. This calculation poses interesting mathematical problems, as the Poincare disk is a noncompact manifold with a metric tensor which diverges when it approaches the boundary. The results presented in this paper are very useful in view of possible extensions to general Riemann surfaces. Moreover, they could also shed some light in the quantization of field theories on manifolds with constant curvature scalars in higher dimensions.
118089538
Gauge Field Theories on Riemann Surfaces
In this paper the free gauge field theories on a Riemann surface of any genus are quantized in the covariant gauge. The propagators of the gauge fields are explicitly derived and their properties are analysed in details. As an application, the correlation functions of a Yang-Mills field theory with gauge group $SU(N)$ are computed at the lowest order.