Cohomology in the pure spinor formalism for the superstring

A manifestly super-Poincaré covariant formalism for the superstring has recently been constructed using a pure spinor variable. Unlike the covariant Green-Schwarz formalism, this new formalism is easily quantized with a BRST operator and tree-level scattering amplitudes have been evaluated in a manifestly covariant manner. In this paper, the cohomology of the BRST operator in the pure spinor formalism is shown to give the usual light-cone Green-Schwarz spectrum. Although the BRST operator does not directly involve the Virasoro constraint, this constraint emerges after expressing the pure spinor variable in terms of SO(8) variables.

Relating the RNS and pure spinor formalisms for the superstring

Recently, the superstring was covariantly quantized using the BRST-like operator Q = ∮ λαdα where λα is a pure spinor and dα are the fermionic Green-Schwarz constraints. By performing a field redefinition and a similarity transformation, this BRST-like operator is mapped to the sum of the Ramond-Neveu-Schwarz BRST operator and η0 ghost. This map is then used to relate physical vertex operators and tree amplitudes in the two formalisms. Furthermore, the map implies the existence of a b ghost in the pure spinor formalism which might be useful for loop amplitude computations.

Supersymmetric Born-Infeld from the pure spinor formalism of the open superstring

Classical BRST invariance in the pure spinor formalism for the open superstring is shown to imply the supersymmetric Born-Infeld equations of motion for the background fields. These equations are obtained by requiring that the left and right-moving BRST currents are equal on the worldsheet boundary in the presence of the background. The Born-Infeld equations are expressed in N = 1 D = 10 superspace and include all abelian contributions to the low-energy equations of motion, as well as the leading non-abelian contributions. © SISSA/ISAS 2003.

Relating a gluon mass scale to an infrared fixed point in pure gauge QCD

The condition for the global minimum of the vacuum energy for a non-Abelian gauge theory with a dynamically generated gauge boson mass scale which implies the existence of a nontrivial IR fixed point of the theory was shown. Thus, this vacuum energy depends on the dynamical masses through the nonperturbative propagators of the theory. The results show that the freezing of the QCD coupling constant observed in the calculations can be a natural consequence of the onset of a gluon mass scale, giving strong support to their claim.

Flat currents in the classical AdS5 × S5 pure spinor superstring

It is proven that the classical pure spinor superstring in an AdS 5 × S5 back-ground has a flat current depending on a continuous parameter. This generalizes the recent result of Bena, et al. for the classical Green-Schwarz superstring. © SISSA/ISAS 2004.

Conformal invariance of the pure spinor superstring in a curved background

It is shown that the pure spinor formulation of the heterotic superstring in a generic gravitational and super Yang-Mills background has vanishing one-loop beta functions. © SISSA/ISAS 2004.

Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring

A ten-dimensional super-Poincaré covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincaré covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and and to construct a suitable b ghost. A super-Poincaré covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N < 4, confirming the perturbative finiteness of superstring theory. One can also prove the Type IIB S-duality conjecture that R4 terms in the effective action receive no perturbative contributions above one loop. © SISSA/ISAS 2004.

Relating the Green-Schwarz and pure spinor formalisms for the superstring

Although it is not known how to covariantly quantize the Green-Schwarz (GS) superstring, there exists a semi-light-cone gauge choice in which the GS superstring can be quantized in a conformally invariant manner. In this paper, we prove that BRST quantization of the GS superstring in semi-light-cone gauge is equivalent to BRST quantization using the pure spinor formalism for the superstring © SISSA/ISAS 2005.

Spinodal decomposition in pure-gauge QCD

Spinodal decomposition in a model of pure-gauge SU(2) theory that incorporates a deconfinement phase transition is investigated by means of real-time lattice simulations of the fully nonlinear Ginzburg-Landau equation. Results are compared with a Glauber dynamical evolution using Monte Carlo simulations of pure-gauge lattice QCD. © 2005 American Institute of Physics.

Effect of thermal treatments on tensile strength of commercially cast pure titanium and Ti-6Al-4V alloys

Heating titanium structures is assumed to relieve tensions induced by the casting process as well as possibly optimizing some mechanical properties. The aim of this investigation was to evaluate the effect of thermal treatments on tensile strength of commercially pure titanium (CP Ti) and Ti-6Al-4V alloy. Thirty dumbbell rods, with diameters of 3.0 mm at the central segment and lengths of 42 mm, were cast for each metal using the Rematitan System. CP Ti and Ti-6Al-4V specimens were randomly divided into three groups of ten: a control group that received no thermal treatment and two test groups. One (T1) was heated at 750°C for 2 h and the other (T2) was annealed at 955°C for 1 h and aged at 620°C for 2 h. Tensile strength was measured with a universal testing machine (MTS model 810). Tensile strength means and standard deviations were statistically compared using a Kruskal-Wallis test at a α = 0.05 significance level. No statistically significant differences in tensile strength were observed among CP Ti groups. For the Ti-6Al-4V alloy, the control and T1 groups revealed statistically higher tensile strengths when compared to the T2 group, with no significant difference between the control and T1 groups. © 2005 Springer Science + Business Media, Inc.

Pure spinor formalism as an N ≤ 2 topological string

Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted ĉ ≤ 3 N ≤ 2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincaré covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action. © SISSA 2005.

Four-point one-loop amplitude computation in the pure spinor formalism

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism. © SISSA 2006.

Vickers hardness of cast commercially pure titanium and Ti-6Al-4V alloy submitted to heat treatments

The purpose of this study was to evaluate the effect of heat treatments on the Vickers hardness of commercially pure titanium and Ti-6Al-4V cast alloys. Six-millimeter-diameter cylindrical specimens were cast in a Rematitan System. Commercially pure titanium and Ti-6Al-4V alloy specimens were randomly assigned to 3 groups (n=10) that received the following heat treatments: control (no heat treatment); treatment 1 (T1): heating at 750°C for 2 h; and treatment 2 (T2): annealing at 955°C for 1 h and aging at 620°C for 2 h. After heat treatments, the specimens were embedded in acrylic resin and their surface was ground and polished and hardness was measured. Vickers hardness means (VHN) and standard deviations were analyzed statistically by Kruskal-Wallis test at 5% significance level. For commercially pure titanium, Vickers hardness means of group T2 (259.90 VHN) was significantly higher than those of the other groups (control - 200.26 VHN and T1 - 202.23 VHN), which presented similar hardness means to each other (p>0.05). For Ti-6Al-4V alloy, statistically significant differences were observed among the three groups: T2 (369.08 VHN), T1 (351.94 VHN) and control (340.51 VHN) (p<0.05). The results demonstrated different hardness of CP Ti and Ti-6Al-4V when different heat treatments were used. For CP Ti, VHN means of T2 group was remarkably higher than those of control and T1 group, which showed similar VHN means to each other. For Ti-6Al-4V alloy, however, VHN means recorded for each group may be presented as follows: T2>T1>control.

One-loop conformal invariance of the type II pure spinor superstring in a curved background

We compute the one-loop beta functions for the Type II superstring using the pure spinor formalism in a generic supergravity background. It is known that the classical pure spinor BRST symmetry puts the background fields on-shell. In this paper we show that the one-loop beta functions vanish as a consequence of the classical BRST symmetry of the action. © SISSA 2007.

Langevin dynamics of the pure SU(2) deconfining transition

We investigate the dissipative real-time evolution of the order parameter for the deconfining transition in the pure SU(2) gauge theory. The approach to equilibrium after a quench to temperatures well above the critical one is described by a Langevin equation. To fix completely the Markovian Langevin dynamics we choose the dissipation coefficient, that is a function of the temperature, guided by preliminary Monte Carlo simulations for various temperatures. Assuming a relationship between Monte Carlo time and real time, we estimate the delay in thermalization brought about by dissipation and noise. © 2007 The American Physical Society.