In recent years maximally supersymmetric gauge theories attracted much attention and served as a theoretical playground promising new insight into the nature of gauge theories beyond usual perturbation theory. This book provides, in a single volume, an introduction to supersymmetry, supergravity and supersymmetric string theory at a level suitable for postgraduate students in theoretical physics. Maximally supersymmetric field theories in various dimensions are believed to possess special properties due to extended supersymmetry. Maximally supersymmetric theories and related theories. In section 3, i will try to provide some motivation as to why the next step should be a supersymmetric extension for the sm. A global symmetry is the symmetry which remains invariant at each point of a manifold manifold can be either of spacetime coordinates or that of internal quantum numbers. The ultraviolet question in maximally supersymmetric field theories. K 1 department of applied mathematics and theoretical physics, damtp we construct lattice action for yang. While the n 4 sym theory is completely on shell uv nite and possesses only the ir divergences, in higher dimensions the situation is the opposite.
In a formal sense, the existence of these quantum field theories can be viewed as predictions of m theory. Supersymmetry and gauge theory kings college london. The maximally supersymmetric fourdimensional gauge theory is n 4 supersymmetric yangmills. S s symmetry article high energy behavior in maximally supersymmetric gauge theories in various dimensions dmitry kazakov 1,2,, leonid bork 3,4, arthur borlakov 1,2, and denis tolkachev 1,5, and dmitry vlasenko 6, 1 bogoliubov laboratory of theoretical physics, joint institute for nuclear research, dubna 141980, russia. From dbranes to adscft a stack of n dirichlet 3branes realizes n4 supersymmetric sun gauge theory in 4 dimensions. Lattice studies of maximally supersymmetric yangmills theories david schaich bern liverpool theoretical physics seminar, 28 november 2018 arxiv.
Technically the standard model is a relativistic quantum gauge field theory. A brief introduction to scaling and to supersymmetric eld theory, with examples, is followed by discussions of nonrenormalization theorems and beta functions. On perturbative scattering amplitudes in maximally. In this thesis we study maximally supersymmetric solutions of gauged supergravity theories, with special focus on antide sitter solutions. The structure of uv divergences in maximally supersymmetric gauge theories a. Introductory comments 2 conformal symmetries of curved spacetime 3 conformal symmetries of curved superspace 4 case study. Here this question is studied in detail at one loop for the branch of the moduli space parameterized by a. In this theory the dynamics is severely restricted by the large amount of supersymmetry, but it is still very nontrivial theory and thus 1. However we will start by considering quantum mechanics and the schr odinger equation. It also creates a curved background of 10d theory of closed. A euclidean lattice formulation of d 5 maximally supersymmetric yangmills theory hje a euclidean lattice formulation of d 5 maximally supersymmetric yangmills theory anosh joseph 0 1 0 university of cambridge, cambridge, cb3 0wa, u. Constraints on higher derivative operators in maximally. Mtheory and maximally supersymmetric gauge theories mtheory and maximally supersymmetric gauge theories lambert, neil 20121123 00. High energy behaviour in maximally supersymmetric gauge.
Pdf mtheory and maximally supersymmetric gauge theories. Supersymmetric gauge field theory and string theory. We focus on the relatively recent construction of m2brane worldvolume theories. Gauge theory, class of quantum field theory, a mathematical theory involving both quantum mechanics and einsteins special theory of relativity that is commonly used to describe subatomic particles and their associated wave fields. The covariant forward and backward difference operators act on the lattice. The more supersymmetry the larger the spectrum of the theory. Supersymmetric deformations of maximally supersymmetric. Maximally supersymmetric backgrounds and partial n2n1. In contrast, in a supersymmetric extension of the standard model, it is possible to maintain the gauge hierarchy while providing a natural framework for elementary scalar. On the origins of gauge theory university of toronto. Basic knowledge of feynman rules in scalar field theory and quantum electrodynamics is assumed, but all other tools are introduced as needed.
Constraints on higher derivative operators in maximally supersymmetric gauge theory. Scattering amplitudes and hidden symmetries in supersymmetric. In four dimensions, they are free from uv divergences but are ir divergent on shell. The result generalizes the known results for separate supersymmetric gauge. Maximally supersymmetric solutions of r2 supergravity. Strongly coupled phases may have holographic descriptions as black branes in various string duality frames, or there may be no gravity dual. My talk today is about the most beautiful of all yangmills theories nonabelian gauge theories, the theory of the strong nuclear interactions, quantum chromodynamics, qcd. Scattering amplitudes in gauge theory and gravity by. Mtheory and maximally supersymmetric gauge theories annual. The relatively old klt relations derived from string theory, and recently discovered relations within quantum.
This is maximally supersymmetric gravity with 32 real supercharges. The presentation also covers amplitudes in perturbative supergravity, 3d chernsimons matter theories, and colorkinematics duality and its connection to gravitygauge theoryxgauge theory. The ultraviolet question in maximally supersymmetric. Numerous topics in three and four dimensional supersymmetric gauge theories are covered. Mtheory and maximally supersymmetric gauge theories. Ediss maximally supersymmetric ads solutions in gauged. The exposition of this theory as well as of some basic facts about lie algebra homology and hochschild homology is given in appendices. Particular focus is made on the relatively recent construction of. Typically, consists of a union of various branches, such as the mesonic branch or the baryonic branch, the coulomb branch or the higgs branch. In a gauge theory there is a group of transformations of the field variables gauge transformations that leaves the basic physics of the quantum field. First we will concentrate on computations with gluonic external states and argue that n 4 supersymmetry implies a simple relation between allordersinepsilon oneloop n 4 super yangmills amplitudes and the first and second. Scattering amplitudes and hidden symmetries in maximally supersymmetric gauge theory. This leads to the question what, if any, of this structure survives at the complement of this one point.
Maximally supersymmetric n 4 yangmills theory msym has attracted a great deal of theoretical interest over the years. In the context of maximally supersymmetric yangmills, we consider two examples in detail to illustrate our point. In what follows, we consider the fourpoint onshell scattering amplitudes in d 6, 8. N 1 supergravity has simply a graviton and one gravitino, and the maximal supergravity in four. D 4 abelian gauge theory where the superspace fieldstrength twoform f d a is constrained to satisfy as usual. Maximally supersymmetric yangmills on the lattice david schaich bern swansea theory seminar 23 november 2018 arxiv. In the next section, i will list several problems apparent in the sm which prohibits it from laying claim to being the ultimate theory.
The organizing principle in this presentation is scaling wilsonian renormalization group. Moduli dynamics as a predictive tool for thermal maximally. The n4 supersymmetric yangmills gauge theory was formulated by us in a previous paper in the lightcone gauge. Supersymmetric gauge theories as curved spacetimes igor klebanov department of physics and pcts. A gauge theory is a mathematical framework for analysing dubious discuss gauge symmetries. It is described by a scalar complex superfield whose. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of nonabelian local gauge. Lattice studies of maximally supersymmetric yang mills. In a rst part we study the generation of a supersymmetric yangmills theory, coupled to an adjoint chiral supereld, from type iib string theory on noncompact calabiyau manifolds, with dbranes wrapping certain subcycles. This became possible due to the development of new computational techniques such as the spinor helicity and the onshell momentum su. In fact, string theory as a candidate theory of quantum gravity or of everything. Prior knowledge of quantum field theory, such as provided by the authors previous book introduction to gauge field theory, is assumed. Supersymmetric deformations of maximally supersymmetric gauge. Maximally supersymmetric gauge theory in four dimensions has a remarkably simple smatrix at the origin of its moduli space at both tree and loop level.
Mtheoryandmaximally supersymmetric gaugetheories arxiv. Dynamical supersymmetry in maximally supersymmetric gauge. Vlasenko4 1bogoliubov laboratory of theoretical physics, joint institute for nuclear research, dubna, russia. Supersymmetric backgrounds in 3d n 2 supergravity 5 4d n 1 maximally symmetric backgrounds 6 maxwell goldstone multiplet for partially broken susy 7 nilpotent chiral super eld in n 2 supergravity 8. On the origins of gauge theory callum quigley april 14, 2003 1 introduction we know the universe to be governed by four fundamental interactions. Oneloop maximally supersymmetric yangmills scattering. It is a driving concept to unify these forces into a single, comprehensive theory. Maximally supersymmetric mass deformation of the baggerlambertgustavsson blg theory corresponds to a noncentral extension of the d3 n8 poincare superalgebra allowed in three dimensions.
Particular focus is made on the relatively recent construction of m2brane worldvolume theories. It is widely believed that the t hooft planar limit of msym, in which the number of colors nc is taken to in nity, is dual at strong coupling g2n c. For the gauge theories with maximal spin 1 one has the following maximally supersymmetric theories. In the first part we classify all maximally supersymmetric solutions of all gauged or deformed supergravity theories in d 3 spacetime dimensions. In this paper, we are going to show that the superspaces 1. In a formal sense, the existence of these quantum field theories can be viewed as predictions of m. In the second project we use supersymmetric localization to compute the partition function of n 2 supersymmetric gauge theories on a foursphere in the presence of a surface defect on a twosphere subspace, taking the form of a twodimensional gauged linear sigma model. This note is devoted to study conformal maximally supersymmetric. Supersymmetric deformations of maximally supersymmetric gauge theories.
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