Classical Yang - Mills Vacua on T 3 : Explicit Constructions
نویسندگان
چکیده
Flat connections for unitary gauge groups on a 3–torus with twisted boundary conditions as well as recently discovered topologically non-trivial flat connections with " nondiagonalizable " triples of holonomies for higher orthogonal and exceptional groups are constructed explicitly in terms of Jacoby theta functions with rational characteristics. The (fractional) Chern-Simons numbers of these vacuum gauge field configurations are verified by direct computation.
منابع مشابه
The Donaldson-Witten function for gauge groups of rank larger than one
We study correlation functions in topologically twisted N = 2, d = 4 supersymmetric Yang-Mills theory for gauge groups of rank larger than one on compact four-manifolds X . We find that the topological invariance of the generator of correlation functions of BRST invariant observables is not spoiled by noncompactness of field space. We show how to express the correlators on simply connected mani...
متن کاملA class of two-dimensional Yang–Mills vacua and their relation to the non-linear sigma model
Classical vacuum pure gauge solutions of Euclidean two-dimensional SU(2) Yang–Mills theories are studied. Topologically non-trivial vacua are found in a class of gauge group elements isomorphic to S2. These solutions are unexpectedly related to the solution of the non-linear O(3) model and to the motion of a particle in a periodic potential. PACS: 11.10.Kk, 11.10.Lm. () On leave of absence from...
متن کاملOn the Analog Strong Cp Problem in the Cp N −1 Models A
Non-perturbative effects can introduce CP violation into the strong interactions. Since no such violations of this discrete symmetry have been observed, an avoidance mechanism must be operative. Although many proposals have been suggested to resolve this issue, the strong CP problem remains one of the outstanding low-energy mysteries of the standard model of particle physics. A four-dimensional...
متن کاملDeformation of Super Yang-Mills Theories in R-R 3-form Background
We study deformation of N = 2 and N = 4 super Yang-Mills theories, which are obtained as the low-energy effective theories on the (fractional) D3-branes in the presence of constant Ramond-Ramond 3-form background. We calculate the Lagrangian at the second order in the deformation parameter from open string disk amplitudes. In N = 4 case we find that all supersymmetries are broken for generic de...
متن کاملHomotopic Classification of Yang–Mills Vacua Taking into Account Causality
In this letter we study the existence of θ-vacuum states in Yang–Mills theories defined over asymptotically flat, stationary space-times taking into account not only the topology but the complicated causal structure of these space-times, too. By a result of Chruściel and Wald, apparently causality makes all vacuum states, seen by a distant observer, homotopically equivalent making the introduct...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000