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| Author | : Matthew Renwick |
| Publisher | : |
| Total Pages | : |
| Release | : 2020 |
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| ISBN | : |
| Author | : Jörg Teschner |
| Publisher | : Springer |
| Total Pages | : 467 |
| Release | : 2015-11-17 |
| Genre | : Science |
| ISBN | : 3319187694 |
This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have been studied in this way are partition functions, expectation values of line operators, and supersymmetric indices. The book also reviews recently discovered connections between SUSY field theories in four dimensions and two-dimensional conformal field theory. These connections have a counterpart in relations between three-dimensional gauge theories and Chern-Simons theory; the book’s closing chapters explore connections with string theory.
| Author | : Julius Eckhard |
| Publisher | : |
| Total Pages | : |
| Release | : 2020 |
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| Author | : Yuji Tachikawa |
| Publisher | : Springer |
| Total Pages | : 236 |
| Release | : 2014-10-15 |
| Genre | : Science |
| ISBN | : 331908822X |
Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides readers through the key milestones in the field, which include the work of Seiberg and Witten, Nekrasov, Gaiotto and many others. As an advanced graduate level text, it assumes that readers have a working knowledge of supersymmetry including the formalism of superfields, as well as of quantum field theory techniques such as regularization, renormalization and anomalies. After his graduation from the University of Tokyo, Yuji Tachikawa worked at the Institute for Advanced Study, Princeton and the Kavli Institute for Physics and Mathematics of the Universe. Presently at the Department of Physics, University of Tokyo, Tachikawa is the author of several important papers in supersymmetric quantum field theories and string theory.
| Author | : Andrea Ferrari |
| Publisher | : |
| Total Pages | : |
| Release | : 2019 |
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| Author | : Alexander Sevrin |
| Publisher | : World Scientific |
| Total Pages | : 433 |
| Release | : 1997-06-19 |
| Genre | : Science |
| ISBN | : 1783264497 |
This volume contains the proceedings of a meeting held at Imperial College which is devoted to recent developments in string theory, supersymmetry and quantum gravity. The volume comprises two different sections. The first consists of five pedagogical reviews by prominent physicists, covering the currently important subjects of supermembranes, duality, D-branes, new non-perturbative methods and string phenomenology. The second section consists of research reports in these areas and also on other currently important topics such as supersymmetric gauge theories, two-dimensional quantum gravity and black holes.
| Author | : Anindya Dey (Ph. D.) |
| Publisher | : |
| Total Pages | : 520 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
The basic objective of this thesis is to apply techniques of supersymmetric localization for studying Mirror Symmetry in N = 4 gauge theories in three space-time dimensions. We start by discussing an M-theory/Type IIA description of Mirror Symmetry for affine quiver gauge theories and present a neat classification of various infinite families of dual theories that arise in this fashion. We then perform an extremely non-trivial check of Mirror Symmetry for a large class of affine A and D type quivers and their truncated versions using partition function on a round sphere as a function of hypermultiplet masses and FI parameters. The computation allows one to explicitly derive the "mirror map" -- a linear map relating masses of a theory with FI parameters of the dual and vice-versa. In addition, we demonstrate that there exists a one-to-one correspondence between the various "building blocks" of the partition function of a given theory and String Theory objects in the Type IIB description of such theories. In the next part of the thesis, we introduce the idea that a very large class of dual quiver gauge theories may be systematically generated starting from dual pairs consisting only of simple linear quivers by appropriately gauging avor symmetries on one side of the duality. The gauging operation on one side of the duality results in a corresponding "ungauging" on the other side. We show that this program can be carried out to obtain various known as well as new families of mirror pairs -- including affine quivers of A-D-E type, star-shaped quivers and quivers with symplectic gauge groups. S3 partition function turns out to be a particularly convenient tool to implement the gauging procedure since it easily generalizes to any arbitrary shape of the quiver as well as arbitrary rank of the gauge group at a given node in the quiver. Additional checks on the new mirror pairs obtained in this fashion are performed using Hilbert Series computation on the Coulomb and Higgs branches of the dual theories in question. Remarkably, we find that our prescription gives a straightforward recipe to construct "good" duals in certain cases where naive mirror duals obtained via S-duality from Type IIB brane construction are "bad" in the Gaiotto-Witten sense.
| Author | : Joel Lamy-Poirier |
| Publisher | : |
| Total Pages | : 99 |
| Release | : 2016 |
| Genre | : Gauge fields (Physics) |
| ISBN | : |
Exact results are a key component for understanding any physical theory. Unfortunately in the context of quantum field theory (QFT) they are in general impossible to obtain, and we need some sort of approximations. However there exists certain non-realistic theories rich in exactly computable quantities, and from those exact quantities we can infer various theoretical implications for realistic quantum field theories. Supersymmetric gauge theories stand out among these non-realistic theories as the best compromise between the contradicting requirements of realism and exact computability. This thesis consists of three projects, in which we explore some exact results in supersymmetric quantum field theory. In the first project we define and describe irregular vertex operators in the H_3^+ Wess-Zumino-Witten model. Irregular vertex operators are a QFT-equivalent of irregular singular points in the theory of differential equations, and their study is motivated by a relation to the partition functions of some asymptotically free four-dimensional N=2 supersymmetric gauge theories. The definition is shown to be compatible with previously defined irregular vertex operators in Liouville theory through a known duality between the H_3^+ and Liouville theories. In the second project we use supersymmetric localization to compute the partition function of N=2 supersymmetric gauge theories on a four-sphere in the presence of a surface defect on a two-sphere subspace, taking the form of a two-dimensional gauged linear sigma model. The result generalizes the known results for separate supersymmetric gauge theories on the separate spaces. We obtain a partition function in the form of a standard partition function on S^4, with a modified instanton partition function and an additional insertion corresponding to a shifted version of the S^2 partition function. In the third project we develop a new method for finding the ground states of fermions in the presence of BPS monopoles. We use it to find the ground states in the case of Abelian BPS monopoles in R^3, which were previously unknown.
| Author | : Sergio Cecotti |
| Publisher | : Cambridge University Press |
| Total Pages | : 425 |
| Release | : 2015-01-08 |
| Genre | : Mathematics |
| ISBN | : 1107053811 |
Adopting an elegant geometrical approach, this advanced pedagogical text describes deep and intuitive methods for understanding the subtle logic of supersymmetry while avoiding lengthy computations. The book describes how complex results and formulae obtained using other approaches can be significantly simplified when translated to a geometric setting. Introductory chapters describe geometric structures in field theory in the general case, while detailed later chapters address specific structures such as parallel tensor fields, G-structures, and isometry groups. The relationship between structures in supergravity and periodic maps of algebraic manifolds, Kodaira-Spencer theory, modularity, and the arithmetic properties of supergravity are also addressed. Relevant geometric concepts are introduced and described in detail, providing a self-contained toolkit of useful techniques, formulae and constructions. Covering all the material necessary for the application of supersymmetric field theories to fundamental physical questions, this is an outstanding resource for graduate students and researchers in theoretical physics.
| Author | : Jeroen Sebastian Wijnhout |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2005 |
| Genre | : |
| ISBN | : |
