1,721,030 research outputs found
Geometry of the gauge algebra in non-commutative yang-mills theory
No full textA detailed description of the infinite-dimensional Lie algebra of ⋆-gauge transformations in non-commutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra u(∞), and of the C∗-algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated
Dimensional reduction over the quantum sphere and non-abelian q-vortices
No full textWe extend equivariant dimensional reduction techniques to the case of quantum spaces which are the product of a Kähler manifold M with the quantum two-sphere. We work out the reduction of bundles which are equivariant under the natural action of the quantum group SU q (2), and also of invariant gauge connections on these bundles. The reduction of Yang–Mills gauge theory on the product space leads to a q-deformation of the usual quiver gauge theories on M. We formulate generalized instanton equations on the quantum space and show that they correspond to q-deformations of the usual holomorphic quiver chain vortex equations on M. We study some topological stability conditions for the existence of solutions to these equations, and demonstrate that the corresponding vacuum moduli spaces are generally better behaved than their undeformed counterparts, but much more constrained by the q-deformation. We work out several explicit examples, including new examples of non-abelian vortices on Riemann surfaces, and q-deformations of instantons whose moduli spaces admit the standard hyper-Kähler quotient construction. <br/
Topological t-duality for twisted tori
Full text linkWe apply the C∗-algebraic formalism of topological T-duality due to Mathai and Rosenberg to a broad class of topological spaces that include the torus bundles appearing in string theory compactifications with duality twists, such as nilmanifolds, as well as many other examples. We develop a simple procedure in this setting for constructing the T-duals starting from a commutative C∗-algebra with an action of Rn. We treat the general class of almost abelian solvmanifolds in arbitrary dimension in detail, where we provide necessary and sufficient criteria for the existence of classical T-duals in terms of purely group theoretic data, and compute them explicitly as continuous-trace algebras with non-trivial Dixmier– Douady classes. We prove that any such solvmanifold has a topological T-dual given by a C∗-algebra bundle of noncommutative tori, which we also compute explicitly. The monodromy of the original torus bundle becomes a Morita equivalence among the fiber algebras, so that these C∗-algebras rigorously describe the T-folds from non-geometric string theory.</p
Double scaling string theory of QCD in two dimensions
No full textWe describe a novel double scaling limit of large N Yang-Mills theory on a two-dimensional torus and its relation to the geometry of the principal moduli spaces of holomorphic differentials. © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.</p
N=2 quiver gauge theories on A-type ALE spaces
Full text linkWe survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in (Formula presented.) gauge theories on ALE spaces based on quiver varieties and the minimal resolution Xk of the Ak-1 toric singularity (Formula presented.) , in light of their recently conjectured duality with two-dimensional coset conformal field theories. We review and elucidate the rigorous constructions of gauge theories for a particular family of ALE spaces, using their relation to the cohomology of moduli spaces of framed torsion-free sheaves on a suitable orbifold compactification of Xk. We extend these computations to generic (Formula presented.) superconformal quiver gauge theories, obtaining in these instances new constraints on fractional instanton charges, a rigorous proof of the Nekrasov master formula, and new quantizations of Hitchin systems based on the underlying Seiberg–Witten geometry.</p
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