Necessary and sufficient conditions for all order vanishing β-functions in supersymmetric Yang-Mills theories

If the matter self-couplings in SYM theories are certain uniquely determined power series of the coupling then it is necessary and sufficient, for the vanishing of all β-functions to all orders, that the gauge β-function and the anomalous dimensions of the matter fields vanish at the one-loop order.     

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

Generalized symmetries of an N=1 supersymmetric Boiti–Leon–Manna–Pempinelli system

The formal series symmetry approach(FSSA), a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the N= 1 supersymmetric Boiti–Leon–Manna–Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely many generalized symmetries with an arbitrary function f(t). Some interesting special cases of symmetry algebras are presented, including a limit case f(t) = 1 related to the commutativity of higher order generalized symmetries.     

An exact identity for σ-model renormalisation β-functions

An alternative derivation of the generalised integrability condition for conformal invariance of Curi and Paffuti is given. In the torsion-free case the perturbation series can be summed up showing that the equation relates at most third derivatives of the β- functions.     

Three-loop β-functions for the superstring and heterotic string

The β-function for the (1,1) superstring is calculated explicitly up to three loops, using two different choices of the fermion quantum field. In both cases the bosonic contribution is exactly cancelled by the fermionic contribution. The calculation is repeated for the heterotic string and the non-vanishing β-function is shown to be compatible with an O(α′²) effective action in which there are no terms cubic in the Riemann tensor- or gauge-field strength. A renormalization group equation for the gauge field is constructed and its β-function is shown to vanish at the two-loop level.     

Exact β-Function in Abelian and non-Abelian $${\cal N} = 1$$ N = 1 Supersymmetric Gauge Models and Its Analogy with the QCD β-Function in the C-scheme

JETP Letters - For $${\cal N} = 1$$ supersymmetric Yang—Mills theory without matter it is demonstrated that there is a class of renormalization schemes, in which the exact Novikov, Shifman,...     

Finiteness of Ricci flatN=2 supersymmetric σ-models

We study the ultraviolet behavior of two dimensional supersymmetric non-linear -models with target space an arbitrary Kähler manifoldM, so that the models areN=2 supersymmetric. We point out that these models have an additional fermionic axial symmetry if and only if the metric onM is Ricci flat. We show that the preservation of this symmetry in perturbation theory implies that both bare and renormalized metrics onM are Ricci flat. Combining this result with the constraint ofN=2 supersymmetry requiring that all counter-terms to the metric beyond one-loop order be cohomologically trivial, we argue thatN=2 models defined on Ricci flat Kähler manifolds are on-shell ultraviolet finite to all orders of perturbation theory.     

Spin and pseudospin symmetries of the Dirac equation with shifted Hulthe′n potential using supersymmetric quantum mechanics

In this paper, we obtain approximate analytical solutions of the Dirac equation for the shifted Hulthe′n potential within the framework of spin and pseudospin symmetry limits for arbitrary spin–orbit quantum number κ using the supersymmetry quantum mechanics. The energy eigenvalues and the corresponding Dirac wave functions are obtained in closed forms.     

Spin and pseudospin symmetries of the Dirac equation with shifted Hulthén potential using supersymmetric quantum mechanics

In this paper, we obtain approximate analytical solutions of the Dirac equation for the shifted Hulthén potential within the framework of spin and pseudospin symmetry limits for arbitrary spin–orbit quantum number κ using the supersymmetry quantum mechanics. The energy eigenvalues and the corresponding Dirac wave functions are obtained in closed forms.     

A heterotic N=2 string with space–time supersymmetry

We reconsider the issue of embedding space–time fermions into the four-dimensional N=2 worldsheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry.     

Locally supersymmetric σ-model with Wess-Zumino term in two dimensions and critical dimensions for strings

We construct an N = 1 locally supersymmetric σ-model with a Wess-Zumino term coupled to supergravity in two dimensions. If one takes the σ-model manifold to be the product of d-dimensional Minkowski space M^d and a group manifold G, and if the radius of G is quantized in appropriate units of the string tension, then the model describes a Neveu-Schwarz-Ramond (NSR)-type string moving on M_d × G. (Our model generalizes earlier work of refs. [1,2] which do not contain a Wess-Zumino term and that of refs. [5,6] which is not locally supersymmetric.) The zweibein and the gravitino field equations yield constraints which generalize those of the NSR model to the case of a non-abelian group manifold. In particular, the fermionic constraint contains a new term trilinear in the fermionic fields. We quantize the theory in the light-cone gauge and derive the critical dimensions. We compute the mass spectrum of a closed string moving on M_d × G and show that massless fermions do not arise for non-abelian G for the spinning string, in agreement with the result of Friedan and Shenker [22].     

Manifestly supersymmetric O(α′) superstring corrections in new D = 10, N = 1 supergravity Yang-Mills theory

A systematic procedure in superspace to derive the O(α′) tree-level superstring corrections to the new D = 10, N = 1 (dual) supergravity Yang-Mills system is established. All the tree-level O(α′) corrections in the closed supersymmetry transformation laws are presented explicitly. These O(α′) corrections are regarded as a generalization of “matter” couplings in D = 10, N = 1 supergravity. The advantage of the superspace approach, based on superspace Bianchi identities, in comparison with the component formulation is elucidated. This new method is applicable to all anomaly-free D ⩽ 10 non-maximal supergravity theories, which utilize the Green-Schwarz mechanism. It also provides a way of introducing general higher-order powers of curvature tensors in D ⩽ 10 supergravity theories.