Kostas Skenderis

Loop calculations in quantum-mechanical non-linear sigma models☆

Abstract By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved spacetime. Although the prescription how to deal with the products of distributions that appear in the computation of Feynman diagrams in configuration space is surprising, this prescription follows unambiguously from the discretized path integral. We check our results by an explicit two-loop calculation.

LOOP CALCULATIONS IN QUANTUM MECHANICAL NON-LINEAR SIGMA MODELS WITH FERMIONS AND APPLICATIONS TO ANOMALIES

Abstract We construct the path integral for one-dimensional non-linear sigma models, starting from a given Hamiltonian operator and states in a Hilbert space. By explicit evaluation of the discretized propagators and vertices we find the correct Feynman rules which differ from those often assumed. These rules, which we previously derived in bosonic systems, are now extended to fermionic systems. We then generalize the work of Alvarez-Gaume and Witten by developing a framework to compute anomalies of an n-dimensional quantum field theory by evaluating perturbatively a corresponding quantum mechanical path integral. Finally, we apply this formalism to various chiral and trace anomalies, and solve a series of technical problems: (i) the correct treatment of Majorana fermions in path integrals with coherent states (the methods of fermion doubling and fermion halving yield equivalent results when used in applications to anomalies), (ii) a complete path integral treatment of the ghost sector of chiral Yang-Mills anomalies, (iii) a complete path integral treatment of trace anomalies, (iv) the supersymmetric extension of the Van Vleck determinant, and (v) a derivation of the spin - 3 2 Jacobian of Alvarez-Gaume and Witten for Lorentz anomalies.

Covariant computation of the low-energy effective action of the heterotic superstring

We derive the low-energy effective action of the heterotic superstring in superspace. This is achieved by coupling the covariantly quantized Green-Schwarz superstring of Berkovits to a curved background and requiring that the sigma model has superconformal invariance at tree level and at one loop in α′. Tree level superconformal invariance yields the complete supergravity algebra, and one-loop superconformal invariance the equations of motion of the low energy theory. The resulting low-energy theory is old-minimal supergravity coupled to a tensor multiplet. The dilation is part of the compensator multiplet.

On the renormalizability and unitarity of the Curci-Ferrari model for massive vector bosons

Abstract We prove the renormalizability of the Curci-Ferrari model with and without auxiliary fields using BRST methods. In both cases we find five Z factors instead of three. We verify our results by explicit one-loop calculations. We determine a set of generators for the “physical states”, many of which have negative norm. Supersymmetrization is considered.

Target space supersymmetric sigma model techniques

We briefly review the covariant formulation of the Green-Schwarz superstring by Berkovits, and describe how a detailed tree-level and one-loop analysis of this model leads, for the first time, to a derivation of the low-energy effective action of the heterotic superstring while keeping target-space supersymmetry manifest. The resulting low-energy theory is old-minimal supergravity coupled to tensor multiplet. The dilaton is part of the compensator multiplet.

Background gauge invariance in the anti-field formalism for theories with open gauge algebras

We show that any BRST-invariant quantum action with open or closed gauge algebra has a corresponding local background gauge invariance. If the BRST symmetry is anomalous, but the anomaly can be removed in the anti-field formalism, then the effective action possesses a local background gauge invariance. The presence of anti-fields (BRST sources) is necessary. As an example we analyse chiral gravity.

TARGET SPACE SUPERSYMMETRIC SIGMA MODEL TECHNIQUES

We briefly review the covariant formulation of the Green-Schwarz superstring by Berkovits, and describe how a detailed tree-level and one-loop analysis of this model leads, for the first time, to a derivation of the low-energy effective action of the heterotic superstring while keeping target-space supersymmetry manifest. The resulting low-energy theory is old-minimal supergravity coupled to tensor multiplet. The dilaton is part of the compensator multiplet.