Complete N=4 Structure of Low-Energy Effective Action in N=4 Super Yang-Mills Theories

Using the ${\cal N}=2$ superfield approach, we construct full ${\cal N}=4$ supersymmetric low-energy effective actions for ${\cal N}=4$ SYM models, with both ${\cal N}=2$ gauge superfield strengths and hypermultiplet superfields included. The basic idea is to complete the known non-holomorphic effective potentials which depend only on ${\cal N}=2$ superfield strengths $W$ and ${\bar W}$ to the full on-shell ${\cal N}=4$ invariants by adding the appropriate superfield hypermultiplet terms. We prove that the effective potentials of the form ${ln} W {ln} \bar W$ can be ${\cal N} = 4$ completed in this way and present the precise structure of the corresponding completions. However, the effective potentials of the non-logarithmic form suggested in hep-th/9811017 and hep-th/9909020 do not admit the ${\cal N}=4$ completion. Therefore, such potentials cannot come out as (perturbative or non-perturbative) quantum corrections in ${\cal N}=4$ SYM models.Comment: 14 pages, Latex, no figures, slight corrections, refs adde

Renormalization group improved gravitational actions: a Brans-Dicke approach

A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG-improved by replacing Newton's constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of $G$ and $\Lambda$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields $G$ and $\Lambda$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed ``background'' fields. The metric satisfies an effective Einstein equation similar to that of Brans-Dicke theory. Its consistency imposes severe constraints on allowed backgrounds. In the new RG-framework, $G$ and $\Lambda$ carry energy and momentum. It is tested in the setting of homogeneous-isotropic cosmology and is compared to alternative approaches where the fields $G$ and $\Lambda$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.Comment: LaTeX, 72 pages, no figure

Density functional study of Aun_n (n=2-20) clusters: lowest-energy structures and electronic properties

We have investigated the lowest-energy structures and electronic properties of the Au$_n$(n=2-20) clusters based on density functional theory (DFT) with local density approximation. The small Au$_n$ clusters adopt planar structures up to n=6. Tabular cage structures are preferred in the range of n=10-14 and a structural transition from tabular cage-like structure to compact near-spherical structure is found around n=15. The most stable configurations obtained for Au$_{13}$ and Au$_{19}$ clusters are amorphous instead of icosahedral or fcc-like, while the electronic density of states sensitively depend on the cluster geometry. Dramatic odd-even alternative behaviors are obtained in the relative stability, HOMO-LUMO gaps and ionization potentials of gold clusters. The size evolution of electronic properties is discussed and the theoretical ionization potentials of Au$_n$ clusters compare well with experiments.Comment: 6 pages, 7 figure

Two-loop N=4 Super Yang Mills effective action and interaction between D3-branes

We compute the leading low-energy term in the planar part of the 2-loop contribution to the effective action of $\N=4$ SYM theory in 4 dimensions, assuming that the gauge group $SU(N+1)$ is broken to $SU(N) x U(1)$ by a constant scalar background $X$. While the leading 1-loop correction is the familiar $c_1 F^4/|X|^4$ term, the 2-loop expression starts with $c_2 F^6/|X|^8$. The 1-loop constant $c_1$ is known to be equal to the coefficient of the $F^4$ term in the Born-Infeld action for a probe D3-brane separated by distance $|X|$ from a large number $N$ of coincident D3-branes. We show that the same is true also for the 2-loop constant $c_2$: it matches the coefficient of the $F^6$ term in the D3-brane probe action. In the context of the AdS/CFT correspondence, this agreement suggests a non-renormalization of the coefficient of the $F^6$ term beyond two loops. Thus the result of hep-th/9706072 about the agreement between the $v^6$ term in the D0-brane supergravity interaction potential and the corresponding 2-loop term in the 1+0 dimensional reduction of $\N=4$ SYM theory has indeed a direct generalization to 1+3 dimensions, as conjectured earlier in hep-th/9709087. We also discuss the issue of gauge theory -- supergravity correspondence for higher order ($F^8$, etc.) terms.Comment: 33 pages, late

Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared

We present recent results for the Landau-gauge gluon and ghost propagators in SU(3) lattice gluodynamics obtained on a sequence of lattices with linear extension ranging from L=64 to L=96 at $\beta = 5.70$, thus reaching "deep infrared" momenta down to 75 MeV. Our gauge-fixing procedure essentially uses a simulated annealing technique which allows us to reach gauge-functional values closer to the global maxima than standard approaches do. Our results are consistent with the so-called decoupling solutions found for Dyson-Schwinger and functional renormalization group equations.Comment: 6 pages, 5 figures. References added, minor changes to match published versio

Strong-coupling study of the Gribov ambiguity in lattice Landau gauge

We study the strong-coupling limit beta=0 of lattice SU(2) Landau gauge Yang-Mills theory. In this limit the lattice spacing is infinite, and thus all momenta in physical units are infinitesimally small. Hence, the infrared behavior can be assessed at sufficiently large lattice momenta. Our results show that at the lattice volumes used here, the Gribov ambiguity has an enormous effect on the ghost propagator in all dimensions. This underlines the severity of the Gribov problem and calls for refined studies also at finite beta. In turn, the gluon propagator only mildly depends on the Gribov ambiguity.Comment: 14 pages, 22 figures; minor changes, matches version to appear in Eur. Phys. J.

Superfield theory and supermatrix model

We study the noncommutative superspace of arbitrary dimensions in a systematic way. Superfield theories on a noncommutative superspace can be formulated in two folds, through the star product formalism and in terms of the supermatrices. We elaborate the duality between them by constructing the isomorphism explicitly and relating the superspace integrations of the star product Lagrangian or the superpotential to the traces of the supermatrices. We show there exists an interesting fine tuned commutative limit where the duality can be still maintained. Namely on the commutative superspace too, there exists a supermatrix model description for the superfield theory. We interpret the result in the context of the wave particle duality. The dual particles for the superfields in even and odd spacetime dimensions are D-instantons and D0-branes respectively to be consistent with the T-duality.Comment: 1+16 pages, no figure; expanded version, references added; Convention for Clifford algebra improve

Curvature Dependence of Running Gauge Coupling and Confinement in AdS/CFT Correspondence

We construct IIB supergravity (viewed as dilatonic gravity) background with non-trivial dilaton and with curved four-dimensional space. Such a background may describe another vacuum of maximally supersymmetric Yang-Mills theory or strong coupling regime of (non)-supersymmetric gauge theory with (power-like) running gauge coupling which depends on curvature. Curvature dependent quark-antiquark potential is calculated where the geometry type of hyperbolic (or de Sitter universe) shows (or not) the tendency of the confinement. Generalization of IIB supergravity background with non-constant axion is presented. Quark-antiquark potential being again curvature-dependent has a possibility to produce the standard area law for large separations.Comment: LaTeX file, 24 pages, presentation is improve

Infrared exponents and the strong-coupling limit in lattice Landau gauge

We study the gluon and ghost propagators of lattice Landau gauge in the strong-coupling limit beta=0 in pure SU(2) lattice gauge theory to find evidence of the conformal infrared behavior of these propagators as predicted by a variety of functional continuum methods for asymptotically small momenta $q^2 \ll \Lambda_\mathrm{QCD}^2$. In the strong-coupling limit, this same behavior is obtained for the larger values of a^2q^2 (in units of the lattice spacing a), where it is otherwise swamped by the gauge field dynamics. Deviations for a^2q^2 < 1 are well parameterized by a transverse gluon mass $\propto 1/a$. Perhaps unexpectedly, these deviations are thus no finite-volume effect but persist in the infinite-volume limit. They furthermore depend on the definition of gauge fields on the lattice, while the asymptotic conformal behavior does not. We also comment on a misinterpretation of our results by Cucchieri and Mendes in Phys. Rev. D81 (2010) 016005.Comment: 17 pages, 12 figures. Revised version (mainly sections I and II); references and comments on subsequent work on the subject added

Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimentions

We develop the BRST approach to Lagrangian formulation for massive higher integer spin fields on a flat space-time of arbitrary dimension. General procedure of gauge invariant Lagrangian construction describing the dynamics of massive bosonic field with any spin is given. No off-shell constraints on the fields (like tracelessness) and the gauge parameters are imposed. The procedure is based on construction of new representation for the closed algebra generated by the constraints defining an irreducible massive bosonic representation of the Poincare group. We also construct Lagrangian describing propagation of all massive bosonic fields simultaneously. As an example of the general procedure, we derive the Lagrangians for spin-1, spin-2 and spin-3 fields containing total set of auxiliary fields and gauge symmetries of free massive bosonic higher spin field theory.Comment: 27 page