Theory department, lebedev physics institute, moscow 117924, russia and. The aim of this book is to present in a clear form the main ideas of the relation between the exact solutions to the supersymmetric susy yangmills theories and integrable systems. These lectures are devoted to the low energy limit of \n2 susy gauge theories, which is described in terms of integrable systems. An old conjecture claims that commuting hamiltonians of the doubleelliptic integrable system are constructed from the thetafunctions associated with riemann surfaces from the seiberg witten family, with moduli treated as dynamical variables and the seiberg witten differential providing the presymplectic structure.
The duality turns out to be an effective tool in constructing the double elliptic integrable system which describes the sixdimensional seiberg witten theory. A summary of results is presented, which provide exact description of the low energy. Seibergwitten theory and integrable systems book, 1999. Seibergwitten theory and integrable systems nasaads. Keywords gauge theory gauge group spectral curve supersymmetric gauge theory gauge algebra. Seiberg witten theory, integrable systems and dbranes. We consider the singular phases of the smooth finitegap integrable systems arising in the context of seiberg witten theory. If the address matches an existing account you will receive an email with instructions to reset your password. The methods here will stimulate new research directions such as the important seiberg witten differential in seiberg witten theory for solving the mass gap problem in quantum yangmills theory. Further, the thetafunction identities that lie behind the poisson commutativity of the threeparticle hamiltonians are proven. Andrei marshakov in the past few decades many attempts have been made to search for a consistent formulation of quantum field theory beyond perturbation theory. This is a survey of the work of seiberg and witten on 4dimensional n2 supersymmetric yangmills theory and of.
In theoretical physics, seiberg witten theory is a theory that determines an exact lowenergy effective action for massless degrees of freedom of a supersymmetric gauge theorynamely the metric of the moduli space of vacua. Good textbook or lecture notes on seibergwitten theory. Seibergwitten theory and integrable systems ebook, 1999. This talk gives an introduction into the subject of seiberg witten curves and their relation to integrable systems. Then the author proceeds to the seiberg witten solutions and show that they are indeed defined by the same data as finitegap solutions to integrable systems. One of the most interesting examples is the seiberg witten ansatz for the n2 susy supersymmetric yangmills gauge theories in four dimensions. Seibergwitten theory, integrable systems and dbranes.
The seiberg witten equations and applications to the topology of smooth fourmanifolds mathematical notes, vol. We give an introduction into and exposition of seibergwitten theory. Seibergwitten theory and the integrable systems ebook. Seibergwitten theory and duality in integrable systems. At the same time, it implies a series of relations between other seiberg witten systems. Lectures on seiberg witten invariants lecture notes in mathematics john d. Extended seiberg witten theory and integrable hierarchy. Integrability and seibergwitten theory curves and periods. Then the author proceeds to the seibergwitten solutions and show that they are indeed defined by the same data as finitegap solutions to integrable systems. Pdf integrability and seibergwitten theory curves and. From quantum cohomology to integrable systems download. The case of the elliptic calogero system, associated with the flow between n 4 and n 2.
Kop seibergwitten theory and the integrable systems av andrei marshakov pa. Seibergwitten theory and the integrable systems andrei. Extended seibergwitten theory and integrable hierarchy. Citeseerx document details isaac councill, lee giles, pradeep teregowda.
Click download or read online button to get from quantum cohomology to integrable systems book now. A summary of results is presented, which provide exact description of the lowenergy. In the context of seiberg witten theory, the elliptic rs integrable system can be linked with the relevant low energy effective action when a compactification from five dimension to four dimension. Singular phases of seibergwitten integrable systems. We summarize recent results on the resolution of two intimately related problems, one physical, the other mathematical. Everyday low prices and free delivery on eligible orders. Notes on seiberg witten theory graduate studies in mathematics. I an introduction to 4dimensional 1\\leq n \\leq 4 supersymmetric yangmills theory, including particle and field contents, n1 and n2 superfield methods and the construction of general invariant lagrangians. Seibergwitten curves and doubleelliptic integrable systems. An introductory chapter tries to describe some of the relevant physics for a reader with no physics background. From nonperturbative susy gauge theories to integrable systems.
Marshakov, seibergwitten theory and integrable systems, world scientific, singapore, 1999. Several toymodel examples of string theory solutions where the structures of integrable systems appear are briefly discussed. We concentrate on the theories with one massive hypermultiplet in the adjoint representation of an arbitrary gauge algebra g. The remaining chapters describe the specific integrable systems used, and include a detailed study of the applications to quantum field theory. Seibergwitten theory and integrable systems world scientific. This connection, though not been clearly understood so far, has become already a beautiful example of appearance of hidden integrable structure in multidimensional quantum gauge theories and, thus, quite a popular topic at many di. This site is like a library, use search box in the widget to get ebook that you want. The complete formulation requires the introduction of certain deformations of the finitegap solutions described in terms of quasiclassical or whitham hierarchies.
In this note it is demonstrated how the seibergwitten solutions and related integrable systems may arise from certain brane. We discuss some motivations and origins of this relation and consider explicit construction of various families of seiberg witten curves in terms of corresponding integrable models. These degenerate limits correspond to the weak and strong coupling regimes of susy gauge theories. Seiberg witten theory and integrable systems andrei marshakov.
Produktinformationen zu seibergwitten theory and the integrable systems ebook pdf in the past few decades many attempts have been made to search for a consistent formulation of quantum field theory beyond perturbation theory. Some subtleties of the formulation of the seiberg witten theory via integrable systems are discussed and interpreted along the lines of general picture os stringm. This is a survey of the work of seiberg and witten on 4dimensional n2 supersymmetric yangmills theory and of some of its recent extensions, written for. In theoretical physics, seibergwitten theory is a theory that determines an exact lowenergy. The riemann surfaces of the seibergwitten theory are explicitly described as spectral curves. In this note it is demonstrated how the seiberg witten solutions and related integrable systems may arise from certain brane configurations in m theory. Integrable hierarchies in donaldsonwitten and seiberg.
The first deals with the resolution of the nonperturbative low energy dynamics of certain n2 supersymmetric yang. Fiantd2900 itepth6300 hepth0011093 seibergwitten theory and duality in integrable systems a. The first deals with the resolution of the nonperturbative low energy dynamics of certain n2 supersymmetric yangmills theories. Seibergwitten theory and integrable systems dhoker, e phong, d. The formulations and results will benefit researchers and students in the fields of phase transitions, integrable systems, matrix models and seiberg. This is a survey of the work of seiberg and witten on 4dimensional n2 supersymmetric yangmills theory and of some of its recent extensions, written for mathematicians. Seibergwitten theory and random partitions springerlink. We present a series of four selfcontained lectures on the following topics. In particular, we show that the blowup function in donaldson witten theory, up to a redefinition.
These lectures are devoted to the low energy limit of \\n2 susy gauge theories, which is described in terms of integrable systems. The riemann surfaces of the seiberg witten theory are explicitly described as spectral curves of lax operators. In the context of seibergwitten theory, the elliptic rs integrable system can be linked with the relevant low energy effective action when a compactification from five dimension to four dimension. Extended seibergwitten theory and integrable hierarchy article pdf available in journal of high energy physics 20071 december 2006 with 32 reads how we measure reads. Introduction let au 0 d be a partial differential equation on a manifold m, s the set of all solutions, g the. Marshakov, seibergwitten theory and integrable systems. Seiberg witten theory and the integrable systems pdf andrei marshakov seiberg witten theory and the integrable systems. Some subtleties of the formulation of the seiberg witten theory via integrable systems are discussed and. Buy seiberg witten theory and the integra ble systems by andrei marshakov isbn. Abstract the interpretation of exact results on the lowenergy limit of 4d n 2 supersymmetric yangmills theory in the language of 1d integrable system of particles is discussed.
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