The Ward Identity from the Background Field Dependence of the Effective Action

The dependence of the effective action for gauge theories on the background field obeys an exact identity. We argue that for Abelian theories the Ward identity follows from the more general background field identity. This observation is particularly relevant for the anomalous Ward identity valid for gauge theories with an effective infrared cutoff as used for flow equations.Comment: 8 page

Wilson Renormalization Group for Supersymmetric Gauge Theories and Gauge Anomalies

We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless Wess-Zumino model and deduce its perturbative expansion. We then consider N=1 supersymmetric Yang-Mills and show that the local gauge symmetry -broken by the regularization- can be recovered by a suitable choice of the RG flow boundary conditions. We restrict our analysis to the first loop, the generalization to higher loops presenting no difficulty due to the iterative nature of the procedure. Furthermore, adding matter fields, we reproduce the one-loop supersymmetric chiral anomaly to the second order in the vector field.Comment: 22 pages, 1 Postscript figure, uses amssym

Gauge invariance and background field formalism in the exact renormalisation group

We discuss gauge symmetry and Ward-Takahashi identities for Wilsonian flows in pure Yang-Mills theories. The background field formalism is used for the construction of a gauge invariant effective action. The symmetries of the effective action under gauge transformations for both the gauge field and the auxiliary background field are separately evaluated. We examine how the symmetry properties of the full theory are restored in the limit where the cut-off is removed.Comment: version to be published in PL

Topological invariants in interacting Quantum Spin Hall: a Cluster Perturbation Theory approach

Using Cluster Perturbation Theory we calculate Green's functions, quasi-particle energies and topological invariants for interacting electrons on a 2-D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This allows to define the parameter range (Hubbard U vs spin-orbit coupling) where the 2D system behaves as a trivial insulator or Quantum Spin Hall insulator. This behavior is confirmed by the existence of gapless quasi-particle states in honeycomb ribbons. We have discussed the importance of the cluster symmetry and the effects of the lack of full translation symmetry typical of CPT and of most Quantum Cluster approaches. Comments on the limits of applicability of the method are also provided.Comment: 7 pages, 7 figures: discussion improved, one figure added, references updated. Matches version published in New J. Phy

Bulk Aluminum at High Pressure: A First-Principles Study

The behavior of metals at high pressure is of great importance to the fields of shock physics, geophysics, astrophysics, and nuclear materials. In order to further understand the properties of metals at high pressures we studied the equation of state of aluminum using first-principles techniques up to 2500 GPa, pressures within reach of the planned L.L.N.L. National Ignition Facility. Our simulations use density-functional theory and density-functional perturbation theory in the generalized gradient approximation at 0K. We found core overlaps to become relevant beyond pressures of 1200 GPa. The equations of state for three phases (fcc, bcc, and hcp) were calculated predicting the fcc-hcp, fcc-bcc, and hcp-bcc transitions to occur at 215 GPa, 307 GPa, and 435 GPa respectively. From the phonon dispersions at increasing pressure, we predict a softening of the lowest transverse acoustic vibrational mode along the [110] direction, which corresponds to a Born instability of the fcc phase at 725 GPa.Comment: 4 pages, 5 figures, accepted to Phys. Rev. B as a Brief Report. This version has update many figures. Moreover we provided updated and more accurate numbers based on further in-depth analyses of potential computational error

Sex hormones in allergic conjunctivitis: altered levels of circulating androgens and estrogens in children and adolescents with vernal keratoconjunctivitis

PURPOSE: Vernal keratoconjunctivitis (VKC) is a chronic allergic disease mainly affecting boys in prepubertal age and usually recovering after puberty. To evaluate a possible role of sex hormones in VKC, serum levels of sex hormones in children and adolescents with VKC were assessed. METHODS: 12 prepubertal and 7 early pubertal boys with active VKC and 6 male patients with VKC in remission phase at late pubertal age and 48 healthy age and sex-matched subjects were included. Serum concentration of estrone, 17 beta-estradiol, dehydroepiandrosterone-sulfate, total testosterone and free testosterone, dihydrotestosterone (DHT), cortisol, delta-4-androstenedione, follicle-stimulating hormone, luteinizing hormone, and sex-hormones binding globuline (SHBG) were evaluated. RESULTS: Serum levels of Estrone were significantly increased in all groups of patients with VKC when compared to healthy controls (P < 0.001). Prepubertal and early pubertal VKC showed a significant decrease in DHT (P = 0.007 and P = 0.028, resp.) and SHBG (P = 0.01 and P = 0.002, resp.) when compared to controls and serum levels of SHBG were increased in late pubertal VKC in remission phase (P = 0.007). CONCLUSIONS AND RELEVANCE: VKC patients have different circulating sex hormone levels in different phases of the disease and when compared to nonallergic subjects. These findings suggest a role played by sex hormones in the pathogenesis and/or activity of VKC

Chiral gauge theories and anomalies in the Wilson renormalization group approach

We extend the Wilson renormalization group (RG) formulation to chiral gauge theories and show that local gauge symmetry can be implemented by a suitable choice of the RG flow boundary conditions. Since the space-time dimension is four, there is no ambiguity in handling the matrix \g_5 and left and right fermions are not coupled. As a result the ultraviolet action contains all possible globally chiral invariant interactions. Nevertheless, the correct chiral anomaly is reproduced.Comment: 16 pages, 4 figures, LaTex, uses epsfig, amssym

Scheme Independence at First Order Phase Transitions and the Renormalisation Group

We analyse approximate solutions to an exact renormalisation group equation with particular emphasis on their dependence on the regularisation scheme, which is kept arbitrary. Physical quantities related to the coarse-grained potential of scalar QED display universal behaviour for strongly first-order phase transitions. Only subleading corrections depend on the regularisation scheme and are suppressed by a sufficiently large UV scale. We calculate the relevant coarse-graining scale and give a condition for the applicability of Langer's theory of bubble nucleation.Comment: 12 pages, LaTeX, 4 figures included (needs epsfig.sty), two equations added, typo correcte

Exact Flow Equations and the U(1)-Problem

The effective action of a SU(N)-gauge theory coupled to fermions is evaluated at a large infrared cut-off scale k within the path integral approach. The gauge field measure includes topologically non-trivial configurations (instantons). Due to the explicit infrared regularisation there are no gauge field zero modes. The Dirac operator of instanton configurations shows a zero mode even after the infrared regularisation, which leads to U_A(1)-violating terms in the effective action. These terms are calculated in the limit of large scales k.Comment: 22 pages, latex, no figures, with stylistic changes and some arguments streamlined, typos corrected, References added, to appear in Phys. Rev.