arXiv subjects

Tatiana A. Ivanova

Publications and source records attributed to Tatiana A. Ivanova.

25 records · Page 2Linked to original sources

arXiv2004

Noncommutative Moduli for Multi-Instantons

There exists a recursive algorithm for constructing BPST-type multi-instantons on commutative R^4. When deformed noncommutatively, however, it becomes difficult to write down non-singular instanton configurations with topological charge greater than one in explicit form. We circumvent this difficulty by allowing for the translational instanton moduli to become noncommutative as well. This makes possible the ADHM construction of 't Hooft multi-instanton solutions with everywhere self-dual field strengths on noncommutative R^4.

hep-th↗

arXiv2003

Hidden Symmetries of the Open N=2 String

It is known for ten years that self-dual Yang-Mills theory is the effective field theory of the open N=2 string in 2+2 dimensional spacetime. We uncover an infinite set of abelian rigid string symmetries, corresponding to the symmetries and integrable hierarchy of the self-dual Yang-Mills equations. The twistor description of the latter naturally connects with the BRST approach to string quantization, providing an interpretation of the picture phenomenon in terms of the moduli space of string backgrounds.

hep-th↗

arXiv2003

Noncommutative Multi-Instantons on R^{2n} x S^2

Generalizing self-duality on R^2 x S^2 to higher dimensions, we consider the Donaldson-Uhlenbeck-Yau equations on R^{2n} x S^2 and their noncommutative deformation for the gauge group U(2). Imposing SO(3) invariance (up to gauge transformations) reduces these equations to vortex-type equations for an abelian gauge field and a complex scalar on R^{2n}_θ. For a special S^2-radius R depending on the noncommutativity θwe find explicit solutions in terms of shift operators. These vortex-like configurations on R^{2n}_θdetermine SO(3)-invariant multi-instantons on R^{2n}_θx S^2_R for R=R(θ). The latter may be interpreted as sub-branes of codimension 2n inside a coincident pair of noncommutative Dp-branes with an S^2 factor of suitable size.

hep-th↗

arXiv2003

On Noncommutative Merons and Instantons

The Yang-Mills (YM) and self-dual Yang-Mills (SDYM) equations on the noncommutative Euclidean four-dimensional space are considered. We introduce an ansatz for a gauge potential reducing the noncommutative SDYM equations to a difference form of the Nahm equations. By constructing solutions to the difference Nahm equations, we obtain solutions of the noncommutative SDYM equations. They are noncommutative generalizations of the known solutions to the SDYM equations such as the Minkowski solution, the one-instanton solution and others. Using the noncommutative deformation of the Corrigan-Fairlie-'t Hooft-Wilzek ansatz, we reduce the noncommutative YM equations to equations on a scalar field which have meron solutions in the commutative limit and show that they have no such solutions in the noncommutative case. To overcome this difficulty, another ansatz reducing the noncommutative YM equations to a system of difference equations on matrix-valued functions is used. For self-dual configurations this system is reduced to the difference Nahm equations.

hep-th↗

arXiv2000

On symmetries of Chern-Simons and BF topological theories

We describe constructing solutions of the field equations of Chern-Simons and topological BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations) are considered. A method of calculating (nonlocal) dressing symmetries in Chern-Simons and topological BF theories is formulated.

hep-th↗

arXiv1999

Moduli Space of Self-Dual Gauge Fields, Holomorphic Bundles and Cohomology Sets

We discuss the twistor correspondence between complex vector bundles over a self-dual four-dimensional manifold and holomorphic bundles over its twistor space and describe the moduli space of self-dual Yang-Mills fields in terms of Cech and Dolbeault cohomology sets. The cohomological description provides the geometric interpretation of symmetries of the self-dual Yang-Mills equations.

math-ph↗

arXiv1998

On infinitesimal symmetries of the self-dual Yang-Mills equations

Infinite-dimensional algebra of all infinitesimal transformations of solutions of the self-dual Yang-Mills equations is described. It contains as subalgebras the infinite-dimensional algebras of hidden symmetries related to gauge and conformal transformations.

math-ph↗