Pure Spinor Integration from the Collating Formula

We use the technique developed by Becchi and Imbimbo to construct a well-defined BRST-invariant path integral formulation of pure spinor amplitudes. The space of pure spinors can be viewed from the algebraic geometry point of view as a collection of open sets where the constraints can be solved and a free independent set of variables can be defined. On the intersections of those open sets, the functional measure jumps and one has to add boundary terms to construct a well-defined path integral. The result is the definition of the pure spinor integration measure constructed in term of differential forms on each single patch.Comment: 22 page

Constructive algebraic renormalization of the abelian Higgs-Kibble model

We propose an algorithm, based on Algebraic Renormalization, that allows the restoration of Slavnov-Taylor invariance at every order of perturbation expansion for an anomaly-free BRS invariant gauge theory. The counterterms are explicitly constructed in terms of a set of one-particle-irreducible Feynman amplitudes evaluated at zero momentum (and derivatives of them). The approach is here discussed in the case of the abelian Higgs-Kibble model, where the zero momentum limit can be safely performed. The normalization conditions are imposed by means of the Slavnov-Taylor invariants and are chosen in order to simplify the calculation of the counterterms. In particular within this model all counterterms involving BRS external sources (anti-fields) can be put to zero with the exception of the fermion sector.Comment: Jul, 1998, 31 page

Search for bbbˉbˉbb\bar{b}\bar{b} tetraquark decays in 4 muons, B+B−B^{+} B^{-}, B0Bˉ0B^0 \bar{B}^0 and Bs0Bˉs0B_s^0 \bar{B}_s^0 channels at LHC

We perform a quantitative analysis of the $bb\bar{b}\bar{b}$ tetraquark decays into hidden- and open-bottom mesons and calculate, for the first time, the $bb\bar{b}\bar{b}$ tetraquark total decay width. On the basis of our results, we propose the $bb\bar{b}\bar{b} \to B^{+} B^{-} (B^0 \bar{B}^0) (B_s^0 \bar{B}_s^0) \to l^{+} l^{-}+\text{X}$ decays as the most suitable channels to observe the $bb\bar{b}\bar{b}$ tetraquark states, since the calculated two-lepton cross section upper limit, $\simeq 39$ fb, is so large as to be potentially detectable with the 2018 LHCb sensitivity, paving the way to the observation of the $bb\bar{b}\bar{b}$ tetraquark in the future LHCb upgrade. The $4\mu$ signal for the ground state, $J^{PC}=0^{++}$, is likely to be too small even for the upgraded LHCb, but it may not be hopeless for the $J^{PC}=2^{++}$ fully-bottom state.Comment: 11 pages, 1 figur

The Complexity of Ising Spin Glasses

We compute the complexity (logarithm of the number of TAP states) associated with minima and index-one saddle points of the TAP free energy. Higher-index saddles have smaller complexities. The two leading complexities are equal, consistent with the Morse theorem on the total number of turning points, and have the value given in [A. J. Bray and M. A. Moore, J. Phys. C 13, L469 (1980)]. In the thermodynamic limit, TAP states of all free energies become marginally stable.Comment: Typos correcte

From Koszul duality to Poincar\'e duality

We discuss the notion of Poincar\'e duality for graded algebras and its connections with the Koszul duality for quadratic Koszul algebras. The relevance of the Poincar\'e duality is pointed out for the existence of twisted potentials associated to Koszul algebras as well as for the extraction of a good generalization of Lie algebras among the quadratic-linear algebras.Comment: Dedicated to Raymond Stora. 27 page

BRS Cohomology of the Supertranslations in D=4

Supersymmetry transformations are a kind of square root of spacetime translations. The corresponding Lie superalgebra always contains the supertranslation operator $\delta = c^{\alpha} \sigma^{\mu}_{\alpha \dot \beta} {\overline c}^{\dot \beta} (\epsilon^{\mu})^{\dag}$. We find that the cohomology of this operator depends on a spin-orbit coupling in an SU(2) group and has a quite complicated structure. This spin-orbit type coupling will turn out to be basic in the cohomology of supersymmetric field theories in general.Comment: 14 pages, CTP-TAMU-13/9

Free Abelian 2-Form Gauge Theory: BRST Approach

We discuss various symmetry properties of the Lagrangian density of a four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge theory is endowed with a Curci-Ferrari type condition which happens to be a key signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the above condition that the nilpotent BRST and anti-BRST symmetries of the theory are found to be absolutely anticommuting in nature. For our present 2-form gauge theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry properties of the Lagrangian densities and derive the corresponding conserved charges. The algebraic structure, obeyed by the above conserved charges, is deduced and the constraint analysis is performed with the help of the physicality criteria where the conserved and nilpotent (anti-)BRST charges play completely independent roles. These physicality conditions lead to the derivation of the above Curci-Ferrari type restriction, within the framework of BRST formalism, from the constraint analysis.Comment: LaTeX file, 21 pages, journal referenc

Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory

We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the four (3 + 1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated (B \wedge F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci-Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion that are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-) BRST symmetry transformations.Comment: LaTeX file, 22 pages, journal versio

Film cooling adiabatic effectiveness measurements of pressure side trailing edge cooling configurations

Nowadays total inlet temperature of gas turbine is far above the permissible metal temperature; as a consequence, advanced cooling techniques must be applied to protect from thermal stresses, oxidation and corrosion the components located in the high pressure stages, such as the blade trailing edge. A suitable design of the cooling system for the trailing edge has to cope with geometric constraints and aerodynamic demands; state-of-the-art of cooling concepts often use film cooling on blade pressure side: the air taken from last compressor stages is ejected through discrete holes or slots to provide a cold layer between hot mainstream and the blade surface. With the goal of ensuring a satisfactory lifetime of blades, the design of efficient trailing edge film cooling schemes and, moreover, the possibility to check carefully their behavior, are hence necessary to guarantee an appropriate metal temperature distribution. For this purpose an experimental survey was carried out to investigate the film covering performance of different pressure side trailing edge cooling systems for turbine blades. The experimental test section consists of a scaled-up trailing edge model installed in an open loop suction type test rig. Measurements of adiabatic effectiveness distributions were carried out on three trailing edge cooling system configurations. The baseline geometry is composed by inclined slots separated by elongated pedestals; the second geometry shares the same cutback configuration, with an additional row of circular film cooling holes located upstream; the third model is equipped with three rows of in-line film cooling holes. Experiments have been performed at nearly ambient conditions imposing several blowing ratio values and using carbon dioxide as coolant in order to reproduce a density ratio close to the engine conditions (DR=1.52). To extend the validity of the survey a comparison between adiabatic effectiveness measurements and a prediction by correlative approach was performed to compare the experimental results with 1D methodologies