UV/IR mixing and the Goldstone theorem in noncommutative field theory

Noncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, $\lambda_1$ and $\lambda_2$, associated to the two noncommutative extensions $\phi^*\star\phi\star\phi^*\star\phi$ and $\phi^*\star\phi^*\star\phi\star\phi$ of the interaction term $|\phi|^4$ on commutative spacetime. It is shown that the symmetric phase is one-loop renormalizable for all $\lambda_1$ and $\lambda_2$ compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if $\lambda_2=0$, a condition required by the Ward identities for global U(1) invariance. Explicit expressions for the noncommutative IR singularities in the 1PI Green functions of both phases are given. They show that UV/IR duality does not hold for any of the phases and that the broken phase is free of quadratic noncommutative IR singularities. More remarkably, the pion selfenergy does not have noncommutative IR singularities at all, which proves essential to formulate the Goldstone theorem at one loop for all values of the spacetime noncommutativity parameter $\theta$.Comment: 30 pages, 7 eps figures. V2: references adde

Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1)

U(1) gauge theory on non-commutative Minkowski space-time in the Feynman-'t Hooft background gauge is studied. In particular, UV divergences and non-commutative IR divergent contributions to the two, three and four-point functions are explicitly computed at one loop. We show that the negative sign of the beta function results from paramagnetism --producing UV charge anti-screening-- prevailing over diamagnetism --giving rise toUV charge screening. This dominance in the field theory setting corresponds to tachyon magnification dominance in the string theory framework. Our calculations provide an explicit realization of UV/IR mixing and lead to an IR renormalization of the coupling constant, where now paramagnetic contributions produce screening and diamagnetic contributions anti-screening.Comment: 39 pages, 7 eps figures; typos corrected, few comments adde

General Properties of Noncommutative Field Theories

In this paper we study general properties of noncommutative field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. We analyze the extension of the Wightman axioms to this context and explore their consequences, in particular we present a proof of the CPT theorem for theories with space-space noncommutativity. We analyze as well questions associated to the spin-statistics connections, and show that noncommutative N=4, U(1) gauge theory can be softly broken to N=0 satisfying the axioms and providing an example where the Wilsonian low energy effective action can be constructed without UV/IR problems, after a judicious choice of soft breaking parameters is made. We also assess the phenomenological prospects of such a theory, which are in fact rather negative.Comment: 39 pages. LaTeX. 4 figures. Typos corrected. Comments and references added. To appear in Nuclear Physics

The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level

We show that U(N) Yang-Mills theory on noncommutative Minkowski space-time can be renormalized, in a BRS invariant way, at the one-loop level, by multiplicative dimensional renormalization of its coupling constant, its gauge parameter and its fields. It is shown that the Slavnov-Taylor equation, the gauge-fixing equation and the ghost equation hold, up to order $\hbar$, for the MS renormalized noncommutative U(N) Yang-Mills theory. We give the value of the pole part of every 1PI diagram which is UV divergent.Comment: Corrected typos. Version to appear in Nuclear Physics

Action principles, restoration of BRS symmetry and the renormalization group equation for chiral non-Abelian gauge theories in dimensional renormalization with a non-anticommuting γ5\gamma_5

The one-loop renormalization of a general chiral gauge theory without scalar and Majorana fields is fully worked out within Breitenlohner and Maison dimensional renormalization scheme. The coefficients of the anomalous terms introduced in the Slavnov-Taylor equations by the minimal subtraction algorithm are calculated and the asymmetric counterterms needed to restore the BRS symmetry, if the anomaly cancellation conditions are met, are computed. The renormalization group equation and its coefficients are worked out in the anomaly free case. The computations draw heavily from the existence of action principles and BRS cohomology theory.Comment: 86 pages, 14 figures, one table, plane te

Morita Duality and Large-N Limits

We study some dynamical aspects of gauge theories on noncommutative tori. We show that Morita duality, combined with the hypothesis of analyticity as a function of the noncommutativity parameter Theta, gives information about singular large-N limits of ordinary U(N) gauge theories, where the large-rank limit is correlated with the shrinking of a two-torus to zero size. We study some non-perturbative tests of the smoothness hypothesis with respect to Theta in theories with and without supersymmetry. In the supersymmetric case this is done by adapting Witten's index to the present situation, and in the nonsupersymmetric case by studying the dependence of energy levels on the instanton angle. We find that regularizations which restore supersymmetry at high energies seem to preserve Theta-smoothness whereas nonsupersymmetric asymptotically free theories seem to violate it. As a final application we use Morita duality to study a recent proposal of Susskind to use a noncommutative Chern-Simons gauge theory as an effective description of the Fractional Hall Effect. In particular we obtain an elegant derivation of Wen's topological order.Comment: 41 pages, Harvmac. Some corrections to section 6.3. Comments added on Hall Effec

Plasma fibronectin as a marker of sepsis

AbstractObjectives: To evaluate the value of plasma fibronectin (pFN) as a diagnostic marker of sepsis.Subjects and methods: Plasma FN was determined in patients showing sepsis-related symptoms who had blood cultures performed. These patients were assigned to one of two groups according to their clinical situation: (1) Clinical Septic Group: patients with sepsis according to American College of Chest Physicians/Society of Critical Care Medicine (ACCP/SCCM) criteria; (2) Fever Peak Group: patients who did not fulfil sufficient ACCP/SCCM criteria for sepsis. Two additional control groups were also established: (3) Non-infectious Diseases Control Group and (4) Healthy Control Group.Results: Plasma FN levels, microbiological and clinical data were compared among the different patient groups. For each group, the number of patients, median and mean pFN levels and the 95% confidence interval of the mean were: (1) n=43, 102mg/l, 122mg/l (100–144); (2) n=70, 185mg/l, 207mg/l (184–231); (3) n=22, 175mg/l, 181mg/l (151–211); and (4) n=22, 256mg/l, 261mg/l (229–292). Bonferroni’s test of multiple comparisons was able to detect a significant difference between pFN concentrations corresponding to the septic group, compared to the remaining groups (pANOVA<0.001).Conclusion: Plasma FN appears to act as a marker of sepsis in that patients showed diminished pFN levels. Along with other clinical and laboratory variables, the use of this marker would allow a rapid diagnosis of sepsis and limit the number of blood cultures to be processed and the number of antibiotic prescriptions, particularly when symptoms are insidious and diagnosis is doubtful. We propose further and more complex studies using a higher number of patients