Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory

The classical analysis of Kazakov and Kostov of the Makeenko-Migdal loop equation in two-dimensional gauge theory leads to usual partial differential equations with respect to the areas of windows formed by the loop. We extend this treatment to the case of U(N) Yang-Mills defined on the noncommutative plane. We deal with all the subtleties which arise in their two-dimensional geometric procedure, using where needed results from the perturbative computations of the noncommutative Wilson loop available in the literature. The open Wilson line contribution present in the non-commutative version of the loop equation drops out in the resulting usual differential equations. These equations for all N have the same form as in the commutative case for N to infinity. However, the additional supplementary input from factorization properties allowing to solve the equations in the commutative case is no longer valid.Comment: 20 pages, 3 figures, references added, small clarifications adde

Morita Duality and Noncommutative Wilson Loops in Two Dimensions

We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the combinatorics of non-planar graphs. Several nonperturbative examples of symmetry breaking under area-preserving diffeomorphisms are thereby presented. Analytic expressions for correlators of Wilson loops with infinite winding number are also derived and shown to agree with results from ordinary Yang-Mills theory.Comment: 32 pages, 9 figures; v2: clarifying comments added; Final version to be published in JHE

On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions

We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.Comment: LaTeX JHEP style, 16 pages, 2 figure

Small deformations of supersymmetric Wilson loops and open spin-chains

We study insertions of composite operators into Wilson loops in N=4 supersymmetric Yang-Mills theory in four dimensions. The loops follow a circular or straight path and the composite insertions transform in the adjoint representation of the gauge group. This provides a gauge invariant way to define the correlator of non-singlet operators. Since the basic loop preserves an SL(2,R) subgroup of the conformal group, we can assign a conformal dimension to those insertions and calculate the corrections to the classical dimension in perturbation theory. The calculation turns out to be very similar to that of single-trace local operators and may also be expressed in terms of a spin-chain. In this case the spin-chain is open and at one-loop order has Neumann boundary conditions on the type of scalar insertions that we consider. This system is integrable and we write the Bethe ansatz describing it. We compare the spectrum in the limit of large angular momentum both in the dilute gas approximation and the thermodynamic limit to the relevant string solution in the BMN limit and in the full AdS_5 x S^5 metric and find agreement.Comment: 40 pages, amstex, 4 figures. V2: Corrected eqn (2.14) and some equations in section 5. Version to appear in JHE

Probability distribution of the index in gauge theory on 2d non-commutative geometry

We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors labeled by the index nu of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. We study the probability distribution of nu by Monte Carlo simulation of the U(1) gauge theory on 2d non-commutative space with periodic boundary conditions. In general the distribution is asymmetric under nu -> -nu, reflecting the parity violation due to non-commutative geometry. In the continuum and infinite-volume limits, however, the distribution turns out to be dominated by the topologically trivial sector. This conclusion is consistent with the instanton calculus in the continuum theory. However, it is in striking contrast to the known results in the commutative case obtained from lattice simulation, where the distribution is Gaussian in a finite volume, but the width diverges in the infinite-volume limit. We also calculate the average action in each topological sector, and provide deeper understanding of the observed phenomenon.Comment: 16 pages,10 figures, version appeared in JHE

Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/\theta Expansion

We analyze the $1/\theta$ and 1/N expansions of the Wilson loop averages $_{U_\theta (N)}$ in the two-dimensional noncommutative $U_\theta (N)$ gauge theory with the parameter of noncommutativity $\theta$. For a generic rectangular contour $C$, a concise integral representation is derived (non-perturbatively both in the coupling constant $g^{2}$ and in $\theta$) for the next-to-leading term of the $1/\theta$ expansion. In turn, in the limit when ${\theta}$ is much larger than the area $A(C)$ of the surface bounded by $C$, the large $\theta$ asymptote of this representation is argued to yield the next-to-leading term of the $1/\theta$ series. For both of the expansions, the next-to-leading contribution exhibits only a power-like decay for areas $A(C)>>\sigma^{-1}$ (but $A(C)<<{\theta}$) much larger than the inverse of the string tension $\sigma$ defining the range of the exponential decay of the leading term. Consequently, for large $\theta$, it hinders a direct stringy interpretation of the subleading terms of the 1/N expansion in the spirit of Gross-Taylor proposal for the $\theta=0$ commutative D=2 gauge theory.Comment: LaTex, 50pp., 9 PostScript figure

A EXPERIÊNCIA DE HOSPITALIZAÇÃO EXPLICADA PELA PRÓPRIA CRIANÇA

O presente estudo foi realizado com 20 crianças, em idade escolar, internadas em unidades pediátricas. Teve como objetivos identificar: como as crianças expressam a percepção de sua doença e hospitalização; os recursos de 'que elas dispõem para obter conhecimento sobre sua experiência de doença e hospitalização; e seus interesses e preocupações

TESS Reveals a Short-period Sub-Neptune Sibling (HD 86226c) to a Known Long-period Giant Planet

The Transiting Exoplanet Survey Satellite mission was designed to find transiting planets around bright, nearby stars. Here, we present the detection and mass measurement of a small, short-period (≈4 days) transiting planet around the bright (V = 7.9), solar-type star HD 86226 (TOI-652, TIC 22221375), previously known to host a long-period (∼1600 days) giant planet. HD 86226c (TOI-652.01) has a radius of 2.16 0.08 R ⊕ and a mass of M ⊕, based on archival and new radial velocity data. We also update the parameters of the longer-period, not-known-to-transit planet, and find it to be less eccentric and less massive than previously reported. The density of the transiting planet is 3.97 g cm-3, which is low enough to suggest that the planet has at least a small volatile envelope, but the mass fractions of rock, iron, and water are not well-constrained. Given the host star brightness, planet period, and location of the planet near both the "radius gap"and the "hot Neptune desert,"HD 86226c is an interesting candidate for transmission spectroscopy to further refine its composition

A hot mini-Neptune in the radius valley orbiting solar analogue HD 110113

We report the discovery of HD 110113 b (TESS object of interest-755.01), a transiting mini-Neptune exoplanet on a 2.5-d orbit around the solar-analogue HD 110113 (Teff = 5730 K). Using TESS photometry and High Accuracy Radial velocity Planet Searcher (HARPS) radial velocities gathered by the NCORES program, we find that HD 110113 b has a radius of 2.05 ± 0.12 R⊕ and a mass of 4.55 ± 0.62 M⊕. The resulting density of $2.90^{+0.75}_{-0.59}$ g cm-3 is significantly lower than would be expected from a pure-rock world; therefore HD 110113 b must be a mini-Neptune with a significant volatile atmosphere. The high incident flux places it within the so-called radius valley; however, HD 110113 b was able to hold on to a substantial (0.1-1 per cent) H-He atmosphere over its ∼4 Gyr lifetime. Through a novel simultaneous Gaussian process fit to multiple activity indicators, we were also able to fit for the strong stellar rotation signal with period 20.8 ± 1.2 d from the RVs and confirm an additional non-transiting planet, HD 110113 c, which has a mass of 10.5 ± 1.2 M⊕ and a period of $6.744^{+0.008}_{-0.009}$ d