Ten-dimensional supersymmetric Yang-Mills theory in terms of four-dimensional superfields

We show that the usual formulation of the N = 4 supersymmetric Yang-Mills theory in terms of N = 1 superfields can be generalized to describe the full ten-dimensional theory.     

On the functional integration measure of supersymmetric Yang-Mills theories

For the simplest N = 1 supersymmetric Yang-Mills theory, we construct a bosonic field transformation which linearizes the Yang-Mills action in each topological sector and whose jacobian equals the product of Fadeev-Popov and Matthews-Salam determinants up to cubic order at least. Some possible implications of this result for the maximally extended N = 4 theory are discussed.     

Integrability and Seiberg-Witten theory curves and periods

The interpretation of exact results on the low-energy limit of 4D N = 2 supersymmetric Yang-Mills theory in the language of 1D integrable system of particles is discussed. The Riemann surfaces of the Seiberg-Witten theory are explicitly described as spectral curves of Lax operators. The case of the elliptic Calogero system, associated with the flow between N = 4 and N = 2 supersymmetric in 4D, is considered in some detail. Equations for the corresponding Riemann surfaces are written down rather explicitly for all the SU(n) groups.     

Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops

We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N=4{\mathcal N=4} supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N=2{\mathcal N=2} and the N=2^*{\mathcal N=2^*} supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional N=2{\mathcal N=2} superconformal gauge theory is treated similarly.     

Schwinger-Dyson equations for <Emphasis Type="Italic">N</Emphasis> = 1 supersymmetric Yang-Mills theory

The Schwinger-Dyson equations for the N = 1 supersymmetric Yang-Mills theory are constructed.     

Braves and the dynamics of QCD

A brane configuration is described that is relevant to understanding the dynamics of N = 1 supersymmetric Yang-Mills theory. Confinement and spontaneous breaking of a discrete chiral symmetry can be understood as consequences of the topology of the brane. Because of the symmetry breaking, there can be domain walls separating different vacua; the QCD string can end on such a domain wall. The model in which these properties can be understood semiclassically does not coincide with supersymmetric Yang-Mills theory but is evidently in the same universality class.     

Supersymmetric gauge anomalies in 2 and 4 dimensions from generalized descent-equations

Via a supersymmetric generalization of the descent-equations we derive in Wess-Zumino gauge explicit expressions for chiral anomalies inN=1 supersymmetric Yang-Mills theory for space-time dimensions 2 and 4.     

Supergraphity: (II). Manifestly covariant rules and higher-loop finiteness

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.     

Background field formalism and construction of effective action for N = 2, d = 3 supersymmetric gauge theories

We review the background field method for three-dimensional Yang-Mills and Chern-Simons models in N = 2 superspace. Superfield proper time (heat kernel) techniques are developed and exact expressions of heat kernels for constant backgrounds are presented. The background field method and heat kernel techniques are applied for evaluating the low-energy effective actions in N = 2 supersymmetric Yang-Mills and Chern-Simons models as well as in N = 4 and N = 8 SYM theories.     

A new derivation of the Picard-Fuchs equations for effective N = 2 super Yang-Mills theories

A new method to obtain the Picard-Fuchs equations of effective, N = 2 supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding N = 2 theory.     

N = 2 supersymmetric Yang-Mills theory and its supercurrent

Using the off-shell two-component formulation of N = 2 supersymmetric Yang-Mills theory and the gauge covariantized supersymmetry transformations for the fields, the non-abelian supercurrent and anomaly multiplets are developed and the transformation rules for their components are obtained. The superfields in N = 2 superspace whose components are the non-abelian supercurrent and anomaly multiplets are written down.     

Quartic mass matrix and renormalization constants in supersymmetric Yang-Mills theories

We derive the general formula for the supertrace of the quartic mass matrix in a general supersymmetric gauge theory, with arbitrary representations for the chiral multiplets. This formula clarifies the non-renormalization theorems in presence of gauge interactions and gives “extended renormalization theorems” for N = 2 and N = 4 supersymmetric Yang-Mills theories. In particular we find the known result that g_ren = g_bare for the N = 4 theory and the new result m_ren = m_bare for the N = 2 gauge interactions of massive hypermultiplets. We give arguments to the extent that the latter non-renormalization theorem persists to all orders in perturbation theory.     

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.     

Superspace gauge theories with central charges

The superspace constraints leading to off-shell formulations of extended supersymmetric Yang-Mills theories for N = 2 and 4 are generalised to N = 6 in the abelian case. This leads to an on-shell representation of linearized N = 6 supergravity.     

Flat coordinates,topological Landau-Ginzburg models and the Seiberg-Witten period integrals

We study the Picard-Fuchs differential equations for the Seiberg-Witten period integrals in N = 2 supersymmetric Yang-Mills theory. For A-D-E gauge groups we derive the Picard-Fuchs equations by using the flat coordinates in the A-D-E singularity theory. We then find that these are equivalent to the Gauss-Manin system for two-dimensional A-D-E topological Landau-Ginzburg models and the scaling relation for the Seiberg-Witten differential. This suggests an interesting relationship between four-dimensional N = 2 gauge theories in the Coulomb branch and two-dimensional topological field theories.     

N = 1 superspace formulation of N = 2 and N = 4 super-Yang-Mills models with central charge

The component models of N = 2 and N = 4 supersymmetric Yang-Mills theories of Sohnius, Stelle and West are reformulated in terms of N = 1 superfields. The non-supersymmetric constraints are supersymmetrized generalizing the linear multiplet in the presence of the non-abelian gauge superfield and (in the N = 4 case) a doublet of chiral superfields. The extended supersymmetry transformations preserving constraints are explicitly given in terms of N = 1 superfields. We are able to introduce the constraints back into the lagrangian using superfield Lagrange multipliers. The on-shell equivalence of this formulation with the formulation of Fayet with one (for N = 2) and three (for N = 4) chiral superfields is shown. The abelian N = 2 model is worked out to show the connection between full superspace treatment and the N = 1 superfield formulation.     

Infrared behaviour of on shell form factors in anN=4 supersymmetric Yang-Mills field theory

We discuss the infrared and mass singular behaviour of some on shell form factors which are calculated up to the two loop level in anN=4 supersymmetric Yang-Mills field theory. One of the outcomes of our investigation is that the finite terms in the perturbation series of the form factor are determined by exponentiating the lowest order term. The same phenomeno has been discovered in some infrared and mass finite quantities.     

Noninvariance of regularization by dimensional reduction: An explicit example of supersymmetry breaking

By a direct calculation it is shown that at the three-loop level the regularization by dimensional reduction of Avdeev, Chochia and Vladimirov breaks supersymmetry relations between couplings in the N = 1, 2, 4 supersymmetric Yang-Mills theories written in terms of component fields. This is a strong limitation to the scope of the regularization.     

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.