D. Zanon

Four-Loop β-Function for the N = 1 And N = 2 Supersymmetric Non-Linear Sigma Model In Two Dimensions

A superspace calculation of the four-loop βT-function is presented for two-dimensional N = 1, 2 supersymmetric non-linear αG-models. It is concluded that besides the one-loop contribution which vanishes on Ricci-flat manifolds, the βT-function receives four-loop contributions which do not vanish in the Ricci-flat case. Implications for the superstring are discussed.

Two-Dimensional Supersymmetric Sigma Models on Ricci Flat Kahler Manifolds Are Not Finite

Abstract We present an explicit superspace calculation of the quantum corrections, up to four-loop order in perturbation theory, for the N = 2 non-linear σ-model in two-dimensions. At the four-loop level we find a non-zero contribution to the β-function which does not vanish on a Ricci-flat Kahler manifold. We discuss the relevance of this result in connection with superstring compactification.

Four-loop divergences for the N=1 supersymmetric non-linear sigma-model in two dimensions

Abstract We describe a calculation of the four-loop β-function for the two-dimensional N=1 supersymmetric nonlinear σ-model defined on a general reimannian manifold. When restricted to Kahler geometry, the result agrees with the previously calculated one for the N=2 σ-model. The four-loop divergence does not vanish on Ricci-flat manifolds nor on locally symmetric spaces.

Sigma-model superstring corrections to the Einstein-Hilbert action

Abstract The action is constructed whose equations of motion coincide with the condition of vanishing four-loop β-function for the N =1 supersymmetric non-linear σ-model in two dimensions. It is shown that it represents the correct generalization of the corresponding effective action derived from the four-graviton scattering amplitude for type II superstrings.

The structure of UV divergences in SS YM theories

Using the background-field method, covariant supergraphs and infrared subtraction techniques we analyse the structure of the higher-loop ultraviolet divergences in supersymmetric Yang-Mills theories. We show that in regularization by dimensional reduction they are given by a specific gauge invariant term constructed outof the vector connection and that they can be obtained by analyzing a special subset of all possible supergraphs. From the structure of the divergences we are able to conclude that in supersymmetric theories if the self-energies of the quantum fields in the presence of the background are finite up to L loops the YM background effective action is finite at (L + 1) loops.

Covariant supergraphs: (I). Yang-Mills theory

Abstract We describe covariant D -algebra methods for the evaluation of supergraphs in supersymmetric Yang-Mills theories. These methods lead to simplifications in the evaluation of higher-loop contributions.

Five-loop divergences for the N = 2 supersymmetric non-linear sigma-model

We present a five-loop calculation of the corrections to the Kahler potential for the N = 2 supersymmetric non-linear σ-model in two dimensions. Although, in dimensional regularization and minimal subtraction a 1/e divergence is present, it can in fact be completely removed by considering conventional subtraction ambiguities associated with lower-loop divergences. We conclude that there is no genuine five-loop contribution to the N = 2 gravitational β-function.

Two-loop β-functions and low-energy string effective action for the two-dimensional bosonic non-linear σ-model with a Wess-Zumino-Witten term

Abstract We compute the two-loop β -function for the two-dimensional bosonic non-linear σ -model with a Wess-Zumino-Witten term. It satisfies an integrability condition which leads to a low-energy effective action relevant for string scattering amplitudes up to quartic terms in the antisymmetric tensor field.

The supercurrent and the Adler-Bardeen theorem

Abstract When supersymmetric theories are regularized by dimensional reduction in superspace the supercurrent is a n-vector and the breaking of superconformal invariance by the regularization gives rise to supertrace anomalies proportional to the β-function. We construct the composite renormalized operator that describes it and study its properties. We construct a distinct four-dimensional composite operator and show that its first component satisfies the Adler-Bardeen theorem. Our results are based on explicit calculations through two-loop order for both the Wess-Zumino model and SSYM, using the background field method and covariant supergraphs.

INFRARED DIVERGENCES AND A NON-LOCAL GAUGE FOR SUPERSPACE YANG-MILLS THEORY

Abstract The usual superspace approach to supersymmetric gauge theories suffers from problems with infrared divergences which greatly complicate multiloop calculations. We eliminate these divergences by introducing a non-local gauge-fixing term. In the background field method this term leads to unusual quantum-background interactions. Functional methods are presented for dealing with these interactions. As an example we compute the two-loop Yang-Mills β-function using the background field method in superspace. We also show how a non-local gauge can be used in ordinary, non-supersymmetric Yang-Mills theory.