Supersymmetric Yang-Mills Fields Research Articles

Tunneling in quantum cosmology and holographic SYM theory

We study the time evolution of early universe which is developed by a cosmological constant $\Lambda_4$ and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker (FRW) space-time. The renormalized vacuum expectation value of energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as $C$. The evolution is controlled by this radiation $C$ and the cosmological constant $\Lambda_4$. For positive $\Lambda_4$, an inflationary solution is obtained at late time. When $C$ is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path-integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.

Massive quark scattering at strong coupling from AdS/CFT

We extend the analysis of Alday and Maldacena for obtaining gluon scattering amplitudes at strong coupling to include external massive quark states. Our quarks are actually the $\mathcal{N}=2$ hypermultiplets which arise when $D7$-brane probes are included in the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ geometry. We work in the quenched approximation, treating the $\mathcal{N}=2$ matter multiplets as external sources coupled to the $\mathcal{N}=4$ supersymmetric Yang-Mills fields. We first derive appropriate massive-particle boundary conditions for the string scattering world sheets. We then find an exact world sheet which corresponds to the scattering of two massive quarks and two massless gluons and extract from this the associated scattering amplitude. We also find the world sheet and amplitude for the scattering of four massive quarks. Our world sheet solutions reduce to the four massless gluon solution of Alday and Maldacena in the limit of zero quark mass. The amplitudes we compute can also be interpreted in terms of 2-2 scattering involving gluons and massive $W$ bosons.

Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory

The constraints imposed by maximal supersymmetry on multi-loop contributions to the scattering of four open superstrings in the U(N) theory are examined by use of the pure spinor formalism. The double-trace term k2 t8(tr F2)2 (where k represents an external momentum and F the Yang-Mills field strength) only receives contributions from L ⩽ 2 (where L is the loop number) while the single-trace term k2 t8(tr F4) receives contributions from all L. These statements are verified up to L = 5, but arguments based on supersymmetry suggest they extend to all L. This explains why the single-trace contributions to low energy maximally supersymmetric Yang-Mills field theory are more divergent in the ultraviolet than the double-trace contributions. We also comment further on the constraints on closed string amplitudes and their implications for ultraviolet divergences in = 8 supergravity.

One-loop effective action in the % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYt % UvgaiyGacqWFneVtaaa!4736! $$ \mathcal{N} $$ =2 supersymmetric massive Yang-Mills field theory

We consider the \( \mathcal{N} \)=2 supersymmetric massive Yang-Mills field theory formulated in the \( \mathcal{N} \)=2 harmonic superspace. We present various gauge-invariant forms of writing the mass term in the action (in particular, using the Stueckelberg superfield), which result in dual formulations of the theory. We develop a gaugeinvariant and explicitly supersymmetric scheme of the loop expansion of the superfield effective action beyond the mass shell. In the framework of this scheme, we calculate gauge-invariant and explicitly \( \mathcal{N} \)=2 supersymmetric one-loop counterterms including new counterterms depending on the Stueckelberg superfield. We analyze the component structure of one of these counterterms.

Hidden Symmetries and Integrable Hierarchy of the $${\mathcal{N}}$$ = 4 Supersymmetric Yang-Mills Equations

We describe an infinite-dimensional algebra of hidden symmetries of $${\mathcal{N}} = 4$$ supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite sequence of flows on the solution space of the $${\mathcal{N}} = 4$$ SYM equations. The dependence of the SYM fields on the parameters along the flows can be recovered by solving the equations of the hierarchy. We embed the $${\mathcal{N}} = 4$$ SYM equations in the infinite system of the hierarchy equations and show that this SYM hierarchy is associated with an infinite set of graded symmetries recursively generated from supertranslations. Presumably, the existence of such nonlocal symmetries underlies the observed integrable structures in quantum $${\mathcal{N}} = 4$$ SYM theory.

Impressions on the algebraic renormalization of theN=2supersymmetric Yang-Mills field theories

We investigate the ultraviolet behavior of a class of N=2 supersymmetric Yang-Mills field theories which are built up in terms of N=1 superfields. Our results are obtained within the framework of the so-called algebraic renormalization technique of Becchi, Rouet, and Stora. Thanks to the algebraic renormalization setup, we have been able to write down the most general local counterterm functional which is compatible with all the classical symmetries of the model in the N=1 superspace. As a consequence of having parametrized both physical and unphysical renormalizations of the theory, we have also been able to present its corresponding Callan-Symanzik equation. In particular, due to the existence of a pair of linearly broken Ward identities, the nonrenormalization property of the gauge ghosts' wave functions is also proven to occur in this broad class of N=2 supersymmetric gauge field models.

Non-abelian Ramond-Neveu-Schwarz string theory

We newly construct a world-sheet matrix string theory described by two-dimensional supergravity coupled to supersymmetric Yang-Mills fields where the string coordinates are non-commuting matrices in the gauge group U( N). We show that our string theory has a free string limit where it becomes N-copies of usual Ramond-Neveu-Schwarz strings and can be described by the orbifold conformal field theory being second quantized string theory. In the weak coupling limit, i.e. g s → 0 where g s is the coupling constant of our theory related with the Yang-Mills coupling as g YM −2 = α′ g s 2, a new additional dimension appears in the string spectrum and it can be speculatively interpreted as the compactified eleven-dimensional coordinate whose dynamics is given by an orbifold O( N) sigma model.

Rotational invariance in the M(atrix) formulation of type IIB theory

The matrix model formulation of M-theory can be generalized by compactification to ten-dimensional type II string theory, formulated in the infinite momentum frame. Both the type IIA and IIB string theories can be formulated in this way. In the M-theory and type IIA cases, the transverse rotational invariance is manifest, but in the IIB case, one of the transverse dimensions materializes in a completely different way from the other seven. The full O(8) rotational symmetry then follows in a surprising way from the electric-magnetic duality of supersymmetric Yang-Mills field theory.

The singlet contribution to the structure function g1( x, Q2) at small x

The resummation of O( α s l+1 ln 2 l x) terms in the evolution of the singlet part of g 1( x, Q 2) is carried out on the basis of the renormalization group equation. The corresponding singlet anomalous dimensions are calculated explicitly referring to amplitude relations derived by Bartels et al. [J. Bartels, B.I. Ermolaev and M.G. Ryskin, DESY 96-025]. The leading small- x contribution to the three-loop splitting function matrix is determined in the MS scheme. Relations are derived for the case of N = 1 supersymmetric Yang-Mills field theory. Numerical results are presented for the polarized singlet and gluon densities, and the structure functions g 1 p ( x, Q 2) and g 1 n ( x, Q 2). They are compared for different assumptio the non-perturbative input distributions, and the stability of the results against presently unknown subleading contributions is investigated.

A GENERALIZED BÄCKLUND TRANSFORMATION FOR THE (SUPER SYMMETRIC) SELF-DUAL YANG-MILLS FIELDS

We derive a Bäcklund transformation for the self-dual Yang-Mills fields by using the method of special Riemann problem with one zero, in which the moving poles in the complex parameter plane are incorporated. This BT is more general than a previously given one and is capable of generating in one step monopole or instanton solutions from a vacuum solution. We further extend this result to the case of the supersymmetric self-dual Yang-Mills fields.

Octonions, superstrings and ten-dimensional spinors

A connection between the group/spin(8) and octonions is investigated and on this basis of octonions the algebra which faithfully represents spin(8) is constructed. This octonion algebra is used to describe the superstring theory. Furthermore, using these spin(8)-covariant octonions, we construct the ten-dimensional space-time octonionic spinors together with finite spinor transformations. In the ten-dimensional spacetime, the octonionic forms of Dirac equations, the action of a supersymmetric Yang-Mills field and the super symmetry transformations are introduced.

Super-Yang-Mills fields in noncovariant supergauges

The use of the superfield calculus is not restricted to those treatments of supersymmetric Yang-Mills fields in which supersymmetry is manifest by the choice of a supersymmetric gauge. Elaborating previous work of two of the present authors a formalism is propposed which allows the introduction of general linear noncovariant supergauges - like the Wess-Zumino gauge - in N = 1 theories, maintaining at the same time the advantages of the superfield formalism.

Ten Dimensional N=1 Supergravity Coupled to Supersymmetric Yang-Mills Fields in Superspace

Ten Dimensional N=1 Supergravity Coupled to Supersymmetric Yang-Mills Fields in Superspace

Constraints and equations of motion in supersymmetric Yang-Mills theories.

The general superspace equations of motion for the physical fields of the N=3,4 non-Abelian supersymmetric Yang-Mills fields are derived from the superspace constraint equations with Bianchi identities imposed.

Geometrical constraints and equations of motion in extended supergravity.

Consequences of geometrical constraints from integrability along all super lightlike lines are examined in N-extended supergravity theories. It is shown that these constraints give rise, through Bianchi identities, to equations of motion of the conformal type for all forms of physical fields, with N>4. Our results point to an integrability program for N>4 supergravity similar to that for N>2 supersymmetric Yang-Mills fields.

On quantum mechanics with extended supersymmetry and nonabelian gauge constraints

We analyze a weakly restricted general class of quantum mechanical models with at least four real supercharges and nonabelian gauge constraints. The innocent-looking restrictions lead automatically and exclusively to the quantum mechanics which are the dimensionally reduced counterparts of supersymmetric Yang-Mills field theories. This result provides in turn an independent proof that N = 1, N = 2 and N = 4 Yang-Mills fields are the only possible supersymmetric gauge field theories (without central charges) in four dimensions.

Infrared behaviour of on shell form factors in anN=4 supersymmetric Yang-Mills field theory

We discuss the infrared and mass singular behaviour of some on shell form factors which are calculated up to the two loop level in anN=4 supersymmetric Yang-Mills field theory. One of the outcomes of our investigation is that the finite terms in the perturbation series of the form factor are determined by exponentiating the lowest order term. The same phenomeno has been discovered in some infrared and mass finite quantities.

Riemann-Hilbert Transforms and Bianchi-Bäcklund Transformations for the Supersymmetric Yang-Mills Fields

Riemann-Hilbert transforms, and their connections with the affine Lie algebra of Kac and Moody, and a two-parameter Bianchi-B\"acklund transformation are given for the constraint equations for the supersymmetric Yang-Mills fields. These are important integrable properties of the supersymmetric Yang-Mills fields; especially for $N>~3$ these constraint equations give equations of motion of the fields.

On the stochastic structure of globally supersymmetric field theories

We reformulate the bosonic sector of globally supersymmetric field theoriesthrough a “fermionisation” of bosonic Feynman graphs. The recipe for the fermionisation gives an explicit realisation of the Nicolai map. The graphical rules for supersymmetric Yang-Mills fields in the reformulated version turn out to be simpler than those of ordinary Yang-Mills fields.

From N = 1 to N = 4 extended supersymmetric Yang-Mills fields in a covariant Wess-Zumino gauge

It is assumed that N = 1 supersymmetric Yang-Mills fields coupled to chiral matter fields can be renormalized in a covariant Wess-Zumino gauge with a minimal number of subtractions so that the Ward identities of supersymmetry, ordinary gauge invariance and matter-field-flavour symmetries are satisfied. The chiral Yukawa couplings are supposed to remain unrenormalized. I show that on the basis of these assumptions an N = 4 extended manifestly O(4) invariant theory can be constructed with finite Yukawa and φ 4 couplings. A consequence of these non-renormalizations is the vanishing of the renormalization group β function.