Asymptotics of LQG fusion coefficients

The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into $SU(2)_L\times SU(2)_R$ semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.Comment: 14 pages, minor change

Hierarchy of general invariants for bivariate LPDOs

We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of general invariants are studied and some examples are presented. We also show that classical Laplace invariants correspond to some particular cases of general invariants.Comment: to appear in J. "Theor.Math.Phys." in May 200

Wilson-'t Hooft operators and the theta angle

We consider $(3+1)$-dimensional $SU(N)/\mathbb Z_N$ Yang-Mills theory on a space-time with a compact spatial direction, and prove the following result: Under a continuous increase of the theta angle $\theta\to\theta+2\pi$, a 't Hooft operator $T(\gamma)$ associated with a closed spatial curve $\gamma$ that winds around the compact direction undergoes a monodromy $T(\gamma) \to T^\prime(\gamma)$. The new 't Hooft operator $T^\prime(\gamma)$ transforms under large gauge transformations in the same way as the product $T(\gamma) W(\gamma)$, where $W(\gamma)$ is the Wilson operator associated with the curve $\gamma$ and the fundamental representation of SU(N).Comment: 7 page

Massive higher spins and holography

We review recent progress towards the understanding of higher spin gauge symmetry breaking in AdS space from a holographic vantage point. According to the AdS/CFT correspondence, N=4 SYM theory at vanishing coupling constant should be dual to a theory in AdS which exhibits higher spin gauge symmetry enhancement. When the SYM coupling is non-zero, all but a handful of HS currents are violated by anomalies, and correspondingly local higher spin symmetry in the bulk gets spontaneously broken. In agreement with previous results and holographic expectations, we find that, barring one notable exception (spin 1 eating spin 0), the Goldstone modes responsible for HS symmetry breaking in AdS have non-vanishing mass even in the limit in which the gauge symmetry is restored. We show that spontaneous breaking a' la Stueckelberg implies that the mass of the relevant spin s'=s-1 Goldstone field is exactly the one predicted by the correspondence.Comment: 8 pages, talk presented by M.B. at the "Fourth Meeting on Constrained Dynamics and Quantum gravity" held in Cala Gonone (Sardinia, Italy), September 12-16, 200

SL(2,Z) Multiplets in N=4 SYM Theory

We discuss the action of SL(2,Z) on local operators in D=4, N=4 SYM theory in the superconformal phase. The modular property of the operator's scaling dimension determines whether the operator transforms as a singlet, or covariantly, as part of a finite or infinite dimensional multiplet under the SL(2,Z) action. As an example, we argue that operators in the Konishi multiplet transform as part of a (p,q) PSL(2,Z) multiplet. We also comment on the non-perturbative local operators dual to the Konishi multiplet.Comment: 14 pages, harvmac; v2: published version with minor change

The EPRL intertwiners and corrected partition function

Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the simplicity constraint? What is a complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective for n-valent vertex in case when it is a map from SO(3) into SO(3)xSO(3) representations. We find, however, that the EPRL map is not isometric. In the consequence, in order to be written in a SU(2) amplitude form, the formula for the partition function has to be rederived. We do it and obtain a new, complete formula for the partition function. The result goes beyond the SU(2) spin-foam models framework.Comment: RevTex4, 15 pages, 5 figures; theorem of injectivity of EPRL map correcte

The broad-band X-ray spectrum of the Seyfert 1 galaxy, MCG+8-11-11

We present a long (100 ks) Suzaku observation of one of the X-ray brightest AGN, MCG+8-11-11. These data were complemented with the 54-month Swift BAT spectrum, allowing us to perform a broad-band fit in the 0.6-150 keV range. The fits performed in the 0.6-10 keV band give consistent results with respect to a previous XMM-Newton observation, i.e. the lack of a soft excess, warm absorption along the line of sight, a large Compton reflection component (R~1) and the absence of a relativistic component of the neutral iron K$\alpha$ emission line. However, when the PIN and Swift BAT data are included, the reflection amount drops significantly (R~0.2-0.3), and a relativistic iron line is required, the latter confirmed by a phenomenological analysis in a restricted energy band (3-10 keV). When a self-consistent model is applied to the whole broadband data, the observed reflection component appears to be all associated to the relativistic component of the iron K$\alpha$ line. The resulting scenario, though strongly model-dependent, requires that all the reprocessing spectral components from Compton-thick material must be associated to the accretion disc, and no evidence for the classical pc-scale torus is found. The narrow core of the neutral iron K$\alpha$ line is therefore produced in a Compton-thin material, like the BLR, similarly to what found in another Seyfert galaxy, NGC7213, but with the notable difference that MCG+8-11-11 presents spectral signatures from an accretion disc. The very low accretion rate of NGC7213 could explain the lack of relativistic signatures in its spectrum, but the absence of the torus in both sources is more difficult to explain, since their luminosities are comparable, and their accretion rates are completely different.Comment: 8 pages, 6 figure, accepted for publication in Astronomy and Astrophysic

Simple model for quantum general relativity from loop quantum gravity

New progress in loop gravity has lead to a simple model of `general-covariant quantum field theory'. I sum up the definition of the model in self-contained form, in terms accessible to those outside the subfield. I emphasize its formulation as a generalized topological quantum field theory with an infinite number of degrees of freedom, and its relation to lattice theory. I list the indications supporting the conjecture that the model is related to general relativity and UV finite.Comment: 8 pages, 3 figure

Single Spin Asymmetries in Semi-Inclusive Electroproduction: Access to Transversity

We discuss the quark transversity distribution function and a possible way to access it through the measurement of single spin azimuthal asymmetry in semi-inclusive single pion electroproduction on a transversely polarized target.Comment: 5 pages, Latex using aipproc.sty (included), to appear in proceedings of "Second Workshop on Physics with an Electron Polarized Light Ion Collider", Sept. 14-16, 2000, MIT, Cambridge, US

Correlation functions in a cascading N=1 gauge theory from supergravity

We study fluctuations around the warped conifold supergravity solution of Klebanov and Tseytlin [hep-th/0002159], known to be dual to a cascading N=1 gauge theory. Although this supergravity background is not asymptotically AdS, corresponding to a non-conformal field theory, it is possible to apply the usual methods of AdS/CFT duality to extract the high energy behavior of field theory correlators by solving linearized equations of motion for fluctuations around the background. We consider the Goldstone vector dual to the anomalous R-symmetry current and compute its mass, which exactly matches the general prediction of [hep-th/0009156]. We find the high energy 2-point functions for the R-current and two other vectors. As expected, the R-current 2-point function has a longitudinal part because R-symmetry is broken. We also calculate the high energy 2-point function of the energy-momentum tensor from fluctuations of modes in the graviton sector. This 2-point function has a trace part corresponding to broken conformal symmetry.Comment: JHEP, 29 page