Superalgebras of non-abelian gauge theories in the Manifestly-Covariant canonical formalism

Zeitschrift für Physik C Particles and Fields -     

Chiral gauge theories in the 1/N expansion

We study the large-N limit of various (SU(N) gauge theories with chiral fermion content. Assuming that the leading N → ∞ behavior is given by a sum of planar diagrams, we find that the gauge interactions must fail to confine color in some models. Other models, assuming both a planar diagram limit and confinement, must contain massless composite fermions.     

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.     

Neutrino radiative decay in N=1 supergravity theories

We show that the supersymmetrization of models where neutrinos acquire mass through the see-saw mechanism allows for tau neutrinos heavier than 15–20 MeV to decay radiatively in a cosmologically safe way (i.e. with a lifetime τ_v⩽5×10³s).     

N = ∞ phase transition in a class of exactly soluble model lattice gauge theories

An exactly soluble class of model U(N) lattice gauge theories is considered. The ground state is discussed as a separable N-fermion problem solved by mathieu functions. Some exact correlation functions are presented. The N = ∞ limit exhibits a third order phase transition demarcating the strong and weak phases at (g²N)^?1 ≈ 0.55.     

Thermodynamic Bethe Ansatz for N = 1 supersymmetric theories

We study a series of N = 1 supersymmetric integrable particle theories in d = 1 + 1 dimensions. These theories are represented as integrable perturbations of specific N = 1 superconformal field theories. Starting from the conjectured S-matrices for these theories, we develop the Thermodynamic Bethe Ansatz (TBA), where we use that the 2-particle S-matrices satisfy a free fermion condition. Our analysis proves a conjecture by E. Melzer, who proposed that these N = 1 supersymmetric. TBA systems are “folded” versions of N = 2 supersymmetric TBA systems that were first studied by P. Fendley and K. Intriligator.     

Reflection matrices for integrable N = 1 supersymmetric theories

We study two-dimensional integrable N = 1 supersymmetric theories (without topological charges) in the presence of a boundary. We find a universal ratio between the reflection amplitudes for particles that are related by supersymmetry and we propose exact reflection matrices for the supersymmetric extensions of the multi-component Yang-Lee models and for the breather multiplets of the supersymmetric sine-Gordon theory. We point out the connection between our reflection matrices and the classical boundary actions for the supersymmetric sine-Gordon theory as constructed by Inami, Odake and Zhang [Phys. Lett. B 359 (1995) 118].     

Magnetic monopoles in SU(N) gauge theories

The potential $\text{A}\text{(}\text{r}\text{) ≡}\text{M}\text{(}\text{r}\text{?}\text{×}\text{n}\text{?}\text{)(r?}\text{r}\text{·}\text{n}\text{?}\text{)}{}^{\mathrm{?1}}$ is a static solution to the classical theory of non-abelian gauge fields coupled to a point magnetic source, for any matrix $\text{M}$ in the Lie algebra of the gauge group G. This solution is rotationally invariant if the eigenvalues of $\text{M}$ in the adjoint representation of G are quantized in half-integer units, but is stable to small perturbations only if all non-vanishing eigenvalues are $\text{±}\text{1}\text{2}$. In this paper, for the gauge groups G = SU(N), it is shown which sets of eigenvalues of $\text{M}$ are consistent with the group structure, which consistent sets are gauge inequivalent, and which consistent gauge inequivalent sets correspond to stable monopoles. It is found that there are N inequivalent stable monopoles, including the trivial case $\text{M}\text{=}\text{0}$. Equivalence here is with respect to non-singular gauge transformations—the symmetry transformations of the classical theory. Singular gauge transformations are, in contrast, not symmetries but they are nevertheless useful for classifying solutions and for relating the above concept of local stability to the global, or topological, stability associated with the Dirac strings. In this context, it is shown that there are N distinct topological classes of monopoles, with the group structure of the center $\text{Z}{}_{\mathrm{N}}\text{?Π}{}_1\text{(}\text{SU}\text{(N)/}\text{Z}{}_{\mathrm{N}}\text{)}$ of SU(N), that each class contains exactly one stable monopole, and that any other monopole in the same class has a strictly larger value of the magnetic charge magnitude $\text{tr}\text{M}{}^2$. This leads to an interesting physical picture of local stability as a consequence of the minimization of magnetic energy. The paper concludes with some comments on related topics: the empirical absence of magnetic charge, `t Hooft's calculation of magnetic energy, magnetic confinement, and spontaneously broken theories.     

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.     

Finite N=1 SUSY field theories and dimensional regularization

A simple algorithm is proposed to construct finite N=1 SUSY field theories within dimensional regularization. This is achieved by choosing the Yukawa couplings to be y_i=g(αⁱ₀+αⁱ₀ϵ+ϵ+αⁱ₂ϵ²+…), where g is the gauge coupling and the coefficients αⁱ₀, αⁱ₁, etc., are calculated order by order of perturbation theory. It is shown that the theory can be made finite in all orders of perturbation theory.     

Superpotentials of $\mathcal{N}=1$ SUSY gauge theories

The European Physical Journal C - An introduction to recent advances in computing effective superpotentials of four dimensional $\mathcal{N}=1$ SUSY gauge theories coupled to matter is presented....