Marcus T. Grisaru

Improved methods for supergraphs

We introduce some new techniques into superfield perturbation theory which allow considerable simplifications in calculations. As a result, we show that all contributions to the effective action can be written as integrals over a single d4θ. We also give the background group field formalism for supersymmetric non-abelian gauge theories. To illustrate our methods, we give examples of loop calculations: in particular, we show that in O(4) extended supersymmetric non-abelian gauge theories all one-loop propagator corrections cancel identically (both infinite and finite parts) and that these theories, at one loop, are finite and have no renormalizations (in the Fermi-Feynman gauge).

Soft Breaking of Supersymmetry

Using superfield methods we discuss systematically explicit soft breaking of global supersymmetry. We find that, in a component field language, dimension-two operators are soft while, in general, dimension-three operators are not and introduce quadratic divergences not present in the unbroken theory. At the one-loop level we give a parallel discussion based on the effective potential.

Non-perturbative formulas for central functions of supersymmetric gauge theories

Abstract For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N = 1 supersymmetric gauge theory. Exact, explicit formulas for SU(Nc) gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality aUV − aIR > 0. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the c-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.

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.

Perturbative computation of glueball superpotentials

Abstract Using N =1 superspace techniques in four dimensions we show how to perturbatively compute the superpotential generated for the glueball superfield upon integrating out massive charged fields. The technique applies to arbitrary gauge groups and representations. Moreover, we show that for U ( N ) gauge theories admitting a large N expansion the computation dramatically simplifies and we prove the validity of the recently proposed recipe for computation of this quantity in terms of planar diagrams of matrix integrals.

Some properties of scattering amplitudes in supersymmetric theories

Properties of S-matrix amplitudes are investigated in theories invariant under global supersymmetry transformations. Many amplitudes are related to each other by supersymmetry and many others have to vanish. In particular a general helicity conservation law holds.

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.

Supergraphity. 2. Manifestly Covariant Rules and Higher Loop Finiteness

Abstract We continue our discussion of the background field formalism in supersymmetric theories, deriving new covariant Feynman rules for chiral superfields. As a result, we obtain improved power-counting rules for both simple and extended supersymmetry which can be used to make the following statements: If the corresponding extended superfield formalism exist, (a) N=2 supersymmetric Yang-Mills theory is finite beyond one loop, (b) N=4 Yang-Mills is finite at all loops, and (c) N=8 supergravity is finite through six loops. We also find that in simple super-Yang-Mills the radiative corrections to the Fayet-Iliopoulos (“D”) term, which are known to vanish for higher loops, also vanish automatically at one loop for arbitrary couplings.