Nilpotent invariants in N=4 SYM

It is shown that there are no nilpotent invariants in N=4 analytic superspace for n≤4 points. It is argued that there is (at least) one such invariant for n=5 points which is not invariant under U(1)_Y. The consequences of these results are that the n=2 and 3 point correlation functions of the N=4 gauge-invariant operators which correspond to KK multiplets in AdS supergravity are given exactly by their tree level expressions, the 4 point correlation functions of such operators are invariant under U(1)_Y and correlation functions with n≥4 points have non-trivial dependence on the Yang-Mills coupling constant.     

N = 4 SYM low-energy effective action in N = 4 harmonic superspace

We apply the N = 4 harmonic superspace with USp(4) harmonic variables for describing the N = 4 SYM low-energy effective action. Scale invariance and gauge symmetry fix the leading term in the low-energy effective action uniquely, up to a constant. The value of the remaining constant can be fixed by the topological quantization condition for the Wess-Zumino term which is present in the component structure of this action.     

On-shell methods for form factors in N = 4 SYM and their applications

Form factors are quantities that involve both asymptotic on-shell states and gauge invariant operators. They provide a natural bridge between on-shell amplitudes and off-shell correlation functions of operators, thus allowing us to use modern on-shell amplitude techniques to probe into the off-shell side of quantum field theory. In particular, form factors have been successfully used in computing the cusp(soft) anomalous dimensions and anomalous dimensions of general local operators. This review is intended to provide a pedagogical introduction to some of these developments. We will first review some amplitudes background using four-point amplitudes as main examples. Then we generalize these techniques to form factors, including(1) tree-level form factors,(2) Sudakov form factor and infrared singularities, and(3) form factors of general operators and their anomalous dimensions. Although most examples we consider are inN= 4 super-Yang-Mill theory, the on-shell methods are universal and are expected to be applicable to general gauge theories.     

The property of maximal transcendentality for the universal anomalous dimension in the N = 4 SYM

We show the results for the universal anomalous dimension γ _uni(j) of Wilson twist-2 operators in the N = 4 Supersymmetric Yang-Mills theory.     

Counting dyons in N = 4 string theory

We present a microscopic index formula for the degeneracy of dyons in four-dimensional N = 4 string theory. This counting formula is manifestly symmetric under the duality group, and its asymptotic growth reproduces the macroscopic Bekenstein-Hawking entropy. We give a derivation of this result in terms of the type 11 five-brane compactified on K3, by assuming that its fluctuations are described by a closed string theory on its world-volume. We find that the degeneracies are given in terms of the denominator of a generalized super Kac-Moody algebra. We also discuss the correspondence of this result with the counting of D-brane states.     

All-order Finiteness in N = 1 SYM Theories: Criteria and Applications

As a motivation, we first recall the possible connection of electric-magnetic duality to finiteness in N = 1 super-Yang-Mills theories (SYM). Then, we present the criterion for all-order finiteness (i.e., vanishing of the β-functions at all orders) in N = 1 SYM. Finally, we apply this finiteness criterion to an SU(5) SGUT. The latter turns out to be all-order finite if one imposes additional symmetries.     

The property of maximal transcendentality: Calculation of anomalous dimensions in the N = 4 SYM and master integrals

We review results for the universal anomalous dimension γ _uni (j) of Wilson twist-2 operators in the N = 4 Supersymmetric Yang-Mills theory having the property of maximal transcendentality. It is shown that the similar property is ibserved in the results for master integrals.     

On quasi-self-dual fields in N=4 supersymmetric Yang-Mills theory

A general representation for a quasi-self-dual gauge field which is a generalization of the 't Hooft ansatz is obtained in the Euclidean conformally invariant Yang-Mills theory with a sextuplet of real scalar fields-the boson sector of N=4 supersymmetric Yang-Mills theory. The existence of an O(4)-symmetric quasi-self-dual solution in the region g ²>0 is proved. An explicit example of the quasi-self-dual instanton in the region g ²<0 is constructed.     

Minimally helicity violating,maximally simple scalar amplitudes in $ \mathcal{N} $ = 4 SYM

Journal of High Energy Physics - We reformulate classical electromagnetism as the statistical mechanics of lines of electric flux with dynamics described by the string action in four dimensions....     

Vanishing three-loop beta function in N = 4 supersymmetric Yang-Mills theory

We have calculated the beta function of the N = 4 supersymmetric Yang-Mills theory through three-loop order and find that it is zero. The calculation was performed using superspace techniques that also allowed the calculation of the complete three-loop chiral-multiplet propagator, which turned out to be quite simple. These results strongly support the speculations that the theory is finite order-by-order in perturbation theory.     

Gauge theory in deformed $$ \mathcal{N} $$ = (1, 1) superspace

We review the non-anticommutative Q-deformations of = (1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ∼ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective action. The text was submitted by the authors in English.     

Dijet production at large rapidity separation in N = 4 supersymmetric Yang-Mills theory

Ratios of azimuthal angle correlations between two jets produced at large rapidity separation are studied in the N = 4 maximally supersymmetric Yang-Mills (MSYM) theory. It is shown that these observables, which directly prove the SL(2,C) symmetry present in gauge theories in the Regge limit, exhibit an excellent perturbative convergence. They are compared to those calculated in QCD for different renormalization schemes concluding that the momentum-substraction scheme with the Brodsky-Lepage-Mackenzie scale-fixing procedure captures the bulk of the MSYM results.     

Supersymmetric,regularization of one-loop Green's functions in N = 4 Yang-Mills theory

Supersymmetric dimensional regularization via dimensional reduction is used for explicit calculation of one-loop two-point Green's functions in an N = 4 supersymmetric Yang-Mills theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 74–79, June, 1989.In conclusion, the authors would like to thank Prof. I. V. Trutin for numerous invaluable discussions.