Quantum parameter space in super Yang-Mills, II

In [1] (hep-th/0211069), the author has discussed the quantum parameter space of the N=1 super Yang-Mills theory with one adjoint Higgs field Phi, tree-level superpotential W_tree = m (Phi^2)/2 + g (Phi^3)/3$, and gauge group U(Nc). In particular, full details were worked out for U(2) and U(3). By discussing higher rank gauge groups like U(4), for which the classical parameter space has a large number of disconnected components, we show that the phenomena discussed in [1] are generic. It turns out that the quantum space is connected. The classical components are related in the quantum theory either through standard singularities with massless monopoles or by branch cuts without going through any singularity. The branching points associated with the branch cuts correspond to new strong coupling singularities, which are not associated with vanishing cycles in the geometry, and at which glueballs can become massless. The transitions discussed recently by Cachazo, Seiberg and Witten are special instances of those phenomena.Comment: 12 pages including 2 large figure

Renormalization of the Non-Linear Sigma Model in Four Dimensions. A two-loop example

The renormalization procedure of the non-linear SU(2) sigma model in D=4 proposed in hep-th/0504023 and hep-th/0506220 is here tested in a truly non-trivial case where the non-linearity of the functional equation is crucial. The simplest example, where the non-linear term contributes, is given by the two-loop amplitude involving the insertion of two \phi_0 (the constraint of the non-linear sigma model) and two flat connections. In this case we verify the validity of the renormalization procedure: the recursive subtraction of the pole parts at D=4 yields amplitudes that satisfy the defining functional equation. As a by-product we give a formal proof that in D dimensions (without counterterms) the Feynman rules provide a perturbative symmetric solution.Comment: Latex, 3 figures, 19 page

Super Yang-Mills, Matrix Models and Geometric Transitions

I explain two applications of the relationship between four dimensional N=1 supersymmetric gauge theories, zero dimensional gauged matrix models, and geometric transitions in string theory. The first is related to the spectrum of BPS domain walls or BPS branes. It is shown that one can smoothly interpolate between a D-brane state, whose weak coupling tension scales as Nc or 1/gs, and a closed string solitonic state, whose weak coupling tension scales as Nc^2 or 1/gs^2. This is part of a larger theory of N=1 quantum parameter spaces. The second is a new purely geometric approach to sum exactly over planar diagrams in zero dimension. It is an example of open/closed string duality.Comment: 11 pages, 2 figures, .cls files included; to appear in the proceedings of the Strings 2004 conference in Pari

Weyl and Marchaud derivatives: a forgotten history

In this paper we recall the contribution given by Hermann Weyl and Andr\'e Marchaud to the notion of fractional derivative. In addition we discuss some relationships between the fractional Laplace operator and Marchaud derivative in the perspective to generalize these objects to different fields of the mathematics.Comment: arXiv admin note: text overlap with arXiv:1705.00953 by other author

Early physics with top quarks at the LHC

The ATLAS and CMS experiments are now in their final installation phase and will be soon ready to study the physics of proton-proton collisions at the Large Hadron Collider. The LHC, by producing 2 $t\bar{t}$ events per second, will provide more than 8 million top events a year at start-up. In this paper, particular emphasis is given to the $t\bar{t}$ physics studies that can be performed at the beginning of the LHC running, with a limited amount of integrated luminosity ($\le$10 fb$^{-1}$).Comment: Proceedings of Moriond QCD 2007. Luminosity contribution to error on top pair production cross-section has been changed from 0.5% to 5.0

Tracking and vertexing at ATLAS

Several algorithms for tracking and for primary and secondary vertex reconstruction have been developed by the ATLAS collaboration following different approaches. This has allowed a thorough cross-check of the performances of the algorithms and of the reconstruction software. The results of the most recent studies on this topic are discussed and compared.Comment: Proceedings of the HCP 2006 conferenc

Relativism, Faultlessness and Parity

Some philosophers, like Mark Richard and Paul Boghossian, have argued against relativism that it cannot account for the possibility of faultless disagreement. However, I will contend that the objections they moved against relativism do not target its ability to account for the possibility of faultless disagreement per se. Ra- ther, they should be taken to challenge its capacity to account for another element of our folk conception of disagreement in certain areas of discourse—what Cris- pin Wright has dubbed parity. What parity demands is to account for the possibil- ity of coherently appreciating, within a committed perspective, that our oppo- nent’s contrary judgement is somehow on a par with our own judgement. Under- stood in this way, Boghossian’s and Richard’s objections put indeed considerable pressure on relativism—or so I will argue. I will consider John MacFarlane’s at- tempt to resist their objections and I will show that, once their arguments are properly understood as targeting parity, the attempt is not successful. In the last section of the paper I will offer a diagnosis of what is at the heart of the relativist inability to account for parity—namely its assumption of a monistic conception of the normativity of truth