Improved Renormalization Group analysis for Yang-Mills theory

We apply an improved renormalization group analysis for pure Yang-Mills theory at one loop order and obtained the result that a non-perturbatively generated pole mass of gluon emerges as $M_P^2/\Lambda^2 \simeq 0.66$, where $\Lambda$ is the $MS$-bar scale.Comment: 1+16 pages, 3 figures; ver 2, typos corrected, and some comments and references added; ver 3, some sentences corrected, a figure replaced and a number corrected; ver 4, in sec 2, the derivation of the main formula is refined, final version to appear in Prog.Theor.Phy

Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models

In the previous study, we formulate a matrix model renormalization group based on the fuzzy spherical harmonics with which a notion of high/low energy can be attributed to matrix elements, and show that it exhibits locality and various similarity to the usual Wilsonian renormalization group of quantum field theory. In this work, we continue the renormalization group analysis of a matrix model with emphasis on nonlocal interactions where the fields on antipodal points are coupled. They are indeed generated in the renormalization group procedure and are tightly related to the noncommutative nature of the geometry. We aim at formulating renormalization group equations including such nonlocal interactions and finding existence of nontrivial field theory with antipodal interactions on the fuzzy sphere. We find several nontrivial fixed points and calculate the scaling dimensions associated with them. We also consider the noncommutative plane limit and then no consistent fixed point is found. This contrast between the fuzzy sphere limit and the noncommutative plane limit would be manifestation in our formalism of the claim given by Chu, Madore and Steinacker that the former does not have UV/IR mixing, while the latter does.Comment: 1+47 pages, no figure; Ver. 2, references and some comments are added; Ver. 3, typos corrected. Version to appear in JHE

Circular loop operators in conformal field theories

We use the conformal group to study non-local operators in conformal field theories. A plane or a sphere (of any dimension) is mapped to itself by some subgroup of the conformal group, hence operators confined to that submanifold may be classified in representations of this subgroup. For local operators this gives the usual definition of conformal dimension and spin, but some conformal field theories contain interesting nonlocal operators, like Wilson or 't Hooft loops. We apply those ideas to Wilson loops in four-dimensional CFTs and show how they can be chosen to be in fixed representations of SL(2,R) x SO(3).Comment: 10 pages, late

To see Symmetry in a Forest of Trees

The exact symmetry identities among four-point tree-level amplitudes of bosonic open string theory as derived by G. W. Moore are re-examined. The main focuses of this work are: (1) Explicit construction of kinematic configurations and a new polarization basis for the scattering processes. These setups simplify greatly the functional forms of the exact symmetry identities, and help us to extract easily high-energy limits of stringy amplitudes appearing in the exact identities. (2) Connection and comparison between D. J. Gross's high-energy stringy symmetry and the exact symmetry identities as derived by G. W. Moore. (3) Observation of symmetry patterns of stringy amplitudes with respect to the order of energy dependence in scattering amplitudes.Comment: 56 pages; v2. Typos corrected. Minor changes; v3. Reorganized the structure and eliminate verbose expressions. References added. Added words of introduction to each section; v4. Reorganized and streamlined significantly. Version to appear in Nucl.Phys.

Open membranes in a constant C-field background and noncommutative boundary strings

We investigate the dynamics of open membrane boundaries in a constant C-field background. We follow the analysis for open strings in a B-field background, and take some approximations. We find that open membrane boundaries do show noncommutativity in this case by explicit calculations. Membrane boundaries are one dimensional strings, so we face a new type of noncommutativity, that is, noncommutative strings.Comment: 23 pages, 1 eps figure, LaTeX2e; v4. a comment added, final versio