The Nonperturbative Gauge Coupling of N=2 Supersymmetric Theories

We argue that the topology of the quantum coupling space and the low energy effective action on the Coulomb branch of scale invariant N=2 SU(n) gauge theories pick out a preferred nonperturbative definition of the gauge coupling up to non-singular holomorphic reparametrizations.Comment: 9 pages latex and 2 figures using psfig.sty; computation of S-duality group corrected and reference adde

Magnon dispersion to four loops in the ABJM and ABJ models

The ABJM model is a superconformal Chern-Simons theory with N=6 supersymmetry which is believed to be integrable in the planar limit. However, there is a coupling dependent function that appears in the magnon dispersion relation and the asymptotic Bethe ansatz that is only known to leading order at strong and weak coupling. We compute this function to four loops in perturbation theory by an explicit Feynman diagram calculation for both the ABJM model and the ABJ extension. We find that all coefficients have maximal transcendentality. We then compute the four-loop wrapping correction for a scalar operator in the 20 of SU(4) and find that it agrees with a recent prediction from the ABJM Y-system of Gromov, Kazakov and Vieira. We also propose a limit of the ABJ model that might be perturbatively integrable at all loop orders but has a short range Hamiltonian.Comment: LaTeX, feynmp, 17 pages; v2: coupling factor in one Feynman diagram corrected: modified result in the ABJ case only, formulations improved, typos fixed, references added; v3: signs of three diagrams corrected, modifying the final resul

Copyright Protection for Tattoos: Are Tattoos Copies?

This Note argues that, although “flash art” and other drawings upon which a tattoo may be based are likely copyrightable subject matter under the Copyright Act of 1976 (Copyright Act), the policy implications of granting copyright protection to tattoos militate against extending such protection. To avoid these consequences, the copyright statute should be interpreted as failing to include the human body as a “copy” within the scope of the Copyright Act and, therefore, tattoos would not be subject to the protection of the Act. Part I provides a background on the statutory framework of the Copyright Act, including the requirements for copyrightable subject matter, copyright ownership, and the exclusive rights granted by the Copyright Act to the copyright owner. Part II provides an overview of three cases in which tattoo artists have alleged that their tattoos, or their drawings upon which a subsequent tattoo are based, are copyrightable subject matter. These tattoo artists have alleged infringement of their works based upon a subsequent reproduction or display of their tattooed work. Part III begins by addressing whether, as a preliminary matter, a tattoo would generally meet the Copyright Act’s copyrightability requirements. Part III then presents several negative policy issues that would likely arise should copyright protection be extended to tattoos. It concludes by arguing that tattoos are not “copies” as defined under the Copyright Act and therefore, they are not subject to copyright protection

Copyright Protection for Tattoos: Are Tattoos Copies?

This Note argues that, although “flash art” and other drawings upon which a tattoo may be based are likely copyrightable subject matter under the Copyright Act of 1976 (Copyright Act), the policy implications of granting copyright protection to tattoos militate against extending such protection. To avoid these consequences, the copyright statute should be interpreted as failing to include the human body as a “copy” within the scope of the Copyright Act and, therefore, tattoos would not be subject to the protection of the Act. Part I provides a background on the statutory framework of the Copyright Act, including the requirements for copyrightable subject matter, copyright ownership, and the exclusive rights granted by the Copyright Act to the copyright owner. Part II provides an overview of three cases in which tattoo artists have alleged that their tattoos, or their drawings upon which a subsequent tattoo are based, are copyrightable subject matter. These tattoo artists have alleged infringement of their works based upon a subsequent reproduction or display of their tattooed work. Part III begins by addressing whether, as a preliminary matter, a tattoo would generally meet the Copyright Act’s copyrightability requirements. Part III then presents several negative policy issues that would likely arise should copyright protection be extended to tattoos. It concludes by arguing that tattoos are not “copies” as defined under the Copyright Act and therefore, they are not subject to copyright protection

Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories

In arXiv:0908.2463 we computed the four-loop correction to a function depending on the 't Hooft coupling(s) that appears in the magnon dispersion relation of the spin chains derived from single trace operators in N=6 superconformal Chern-Simons theories. In this paper we give detailed descriptions of this calculation and the computation of the four-loop wrapping corrections for a length four operator in the 20 of SU(4), the R-symmetry group for these theories. Here, we give all relevant Feynman diagrams and loop integrals explicitly, and also demonstrate the cancellation of double poles in the logarithm of the renormalization constant.Comment: LaTeX, feynmp, 70 pages; v2: signs of three diagrams due to inconsistent Feynman rules corrected, modifying the final result, typos corrected, formulations improve

ADE-Quiver Theories and Mirror Symmetry

We show that the Higgs branch of a four-dimensional Yang-Mills theory, with gauge and matter content summarised by an ADE quiver diagram, is identical to the generalised Coulomb branch of a four-dimensional superconformal strongly coupled gauge theory with ADE global symmetry. This equivalence suggests the existence of a mirror symmetry between the quiver theories and the strongly coupled theories.Comment: 8 pages, 4 figures. Talk delivered by UL at D.V. Volkov Memorial Conference, July 25-29, 2000, Kharkov, to be published in the proceeding

From polymers to quantum gravity: triple-scaling in rectangular matrix models

Rectangular $N\times M$ matrix models can be solved in several qualitatively distinct large $N$ limits, since two independent parameters govern the size of the matrix. Regarded as models of random surfaces, these matrix models interpolate between branched polymer behaviour and two-dimensional quantum gravity. We solve such models in a `triple-scaling' regime in this paper, with $N$ and $M$ becoming large independently. A correspondence between phase transitions and singularities of mappings from ${\bf R}^2$ to ${\bf R}^2$ is indicated. At different critical points, the scaling behavior is determined by: i) two decoupled ordinary differential equations; ii) an ordinary differential equation and a finite difference equation; or iii) two coupled partial differential equations. The Painlev\'e II equation arises (in conjunction with a difference equation) at a point associated with branched polymers. For critical points described by partial differential equations, there are dual weak-coupling/strong-coupling expansions. It is conjectured that the new physics is related to microscopic topology fluctuations.Comment: 29 page