Machiko Hatsuda, Yu-tin Huang, Warren Siegel
We present simple first-class-constraint actions and BRST operators for the 4D N=4 superparticle. Each generation of ghosts has 2 super-indices, like the coordinates. The constraints that define projective superspace close in a super Yang-Mills background due to the presence of a (non-central) U(1) generator in the algebra.
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We attempt to resolve the cosmological constant problem through the key concept of the quantized number of spatial degrees of freedom in the modified Yang's quantized space-time, $n_{\rm {dof}} (V_3^{R(τ)})$.
The entire geometric formulations of the BRST and the anti-BRST structures are worked out in presence of the Nakanishi-Lautrup field. It is shown that in the general form of gauge fixing mechanisms within the Faddeev-Popov quantization approach, the antiBRST invariance reflects thoroughly the classical symmetry of the Yang-Mills theories with respect to gauge fixing methods. The Nakanishi-Lautrup field is also defined and worked out as a geometric object. This formulation helps us to introduce two absolutely new topological invariants of quantized Yang-Mills theories, so called the Nakanishi-L…
In the preceding paper, we derived a kind of kinematical holographic relation (KHR) in the Lorentz-covariant Yang's quantized space-time algebra (YSTA). It essentially reflects the fundamental nature of the noncommutative geometry of YSTA and its representation, that is, a definite kinematical reduction of spatial degrees of freedom in comparison with the ordinary lattice space. On the basis of the relation and its extension to various spatial dimensions, we derive a new area-entropy relation in a simple $D_0$ brane gas system subject to YSTA, following the idea of M-theory. Furthermore, we ma…
We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang's quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, $λ$ and $R$, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, we find a certain kind of kinematical holographic relation in YSTA, which ma…
The present-day significance of Yang's quantized space-time algebra (YST) is pointed out from the holographic viewpoint. One finds that the D-dimensional YST and its modified version (MYST) have the background symmetry SO(D+1,1) and SO(D,2), which are well known to underlie the dS/CFT and AdS/CFT correspondences, respectively. This fact suggests a new possibility of dS/YST and AdS/MYST in parallel with dS/CFT and AdS/CFT, respectively. The spatial components of quantized space-time and momentum operators of YST have discrete eigenvalues and their respective minimums, $a$ and 1/R, without contr…
This is a personally colored account of the history behind N=4 Yang-Mills Theory.
We consider quantized Yang-Mills theories in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S-matrix. The most general coupling which is gauge invariant in first order contains a two-parametric ambiguity in the ghost sector - a divergence- and a coboundary-coupling may be added. We prove (not completely) that the higher orders with these two additional couplings are gauge invariant, too. Moreover we show that the ambiguities of the n-point distributions restricted to the p…
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.
Yang-Mills theories at finite temperature quantized in linear covariant gauges: gauge copies and semi-non-perturbative effects
该研究针对有限温度下最大阿贝尔规范和线性协变规范中量子化的四维欧几里得杨-米尔斯理论，通过混合方法探索有限温度效应与移除格里博副本的相互作用，验证了胶子自由度的三种相。
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.
We investigate a possible inner relation between the familiar Bekenstein-Hawking area-entropy relation and ours presented in a simple $D_0$ brane gas model on the basis of the kinematical holographic relation [KHR] in the Yang's quantized space-time algebra (YSTA). We find out that the relation between them is well understood through the idea of an {\it elementary} Schwarzschild black hole realized on a single $[site]$ of Planckian scale in our scheme. Related arguments possibly explain the origin of a certain kind of universality as seen in $η=1/4$ in the Bekenstein-Hawking relation and lead …
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.
We present simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with $k=-1$, finite density of microstates and a resolved Big Bang. At late times, a linear coasting cosmology $a(t) \propto t$ is obtained, which is remarkably close to observation. The solution consists of two sheets with opposite intrinsic chiralities, which are connected in a Euclidean pre-big bang era.
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.
We define a natural generalized symmetry of the Yang-Mills equations as an infinitesimal transformation of the Yang-Mills field, built in a local, gauge invariant, and Poincaré invariant fashion from the Yang-Mills field strength and its derivatives to any order, which maps solutions of the field equations to other solutions. On the jet bundle of Yang-Mills connections we introduce a spinorial coordinate system that is adapted to the solution subspace defined by the Yang-Mills equations. In terms of this coordinate system the complete classification of natural symmetries is carried out in a st…
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.
We propose $N=2$ holomorphic Yang-Mills theory on compact Kähler manifolds and show that there exists a simple mapping from the $N=2$ topological Yang-Mills theory. It follows that intersection parings on the moduli space of Einstein-Hermitian connections can be determined by examining the small coupling behavior of the $N=2$ holomorphic Yang-Mills theory. This paper is a higher dimensional generalization of the Witten's work on physical Yang-Mills theory in two dimensions.
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.
Strongly self-dual Yang-Mills fields in even dimensional spaces are characterised by a set of constraints on the eigenvalues of the Yang-Mills fields $F_{μν}$. We derive a topological bound on ${\bf R}^8$, $\int_{M} ( F,F )^2 \geq k \int_{M} p_1^2$ where $p_1$ is the first Pontrjagin class of the SO(n) Yang-Mills bundle and $k$ is a constant. Strongly self-dual Yang-Mills fields realise the lower bound.
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 investigate the possible inner relation between the familiar Bekenstein-Hawking area-entropy relation and ours presented in a simple $D_0$ brane gas system on the basis of the kinematical holographic relation [KHR] in the Yang's quantized space-time. We find out that the relation between them is well understood through the idea of {\it elementary} Schwarzschild black hole realized on a single $[site]$ of Planckian scale in our scheme. Related arguments explain the origin of a certain kind of universality as seen in $η=1/4$ in the Bekenstein-Hawking relation and lead us to notice the similar…
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.
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