The action of the supersymmetric N = 2 gauge theory in harmonic superspace

We consider a solution of constraints for the analytic representation of the harmonic superfield connection in the N = 2 supersymmetric gauge theory. A simple geometric expression for the action of this theory is obtained in the form of the integral over the N = 2 superspace.     

N = 1 complex supersymmetric theory in the harmonic superspace

The N = 1 complex supersymmetric algebra is studied using the harmonic techniques. The massless representations and the classification of their field content in terms of SU(2) n-uplets is obtained. The superspace formulation is developed and the U(1) × U(1) gauge supermultiplet is examined. Other features are discussed.     

N=1 supersymmetric truncations and the superstring low-energy effective theory

The question of discarding heavy fields in N=1 supersymmetric theories is analyzed. The analysis is applied to the compactification of the E₈ × E₈ superstring.     

F-theory,T-duality on K3 surfaces,and N = 2 supersymmetric gauge theories in four dimensions

We construct T-duality on K3 surfaces. The T-duality exchanges a 4-brane RR charge and a 0-brane RR charge. We study the action of the T-duality on the moduli space of 0-branes located at points of K3 and 4-branes wrapping it. We apply the construction to F-theory compactified on a Calabi-Yau 4-fold and study the duality of N = 2 SU(N_c) gauge theories in four dimensions. We discuss the generalization to the N = 1 duality scenario.     

The N = 4 supersymmetric E8 gauge theory and coset space dimensional reduction

Reasons are given to suggest that the N = 4 supersymmetric E₈ gauge theory be considered as a serious candidate for a physical theory. The symmetries of this theory are broken by a scheme based on coset space dimensional reduction. The resulting theory possesses four conventional generations of low-mass fermions together with their mirror particles.     

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.     

General N=1 supersymmetric flux vacua of massive type IIA string theory

We derive conditions for the existence of four-dimensional N=1 supersymmetric flux vacua of massive type IIA string theory with general supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show that such flux vacua exist when the internal geometry is nearly K?hler. The geometry is not warped, all the allowed fluxes are proportional to the mass parameter, and the dilaton is fixed by a ratio of (quantized) fluxes. The four-dimensional cosmological constant, while negative, becomes small in the vacuum with the weak string coupling.     

Anomalous generation of Chern-Simons terms in D=3, N=2 supersymmetric gauge theories

Parity-invariant three-dimensional gauge theories with N=2 extended supersymmetry are studied by the heat kernel method. The parity-anomalous part of the one-loop effective action is exactly found. It is expressed in terms of the N=2 supersymmetric Chern-Simons term and is identified as a N=2 superspace Atiyah-Patodi-Singer eta-invariant.     

Superalgebras in N = 1 gauge theories

N = 1 supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the gauge group is SO(n_c), with vector matter, it is a W-algebra, and the primary invariants form one of its representation. The same superalgebra exists in the dual theory, but its construction in terms of the dual fields suggests that duality may be understood in terms of a charge conjugation within the algebra. We extend the analysis to the gauge group E₆.