The topological classification of compact differentiable manifolds without boundary according to dimension. We explain how this gauge theory provides the quantization of the classical integrable system underlying the moduli space of. Any m2 metric h can be written in the conformally flat form h e2. Dimension 1 is trivial by any definition dimension 2 is don. Neither of the authors has had the privilege of collaborating with stanley deser, much to our regret. The former were constructed by donagimarkman 22 from any complete family. Pdf solutions of fourdimensional field theories via m. Wittenmonopoles, duality, and chiral symmetry breaking in n 2 supersy in metric qcd.
Effective prepotential from extended seibergwitten system. Seibergwitten integrable system it is remarkable that the susy vacua of our theory are. Lecture notes on seibergwitten invariants revised second. Seibergwitten theory, integrable systems and dbranes. Witten, supersymmetric yangmills theory and integrable. These keywords were added by machine and not by the authors. In proceedings of symposia in pure mathematics, volume 62, pages 344. 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. Summer research institute on algebraic geometry, july 929, 1995, university of california, santa cruz proceedings of symposia in pure mathematics pt. The seibergwitten moduli space and its structure are described in section 2. Marshakov, seibergwitten theory and integrable systems world scientific, singapore 1999.
Retrieve articles in proceedings of the american mathematical society with msc 2000. The terminology is motivated by seibergwitten theory in. Lecture notes on seibergwitten invariants revised second edition john douglas moore july, 2010. Seibergwitten equations ushered in a new era in gauge theory and enabled mathematicians to find simpler proofs of some of the deepest results of donaldson and others. Witten, supersymmetric yangmills theory and integrable systems, nucl. The point of view is that of algebraic geometry and integrable systems. We check, as an expansion in the instanton number, that the aforementioned partition functions are eigenfunctions of an elliptic integrable manybody system, which quantizes the seibergwitten geometry of the fivedimensional gauge theory. Classical integrable systems the relation between the seibergwitten theory and the classical integrable system has been studied gorsky et al. In particular we discuss the nekrasovshatashvili limit of the refined amplitudes. Mironov theory department, lebedev physics institute, moscow 117924, russia an. One way to interpret this is that these variables a and its dual can be expressed as periods of a meromorphic differential on a riemann surface called the seiberg witten curve relation to integrable systems.
Donagi and markman 1993 have shown that the infinitesimal period map for an algebraic completely integrable hamiltonian system acihs is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. The relation between gauge theory and integrable system has various generalizations. Seibergwitten theory and the integrable systems ebook. This book deals with some aspects of this relation, the main focus being on the algebraic geometry of the level manifolds of integrable systems and the construction of integrable systems, starting from algebraic geometric data. I am no great expert, so i will simply give some overview of the question. This process is experimental and the keywords may be updated as the learning algorithm improves. Modular structures in superconformal field theories by madhusudhan raman phys10201205002 the institute of mathematical sciences, chennai a thesis submitted to the. A new parametrization for the calogeromoser spectral curves is found, which exhibits the classical vacuum expectation values of the scalar field of the gauge. Donagi, upenn, on leave at ias submitted on 7 may 1997 abstract. Hyperelliptic integrable systems on k3 and rational. Krichever in unpublished work, gorsky and nekrasov, and martinec 4 recognized that. The seibergwitten curve is written as associated integrable system is hitchin system on whose spectral curve is. We explain how these computations are connected with both classical and quantum integrable systems.
What is the physical motivation of seibergwitten theory. This is an avatar of the cubic condition of donagi and markman 11. M5branes and hitchin systems donagi witten, witten 97, gaiotto 09 in general, n2, su2 gauge theories can be induced from 2 m5branes wrapped on riemann surfaces. Seibergwitten theory and calogeromoser systems eric dhoker1 and d. 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. Advances in theoretical and mathematical physics, 75. Fiantd2900 itepth6300 hepth0011093 seibergwitten theory and duality in integrable systems a. We consider the singular phases of the smooth finitegap integrable systems arising in the context of seibergwitten theory. Deformed prepotential, quantum integrable system and. Marshakov 2 we discuss the properties of n 2 supersymmetric gauge theories underlying the.
Request pdf seibergwitten theory and duality in integrable systems these lectures are devoted to the low energy limit of \n2 susy gauge theories, which is described in terms of integrable. Modular structures in superconformal field theories. Extended seibergwitten theory and integrable hierarchy. Quantization of integrable systems and four dimensional. Seibergwitten theory and duality in integrable systems.
Let p xbe the principal so4bundle associated to the tangent bundle tx x, and let p. Presumably, this integrable system will be equivalent to the spin chain that gorsky et al. We discuss refined topological string theory on calabiyau manifolds, and application to seibergwitten gauge theory and nekrasov function. Singular phases of seibergwitten integrable systems. University of notre dame department of mathematics notre dame, in 465564618, usa nicolaescu. With these methods we construct calabiyau integrable systems from complete families of compact calabiyau threefolds in a di. Pestun, seibergwitten geometry of four dimensional.
Theory department, lebedev physics institute, moscow 117924, russia and. Double quantization of seibergwitten geometry and walgebras. Pandharipande notes on stable maps and quantum cohomology mr 1492534 richard hain and eduard looijenga mapping class groups and moduli spaces of curves mr 1492535. It appeared di cult to generalize directly the donagi witten construction of hitchin systems to arbitrary g, and it was thus natural to seek this generalization directly amongst the elliptic calogeromoser integrable systems. Defects and quantum seibergwitten geometry pdf paperity. These degenerate limits correspond to the weak and strong coupling regimes of susy gauge theories. On n2 susy gauge theories and integrable systems arxiv. Witten, supersymmetric yangmills theory and integrable systems 1996 nucl.
Some physics background electromagnetism yangmills theory quantization supersymmetry n 2 super yangmills duality the seiberg witten solution adding matter 2. Integrable systems are related to algebraic geometry in many different ways. Other readers will always be interested in your opinion of the books youve read. Seiberg witten theory and the integrable systems marshakov. We solve the limit shape equations derived from the gauge theory and identify the space m of vacua of the theory with the moduli. Markman, spectral curves, algebraically completely.
On integrable systems and supersymmetric gauge theories. Supersymmetric yangmills theory and integrable systems. We study four dimensional n2 supersymmetric gauge theory in the omegabackground with the two dimensional n2 superpoincare invariance. Ams proceedings of the american mathematical society. The seibergwitten curve and differential for n 2 supersymmetric sun gauge theory, with a massive hypermultiplet in the adjoint representation of the gauge group, are analyzed in terms of the elliptic calogeromoser integrable system.
Donagi seibergwitten integrable systems mr 1492533 w. We discuss many examples of the donagi witten integrable system for the theories of the form hypvg, and discuss the relation to the hitchin system on an auxiliary riemann surface with. On integrable systems and supersymmetric gauge theories on integrable systems and supersymmetric gauge theories marshakov, a. The seibergwitten moduli space the seibergwitten equations. Riemannian, symplectic and complex geometry are often studied by means of solutions to systems of nonlinear di erential equations, such as the equations of geodesics, minimal surfaces, pseudoholomorphic curves and yang. Donagi,witten nakajima hanany, oz klemm, lerche mayr,warner, vafa dorey hollowood khoze ooguri mattis vafa. The mathematical formalism of the seibergwitten equations is straightforward but i was wondering about its physical motivation. One of the most interesting examples is the seibergwitten ansatz for the n2 susy supersymmetric yangmills gauge theories in four dimensions. Seibergwitten monopole equations and riemann surfaces. Starting from this point of view, we propose an integrable system relevant to the n 2. Seibergwitten geometry of mass deformed n2 superconformal ade quiver gauge theories in four dimensions is determined. Seibergwitten curves and doubleelliptic integrable systems. Mupdf amazoncom free shipping on qualifying offers seiberg witten theory and. 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.
Forsun gauge group, donagi and witten 3 proposed that the spectral curves of the sun hitchin system should play the role of the seiberg witten curves. An old conjecture claims that commuting hamiltonians of the doubleelliptic integrable system are constructed from the thetafunctions associated with riemann surfaces from the seibergwitten family, with moduli treated as dynamical variables and the seibergwitten differential providing the presymplectic structure. Section 7 ends the paper with concluding remarks concerning riemann surfaces, integrable systems and the seibergwitten equations. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. Seibergwitten curve spectral curve meromorphic one form symplectic form. N 2 supersymmetric gauge theories in four dimensions are studied by formulating them as the quantum field theories derived from configurations of fourbranes, fivebranes, and sixbranes in type iia superstrings, and then reinterpreting those configurations in mtheory. The special kahler geometry on the moduli space of vacua in seiberg witten theory can be identified with the geometry of the base of complex completely integrable system. Aspects of calabiyau integrable and hitchin systems. Quantum integrable systems, matrix models, and agt. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Seibergwitten prepotential from instanton counting. By this construction, the usual hitchin system on x with singularities in d. These give rise to complex integrable systems if they admit a special section, namely an abstract seibergwitten di.