N. E. J. Bjerrum-Bohr, Poul H. Damgaard, Bo Feng, Thomas Sondergaard
Using only general features of the S-matrix and quantum field theory, we prove by induction the Kawai-Lewellen-Tye relations that link products of gauge theory amplitudes to gravity amplitudes at tree level. As a bonus of our analysis, we provide a novel and more symmetric form of these relations. We also establish an infinite tower of new identities between amplitudes in gauge theories.
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This is a personally colored account of the history behind N=4 Yang-Mills Theory.
A generalization of the two-dimensional Yang-Mills and generalized Yang-Mills theory is introduced in which the building B-F theory is nonlocal in the auxiliary field. The classical and quantum properties of this nonlocal generalization are investigated and it is shown that for large gauge groups, there exist a simple correspondence between the properties a nonlocal theory and its corresponding local theory.
Using an infinite number of fields, we construct actions for D=4 self-dual Yang-Mills with manifest Lorentz invariance and for D=10 super-Yang-Mills with manifest super-Poincaré invariance. These actions are generalizations of the covariant action for the D=2 chiral boson which was first studied by McClain, Wu, Yu and Wotzasek.
We will discuss an integrable structure for weakly coupled superconformal Yang-Mills theories, describe certain equivalences for the Yangian algebra, and fill a technical gap in our previous study of this subject.
The planar Yang-Mills theory in three spatial dimensions is examined in a particular representation which explicitly embodies factorization. The effective planar Yang-Mills theory Hamiltonian is constructed in this representation.
Recent developments in the determination of the planar S-matrix of N=4 Super Yang-Mills are closely related to its Yangian symmetry. Here we provide evidence for a yet unobserved additional symmetry: the Yangian level-one helicity operator.
The BCFW recursion relation in $\mathcal{N}=4$ super-Yang-Mills theory is solved using Yang-Baxter $R$-operators in the NMHV sector. Explicit expressions for $\mathcal{R}$-invariants are obtained in terms of the chains of $R$-operators acting on an appropriate basic state.
The large-N behavior of Yang-Mills and generalized Yang-Mills theories in the double-scaling limit is investigated. By the double-scaling limit, it is meant that the area of the manifold on which the theory is defined, is itself a function of N. It is shown that phase transitions of different orders occur, depending on the functional dependence of the area on N. The finite-size scalings of the system are also investigated. Specifically, the dependence of the dominant representation on A, for large but finite N is determined.
We present new relations for scattering amplitudes of color ordered gluons and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary multiplicities and polarizations involving up to three gravitons and up to two color traces are reduced to partial amplitudes of pure Yang-Mills theory. In fact, the double-trace identities apply to Einstein-Yang-Mills extended by a dilaton and a B-field. Our results generalize recent work of Stieberger and Taylor for the single graviton case with a single color trace. As the derivation is made in the dimension-agnostic Cachazo-He-Yuan forma…
It is shown that pure Yang-Mills theory in the modified formulation admits soliton solutions of classical field equations.
We analyze in an effective Lagrangian framework the connection between Super QCD (Super Yang Mills) and QCD (Yang Mills) by highlighting the crucial role that the zero modes play in the process of decoupling gluinos and squarks.
We show that the solutions of SU(2) Yang-Mills-dilation and Einstein-Yang-Mills-dilaton theories described in a sequence of papers by Kleihaus and Kunz are not regular in the gauge field part.
The existence of a "bonus" U(1) level-one Yangian symmetry of N=4 super-Yang-Mills has recently been proposed. We provide evidence for this proposal by constructing the BRST-invariant nonlocal charge in the pure spinor sigma model corresponding to this bonus level-one symmetry. We also construct analogous charges for bonus U(1) symmetries at all odd levels of the Yangian.
Topological Yang-Mills theory is derived in the framework of Lagrangian BRST cohomology.
Natural Symmetries of the Yang-Mills Equations
我们将杨-米尔斯方程的自然广义对称性定义为杨-米尔斯场的无穷小变换，以局部、规范不变和庞加莱不变的方式从杨-米尔斯场强度及其导数到任何阶，将场方程的解映射到其他解。在Yang-Mills联络的喷流丛上，我们引入了一个旋量坐标系，它适合于由Yang-Mills方程定义的解子空间。根据这个坐标系，自然对称性的完整分类是以一种直接的方式进行的。我们发现杨-米尔斯方程的所有自然对称性都源于方程所承认的规范变换。
For semisimple groups, possibly multiplied by U(1)'s, the number of Yang-Mills gauge fields is equal to the number of generators of the group. In this paper, it is shown that, for non-semisimple groups, the number of Yang-Mills fields can be larger. These additional Yang-Mills fields are not irrelevant because they appear in the gauge transformations of the original Yang-Mills fields. Such non-semisimple Yang-Mills theories may lead to physical consequences worth studying. The non-semisimple group with only two generators that do not commute is studied in detail.
A gauge invariant infrared regularization of the Yang-Mills theory applicable beyond perturbation theory is constructed.
Contour gauges are discussed in the framework of canonical formalism. We find flux operator algebras with the structure constants of underlying Yang-Mills theory.
Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of tree level single trace Einstein-Yang-Mills (EYM) amplitudes with arbitrary number of gluons and gravitons, which is valid for general spacetime dimensions and any helicity configurations. The recursion is written in terms of fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be further carried out until we reach an expansion in terms of pure YM amplitudes in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning tree structure rooted on gluons whose vertices are gravitons…
This article contains lecture notes of M. Shifman from the Saalburg Summer School 2004. The topic is supersymmetric Yang-Mills theory, in particular the gluino condensate in pure SUSY gluodynamics.
We construct a four-parameter class of self-dual instanton solutions of the classical SU(2)-Yang-Mills equations in a closed Euclidean Robertson-Walker space-time.
Using the first order formalism (BFYM) of the Yang-Mills theory we show that it displays an embedded topological sector corresponding to the field content of the Topological Yang-Mills theory (TYM). This picture arises after a proper redefinition of the fields of BFYM and gives a clear representation of the non perturbative part of the theory in terms of the topological sector. In this setting the calculation of the $vev$ of a YM observable is translated into the calculation of a corresponding (non topological) quantity in TYM. We then compare the topological observables of TYM with a similar …
The large-group behavior of the nonlocal YM$_2$'s and gYM$_2$'s on a cylinder or a disk is investigated. It is shown that this behavior is similar to that of the corresponding local theory, but with the area of the cylinder replaced by an effective area depending on the dominant representation. The critical areas for nonlocal YM$_2$'s on a cylinder with some special bounary conditions are also obtained.
The leading short-time behaviour of the Yang-Mills Schroedinger functional is obtained within a local expansion in the fields.
Recently, Witten proposed a topological string theory in twistor space that is dual to a weakly coupled gauge theory. In this lectures we will discuss aspects of the twistor string theory. Along the way we will learn new things about Yang-Mills scattering amplitudes. The string theory sheds light on Yang-Mills perturbation theory and leads to new methods for computing Yang-Mills scattering amplitudes.
It is known that the Yangian of PSU(2,2|4) is a symmetry of the tree-level S-matrix of N=4 super Yang-Mills. On the other hand, the complete one-loop dilatation operator in the same theory commutes with the level-one Yangian generators only up to certain boundary terms found by Dolan, Nappi and Witten. Using a result by Zwiebel, we show how the Yangian symmetry of the tree-level S-matrix of N=4 super Yang-Mills implies precisely the Yangian invariance, up to boundary terms, of the one-loop dilatation operator.
Holomorphic Yang-Mills Theory on Compact Kähler Manifolds
我们在紧致Kähler流形上提出了$N=2$全纯Yang-Mills理论，并证明了存在一个简单的从$N=2$拓扑Yang-Mills理论映射.由此可见，爱因斯坦-厄米联络的模空间上的交配对可以通过考察$N=2$全纯杨-米尔斯理论的小耦合行为来确定。本文是Witten关于二维物理Yang-Mills理论工作的高维推广。
We conjecture that every rational Yangian invariant in N=4 SYM theory satisfies a recently introduced notion of cluster adjacency. We provide evidence for this conjecture by using the Sklyanin Poisson bracket on Gr(4,n) to check numerous examples.
The self-duality Yang-Mills equations in pseudoeuclidean spaces of dimensions $d\leq 8$ are investigated. New classes of solutions of the equations are found. Extended solutions to the D=10, N=1 supergravity and super Yang-Mills equations are constructed from these solutions.
Self-Dual Yang-Mills Fields in Eight Dimensions
偶数维空间中的强自对偶杨-米尔斯场的特征是对杨-米尔斯场$F_{μν}$的特征值的一组约束.我们得到了${\bf R}^8$上的一个拓扑界，即$\int_{M} ( F,F )^2 \geq k \int_{M} p_1^2$，其中$p_1$是SO（n）Yang-Mills丛的第一个Pontrjagin类，$k$是一个常数.强自对偶杨-米尔斯场实现了下界。
The Sp(3) BRST symmetry for Yang-Mills theory is derived in the framework of the antibracket-antifield formalism.
We write a gravity theory with Yang-Mills type action using the biconformal gauging of the conformal group. We show that the resulting biconformal Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity in the case of slowly changing fields. In addition, we systematically extend arbitrary 4-dim Yang-Mills theories to biconformal space, providing a new arena for studying flat space Yang-Mills theories. By applying the biconformal extension to a 4-dim pure Yang-Mills theory with conformal symmetry, we establish a 1-1, onto mapping between a set of gravitational gauge theor…
We investigate Yang-Mills instantons on a 7-dimensional manifold of G_2 holonomy. By proposing a spherically symmetric ansatz for the Yang-Mills connection, we have ordinary differential equations as the reduced instanton equation, and give some explicit and numerical solutions.
The analysis in previous publications of the instanton constraints required to produce a finite action of the theory is carried out also for N=2 supersymmetric Yang-Mills theory.
We will describe some mathematical ideas of K. T. Chen on calculus on loop spaces. They seem useful to understand non-abelian Yang--Mills theories.
Non-commutative supersymmetric Yang-Mills with rational Theta is dual to an ordinary supersymmetric Yang-Mills with a 't Hooft flux. It is believed that the simplest description is via the ordinary supersymmetric Yang-Mills. We claim, however, that the two descriptions form a hierarchy. The SYM description is the proper description in the ultra violet while the non-commutative description takes over in the infra red.
The structure of super Yang_Mills theories is discussed in its relation to QCD with one flavor of (tricolored) quark
Gauge independence of dimension two condensate in Yang-Mills theory is demonstrated by using a noncommutative theory technique.
We consider a Yang-Mills theory in loop space with an affine Lie gauge group. The Chapline-Manton coupling, the coupling between Yang-Mills fields and an abelian antisymmetric tensor field of second rank via the Chern-Simons term, is systematically derived within the framework of the Yang-Mills theory. The generalized Chapline-Manton couplings, the couplings among non-abelian tensor fields of second rank, Yang-Mills fields, and an abelian tensor field of third rank, are also derived by applying the non-linear realization method to the Yang-Mills theory. These couplings are accompanied by {\it …
We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang-Mills equations to phi^4-kink equations on R. Depending on the boundary conditions and torsion, we obtain solutions to the Yang-Mills equations describing instantons, chains of instanton-anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on R x G…
In this short note I show that the soft limit for colour-ordered tree-level Yang-Mills amplitudes contains a sub-leading divergent term analogous to terms found recently by Cachazo and Strominger for tree-level gravity amplitudes.
A hypothetical picture of massive excitations of 4-dimensional Yang-Mills quantum field theory as closed knotted fat strings is described.
We use fractional and wrapped branes to describe perturbative and non-perturbative properties of N=1 super Yang-Mills living on their world-volume. (Talk given at the 1st Nordstrom Symposium, Helsinki, August 2003.)
We show that a recently discovered relation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with one graviton and $(n-1)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons, can be derived from the CHY representation. In addition we show that there is a generalisation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with $r$ gravitons and $(n-r)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons. We present a general formula for this case.
The renormalizability of the Yang-Mills quantum field theory in four-dimensional space-time is discussed in the background field formalism.
A new fomulation of the Yang-Mills theory which allows to avoid the problem of Gribov ambiguity of the gauge fixing is proposed.
A recent paper proposes a way of constructing infinite dimensional symmetries of the non-supersymmetric self-dual Yang-Mills action using isometries of the space-time. We review the Lagrangian formulation of N = 4 super Yang-Mills MHV rules and extend the approach taken for the non-supersymmetric case to construct infinite dimensional symmetries of self-dual N = 4 super Yang-Mills.
We compute the ultraviolet divergences in the self-dual Yang-Mills theory, both in the purely perturbative (zero instanton charge) and topologically non-trivial sectors. It is shown in particular that the instanton measure is precisely the same as the one-loop result in the standard Yang-Mills theory.
After adding 7 auxiliary scalars to the d=10 super-Yang-Mills action, 9 of the 16 supersymmetries close off-shell. In this paper, these 9 supersymmetry generators are related by dimensional reduction to scalar and vector topological symmetry in $\N$=2 d=8 twisted super-Yang-Mills. Furthermore, a gauge-invariant superspace action is constructed for d=10 super-Yang-Mills where the superfields depend on 9 anticommuting theta variables.
A surface of codimension higher than one embedded in an ambient space possesses a connection associated with the rotational freedom of its normal vector fields. We examine the Yang-Mills functional associated with this connection. The theory it defines differs from Yang-Mills theory in that it is a theory of surfaces. We focus, in particular, on the Euler-Lagrange equations describing this surface, introducing a framework which throws light on their relationship to the Yang-Mills equations.
We compute the even part of the planar two-loop MHV amplitude in N=4 supersymmetric Yang-Mills theory, for an arbitrary number of external particles. The answer is expressed as a sum of conformal integrals.
In the previous paper, we generalized the method of Abelian decomposition to the case of SO(N) Yang-Mills theory. This method that was proposed by Faddeev and Niemi introduces a set of variables for describing the infrared limit of a Yang-Mills theory. Here, we extend the decomposition method further to the general case of four-dimensional Sp(2N) Yang-Mills theory. We find that the Sp(2N) connection decomposes according to irreducible representations of SO(N).
See hep-th/0005054.
Algebraic Structures of Topological Yang-Mills Theory
我们讨论的代数结构的各种BRST对称性与拓扑杨米尔斯理论作为推广的BRS分析开发的非阿贝尔异常的本地杨米尔斯理论。我们证明了我们的BRST代数导致一个扩展的{ \it Russian公式\/}和{ \it下降方程}，其中包含Yang-Mills理论的下降方程作为子关系.利用推广的下降方程，我们提出了拓扑杨-米尔斯理论中的非阿贝尔反常对应。我们还讨论了我们的BRST对称的几何结构和一些显式解的扩展下降方程的计算。
The ground state of reduced Yang-Mills theory
本文研究最简膜矩阵模型（对应三维约化SU(2) Yang-Mills理论），给出了该模型基态波函数的形式，为相关理论研究提供了基础结果。
We consider the coupling of nonminimal scalar multiplets to supersymmetric Yang-Mills in four dimensions and compute the one-loop contribution to the low-energy effective action in the abelian sector. We show that the resulting theory realizes the dual version of the corresponding one from N=2 supersymmetric Yang-Mills.
We show how to obtain the critical exponent of magnetization in the Lee-Yang edge singularity model coupled to two-dimensional quantum gravity.
The paper has been withdrawn by the author.
Talk presented at the 9th Max Born Symposion, Karpacz, September 1996
The Coulomb branch of the potential between two static colored sources is calculated for the Yang-Mills theory using the electric Schroedinger representation.
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