Branched Coverings and Interacting Matrix Strings in Two Dimensions

We construct the lattice gauge theory of the group G_N, the semidirect product of the permutation group S_N with U(1)^N, on an arbitrary Riemann surface. This theory describes the branched coverings of a two-dimensional target surface by strings carrying a U(1) gauge field on the world sheet. These are the non-supersymmetric Matrix Strings that arise in the unitary gauge quantization of a generalized two-dimensional Yang-Mills theory. By classifying the irreducible representations of G_N, we give the most general formulation of the lattice gauge theory of G_N, which includes arbitrary branching points on the world sheet and describes the splitting and joining of strings.Comment: LaTeX2e, 25 pages, 4 figure

Matrix strings from generalized Yang-Mills theory on arbitrary Riemann surfaces

We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically non-trivial loops. These sectors, that must be discarded in the usual quantization due to divergences occurring when two eigenvalues coincide, can be consistently kept if one modifies the action by introducing a coupling of the field strength to the space-time curvature. This leads to a generalized Yang-Mills theory whose action reduces to the usual one in the limit of zero curvature. After integrating over the non-diagonal components of the gauge fields, the theory becomes a free string theory (sum over unbranched coverings) with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to a lattice theory with a gauge group which is the semi-direct product of S_N and U(1)^N. By using well known results on the statistics of coverings, the partition function on arbitrary Riemann surfaces and the kernel functions on surfaces with boundaries are calculated. Extensions to include branch points and non-abelian groups on the world-sheet are briefly commented upon.Comment: Latex2e, 29 pages, 2 .eps figure

N=2 SYM RG Scale as Modulus for WDVV Equations

We derive a new set of WDVV equations for N=2 SYM in which the renormalization scale $\Lambda$ is identified with the distinguished modulus which naturally arises in topological field theories.Comment: 6 pages, LaTe

Meromorphic Scaling Flow of N=2 Supersymmetric SU(2) Yang-Mills with Matter

Beta-functions are derived for the flow of N=2 SUSY SU(2) Yang-Mills in 4-dimensions with massless matter multiplets in the fundamental representation of the gauge group. The beta-functions represent the flow of the couplings as the VEV of the Higgs field is lowered and are modular forms of weight -2. They have the correct asymptotic behaviour at both the strong and weak coupling fixed points. Corrections to the massless beta-functions when masses are turned on are discussed.Comment: 23 pages, 4 figures, typset using JHEP3 style. References updated and minor typos fixed in v

Buoyancy and local friction effects on rockfill settlements: A discrete modelling

AbstractMeasured displacements in the upstream shell of rockfill dams show some settlements which can reach a few meters with water levels changes, especially during the first impounding, whereas downstream displacements are smaller. Complementary phenomena are responsible for rockfill collapse due to wetting. Here we numerically investigate the effects of buoyancy forces and the decrease in the coefficient of friction with water on a rockfill column maintained by vertical rigid walls and progressively filled with water. Numerical simulations of the settlements of the rockfill column, using the Contact Dynamics method, are presented. Buoyancy forces seem to have only a negligible influence on the granular pile. Decrease in the friction angle of the rock with water induces rearrangements of the medium, all the more as the decrease is significant. These dynamic rearrangements exhibit an irregular temporal evolution of the granular medium which can be characterized by a phenomenon of local “crisis”. Analysis of the settlements shows that these two combined effects are not the major cause of the settlements observed in rockfill dams and that they cannot in particular explain the settlements

Matrix string states in pure 2d Yang Mills theories

We quantize pure 2d Yang-Mills theory on a torus in the gauge where the field strength is diagonal. Because of the topological obstructions to a global smooth diagonalization, we find string-like states in the spectrum similar to the ones introduced by various authors in Matrix string theory. We write explicitly the partition function, which generalizes the one already known in the literature, and we discuss the role of these states in preserving modular invariance. Some speculations are presented about the interpretation of 2d Yang-Mills theory as a Matrix string theory.Comment: Latex file of 38 pages plus 6 eps figures. A note and few references added, figures improve

Superstrings in type IIB R-R plane-wave in semi-light-cone gauge and conformal invariance

We reconsider the analysis done by Kazama and Yokoi in arXiv:0801.1561 (hep-th). We find that although the right vacuum of the theory is the one associated to massless normal ordering (MNO), phase space normal ordering (PNO) plays crucial role in the analysis in the following way. While defining the quantum energy-momentum (EM) tensor one needs to take into account the field redefinition relating the space-time field and the corresponding world-sheet coupling. We argue that for a simple off-shell ansatz for the background this field redefinition can be taken to be identity if the interaction term is ordered according to PNO. This definition reproduces the correct physical spectrum when the background is on-shell. We further show that the right way to extract the effective equation of motion from the Virasoro anomaly is to first order the anomaly terms according to PNO at a finite regularization parameter \eps and then take the \eps \to 0 limit. This prescription fixes an ambiguity in taking the limit for certain bosonic and fermionic contributions to the Virasoro anomaly and is the natural one to consider given the above definition of the EM tensor.Comment: 22 page

RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM

We determine the exact beta function and a RG flow Lyapunov function for N=2 SYM with gauge group SU(n). It turns out that the classical discriminants of the Seiberg-Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the non-perturbative identity relating the $u$-modulus and the superconformal anomaly, indicate the existence of a four dimensional analogue of the c-theorem for N=2 SYM which we formulate for the full SU(n) theory. Our investigation provides further evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References added. Version published in PR