We compute the penetration depth of a light quark moving through a large $N_c$, strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills plasma using gauge/gravity duality and a combination of analytic and numerical techniques. We find that the maximum distance a quark with energy $E$ can travel through a plasma is given by $Δx(E) = (\mathcal C/T) (E/T \sqrtλ)^{{1}/{3}}$ with $\mathcal C \approx 0.5$.
We compute the soft contribution to the static energy of two heavy colour sources interacting via a N=4 supersymmetric Yang-Mills theory. Both singlet and octet colour configurations are considered. Our calculations complete recent considerations of the ultrasoft contributions.
The energy density wake produced by a heavy quark moving through a strongly coupled N=4 supersymmetric Yang-Mills plasma is computed using gauge/string duality.
We reformulate 5D maximally supersymmetric Yang-Mills in 4D Superspace, for a manifold with boundaries. We emphasise certain features and conventions necessary to allow for supersymmetric model building applications. Finally we apply the holographic interpretation of a slice of AdS and show how to generate Dirac soft masses between external source fields, as well as kinetic mixing, as a boundary effective action.
We introduce new local gauge invariant variables for N=1 supersymmetric Yang-Mills theory, explicitly parameterizing the physical Hilbert space of the theory. We show that these gauge invariant variables have a geometrical interpretation, and can be constructed such that the emergent geometry is that of N=1 supergravity: a Riemannian geometry with vector-spinor generated torsion. Full geometrization of supersymmetric Yang-Mills theory is carried out, and geometry independent divergences associated to the inversion of a differential operator with zero modes -- that were encountered in the non-s…
I discuss similarities and differences between the resurgence program in quantum mechanics and the operator product expansion in strongly coupled Yang-Mills theories. In ${\mathcal N}=1$ super-Yang-Mills renormalons possess peculiar features that make them different from renormalons in QCD. Their conventional QCD interpretation does not seem to be applicable in supersymmetric Yang-Mills in a straightforward manner.
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, I analyze the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for $N_f < N_c$, in which the superpotential is generated nonperturbatively, N=2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effective coupling is described geometrically, and supersymmetric QCD for N_f large, in which the theory ill…
We study the high energy limit of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory for finite N_c. We make use of the framework of perturbative resummation of large logarithms of the energy. More specifically, we apply the (extended) generalized leading logarithmic approximation. We find that the same conformally invariant two-to-four gluon vertex occurs as in non-supersymmetric Yang-Mills theory. As a new feature we find a direct coupling of the four-gluon t-channel state to the R-current impact factor.
Supersymmetric pure Yang-Mills theory is formulated with a local, i.e. space-time dependent, complex coupling in superspace. Super-Yang-Mills theories with local coupling have an anomaly, which has been first investigated in the Wess-Zumino gauge and there identified as an anomaly of supersymmetry. In a manifest supersymmetric formulation the anomaly appears in two other identities: The first one describes the non-renormalization of the topological term, the second relates the renormalization of the gauge coupling to the renormalization of the complex supercoupling. Only one of the two identit…
We resolve an ambiguity in the sign of the gaugino determinant in supersymmetric models. The result, that the gaugino determinant can be taken positive for all background gauge configurations, is necessary for application of QCD inequalities and lattice Monte Carlo methods to supersymmetric Yang-Mills models.
We construct an exact analytical solution to the integral equation which is believed to describe logarithmic growth of the anomalous dimensions of high spin operators in planar N=4 super Yang-Mills theory and use it to determine the strong coupling expansion of the cusp anomalous dimension.
We perform dimensional reductions of recently constructed self-dual $~N=2$~ {\it supersymmetric} Yang-Mills theory in $~2+2\-$dimensions into two-dimensions. We show that the universal equations obtained in these dimensional reductions can embed supersymmetric exactly soluble systems, such as $~N=1$~ and $~N=2$~ supersymmetric Korteweg-de Vries equations, $~N=1$~ supersymmetric Liouville theory or supersymmetric Toda theory. This is the first supporting evidence for the conjecture that the $~2+2\-$dimensional self-dual {\it supersymmetric} Yang-Mills theory generates {\it supersymmetric} solub…
We show that recently formulated four-dimensional self-dual supersymmetric Yang-Mills theory, which is consistent background for open $~N=2$~ superstring, generates two-dimensional $~N=(1,1),~\, N=(1,0) $~ and $~N=(2,0)$~ supersymmetric gauged Wess-Zumino-Novikov-Witten $~\s\-$models on coset manifolds $~G/H$, after appropriate dimensional reductions. This is supporting evidence for the conjecture that the self-dual supersymmetric Yang-Mills theory will generate lower-dimensional supersymmetric integrable models after dimensional reductions.
We use the gauge-gravity duality conjecture to compute spectral functions of the stress-energy tensor in finite temperature N=4 supersymmetric Yang-Mills theory in the limit of large Nc and large coupling. The spectral functions exhibit peaks characteristic of hydrodynamic modes at small frequency, and oscillations at intermediate frequency. The non-perturbative spectral functions differ qualitatively from those obtained in perturbation theory. The results may prove useful for lattice studies of transport processes in thermal gauge theories.
We study the perturbation expansion of the free energy of N=4 supersymmetric SU(N) Yang-Mills at finite temperature in powers of 't Hooft's coupling g^2 N in the large N limit. Infrared divergences are controlled by constructing a hierarchy of two 3 dimensional effective field theories. This procedure is applied to the calculation of the free energy to order (g^2 N)^(3/2), but it can be extended to higher order corrections.
The renormalization of supersymmetric Yang-Mills theories with soft supersymmetry breaking is presented using spurion fields for introducing the breaking terms. It is proven that renormalization of the fields and parameters in the classical action yields precisely the correct counterterms to cancel all divergences. In the course of the construction of higher orders additional independent parameters appear, but they can be shown to be irrelevant in physics respects. Thus, the only parameters with influence on physical amplitudes are the supersymmetric and the well-known soft breaking parameters…
The high energy limit of scattering amplitudes in the N=4 supersymmetric Yang-Mills theory is studied by solving the corresponding BFKL equation in the next-to-leading approximation. The gluon Green's function is analysed using a newly proposed method suitable for investigating the contribution from higher conformal spins. From this new approach complete agreement is obtained with the results of Kotikov and Lipatov on conformal spins and angular dependence.
The one-loop corrections to the supersymmetric Ward-Takahashi identity (WTi) are investigated in the off-shell regime in the Wilson formulation of the discretized N=1 Super Yang-Mills (SYM) theory. The study of the continuum limit as well as the renormalization procedure for the supercurrent are presented.
The interest in the thermodynamics of supersymmetric Yang-Mills started after Maldacena proposed the duality between string theory on AdS backgrounds and the large-N limit of SYM theories. One of the motivations to study the thermal properties of ${\cal N}=4$ supersymmetric Yang-Mills in four dimensions (SYM$_{4,4}$) is that at high temperatures, the weak-coupling limit of this theory has many similarities with high temperature quantum chromodynamics (QCD). In this proceedings contribution, we review recent calculations of the resummed perturbative free energy of ${\cal N}=4$ supersymmetric Ya…
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.
Using gauge/gravity duality, we study the creation and evolution of anisotropic, homogeneous strongly coupled $\mathcal N=4$ supersymmetric Yang-Mills plasma. In the dual gravitational description, this corresponds to horizon formation in a geometry driven to be anisotropic by a time-dependent change in boundary conditions.
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.
We show that $~N=1$~ {\it supersymmetric} Kadomtsev-Petviashvili (SKP) equations can be embedded into recently formulated $~N=1$~ self-dual {\it supersymmetric} Yang-Mills theories after appropriate dimensional reduction and truncation, which yield three-dimensional supersymmetric Chern-Simons theories. Based on this result, we also give conjectural \hbox{$N=2~$} SKP equations. Subsequently some exact solutions of these systems including fermionic fields are given.
A supersymmetric collective coordinate expansion of the monopole solution of $N=4$ Yang-Mills theory is performed resulting in an $N=4$ supersymmetric quantum mechanics on the moduli space of monopole solutions.
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.
Using gauge/gravity duality, we study the creation and evolution of boost invariant anisotropic, strongly coupled N = 4 supersymmetric Yang-Mills plasma. In the dual gravitational description, this corresponds to horizon formation in a geometry driven to be anisotropic by a time-dependent change in boundary conditions.
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 determine the action for five-dimensional maximally supersymmetric Yang-Mills in off-shell supergravity backgrounds. The resulting theory contains novel five-dimensional BF type couplings as well as cubic scalar interactions which vanish in flat space.
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 propose a method for the evaluation of Witten index in D=2 supersymmetric Yang-Mills quantum mechanics. We rederive a known result for the SU(2) gauge group and generalize it to any SU(N) gauge group.
We make a preliminary algebraic study of supersymmetric deformations of N=1 Yang-Mills theory in dimension ten with an arbitrary gauge group. This is done in a context of Lie algebra deformation theory. The tangent space to the space of deformation is computed.
The hamiltonian formulation of Supersymmetric Yang-Mills quantum mechanics (SYMQM) is discussed. We focus on the Fock space formulation of the models since it is convenient for the numerical analysis, however some novel analytical results are also pointed out.
An ``anomalous'' supersymmetry transformation of the gaugino axial current is given in supersymmetric Yang-Mills theory. The contact term is computed to one-loop order by a gauge-invariant point-splitting procedure. We reexamine the supercurrent anomaly in this method.
The role of instantons in three dimensional N=2 supersymmetric SU(2) Yang-Mills theory is studied, especially in relation to the issue of confinement. The instanton-induced low energy effective action is derived by extending the dilute gas approximation to the super-moduli space of instantons. Following Polyakov's description of confinement in compact U(1) gauge theory, it is argued that there is no confinement in N=2 supersymmetric Yang-Mills theory.
The supersymmetric Lee-Yang model is arguably the simplest interacting supersymmetric field theory in two dimensions, albeit non-unitary. A natural question is if there is an analogue of supersymmetric Lee-Yang fixed point in higher dimensions. The absence of any $\mathbb{Z}_2$ symmetry (except for fermion numbers) makes it impossible to approach it by using perturbative $ε$ expansions. We find that the truncated conformal bootstrap suggests that candidate fixed points obtained by the dimensional continuation from two dimensions annihilate below three dimensions, implying that there is no supe…
We present a model for supersymmetric Yang-Mills theory in 10+2 dimensions. Our construction uses a constant null vector, and leads to a consistent set of field equations and constraints. The model is invariant under generalized translations and an extra gauge transformation. Ordinary dimensional reduction to ten dimensions yields the usual supersymmetric Yang-Mills equations, while dimensional reduction to 2+2 yields supersymmetric Yang-Mills equations in which the Poincaré supersymmetry is reduced by a null vector. We also give the corresponding formulation in superspace.
Supersymmetric Yang Mills theory is directly accessible to lattice simulations using current methodology, and can provide a non-trivial check of recent exact results in SQCD. In order to tune the lattice simulation to the supersymmetric point it is neccessary to understand the behavior of the theory with a small supersymmetry breaking gaugino mass. We introduce a soft breaking gaugino mass in a controlled fashion using a spurion analysis. We compute the gluino condensate, vacuum energy and bound-state masses as a function of the gaugino mass, providing more readily accessible predictions which…
We present results for the universal anomalous dimension γ_{uni}(j) of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory in the first four orders of perturbation theory.
We obtain the Picard-Fuchs equations of N=2 supersymmetric Yang-Mills theory with the exceptional gauge group E_6. Such equations are based on E_6 spectral curve.
D0-brane theory on a torus with a nonvanishing B field is embedded into a string theory in the weak coupling limit. It is shown that the usual supersymmetric Yang-Mills theory on a noncommutative torus can not be the whole story. The Born-Infeld action survives the noncommutative torus limit.
Reducing Supersymmetric Yang-Mills Field Theory to a single point in the three dimensional space results in the Supersymmetric Yang-Mills Quantum Mechanics (SYMQM) which basically is the effective quantum mechanics of zero momentum modes of the original theory. Such a system is still quite non-trivial and usually inherits many properties of the original field theory. In this talk some beautiful features of the three-dimensional model will be reviewed and illustrated with the aid of the recent, quantitative solution. In particular the structure of the supersymmetric vacua and condensates will b…
We present an action for noncommutative supersymmetric Yang-Mills theory in ten-dimensions, and confirm its invariance under supersymmetry. We next add higher-order derivative terms to such a noncommutative supersymmetric action. These terms contain fields as high as the quartic order. This resulting action can be regarded as supersymmetric generalization of noncommutative non-Abelian Dirac-Born-Infeld action. Some ambiguities related to field redefinitions are also clarified.
Action of 4 dimensional N=4 supersymmetric Yang-Mills theory is written by employing the superfields in N=4 superspace which were used to prove the equivalence of its constraint equations and equations of motion. Integral forms of the extended superspace are engaged to collect all of the superfields in one "master" superfield. The proposed N=4 supersymmetric Yang-Mills action in extended superspace is shown to acquire a simple form in terms of the master superfield.
We construct BPS saturated regular configurations of N=4 SU(3) supersymmetric Yang-Mills theory carrying non-parallel electric and magnetic charges. These field theory BPS states correspond to the string theory BPS states of 3-string junctions connecting three different D3-branes by regarding the N=4 supersymmetric Yang-Mills theory as an effective field theory on parallel D3-branes.
We construct lattice action for five-dimensional maximally supersymmetric Yang-Mills theory. This supersymmetric lattice formulation can be used to explore the non-perturbative regime of the continuum target theory, which has a known gravitational dual.
In this paper we examine the supersymmetric Lee-Yang model in the presence of boundaries. We determine the reflection factors for the Neveu-Schwarz type boundary conditions from the reduction of the supersymmetric sine-Gordon model and check them by using Boundary Truncated Conformal Space Approach in the massless case. We explore the boundary renormalisation groups flows using boundary TBA and TCSA.
The action for classical and consequently quantum N=1, D=4, supersymmetric Yang-Mills theories is proven to be written as a BRST exact term. In order to show this, the space of fields in the theory must be enlarged to include an extrafield as a non dynamical auxiliary field.
Using the shadow dependent decoupled Slavnov-Taylor identities associated to gauge invariance and supersymmetry, we discuss the renormalization of the N=4 super-Yang-Mills theory and of its coupling to gauge-invariant operators. We specify the method for the determination of non-supersymmetric counterterms that are needed to maintain supersymmetry.
We discuss the physics of four-dimensional compact U(1) lattice gauge theory from the point of view of softly broken N=2 supersymmetric SU(2) Yang-Mills theory. We provide arguments in favor of (pseudo-)critical mass exponents 1/3, 5/11 and 1/2, in agreement with the values observed in the computer simulations. We also show that the J^{CP} assignment of some of the lowest lying states can be naturally explained.
By exploiting standard facts about $N=1$ and $N=2$ supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric Yang-Mills theory.
We study the spectrum of the softly broken generalized Veneziano-Yankielowicz effective action for N=1 SUSY Yang-Mills theory. Two dual formulations of the effective action are given. The spurion method is used for the soft SUSY breaking. Masses of the bound states are calculated and mixing patterns are discussed. Mass splittings of pure gluonic states are consistent with predictions of conventional Yang-Mills theory. The results can be tested in lattice simulations of the SUSY Yang-Mills model.
For the SU(N) invariant supersymmetric matrix model related to membranes in 4 space-time dimensions we argue that <Psi,chi> = 0 for the previously obtained solution of Q chi = 0, Q^{dagger} Psi = 0.
This note reviews the progress on the low energy dynamics of N=2 supersymmetric Yang-Mills theories after the works of Seiberg and Witten. Specifically, the theory of prepotential for non-specialists is reviewed.
We study N=1 supersymmetric SU(N) Yang-Mills theory on the lattice at strong coupling. Our method is based on the hopping parameter expansion in terms of random walks, resummed for any value of the Wilson parameter r in the small hopping parameter region. Results are given for the mesonic (2-gluino) and fermionic (3-gluino) propagators and spectrum.
We present families of algebraic curves describing the moduli-space of $N\!=\!2$ supersymmetric Yang-Mills theory with gauge group $SO(2n)$. We test our curves by computing the weak coupling monodromies and the number of $N\!=\!1$ vacua.
Supersymmetric Yang-Mills theory is formulated in six dimensions, without the use of anti-commuting variables. This is achieved using a new Nicolai map, to third order in the coupling constant. This is the second such map in six dimensions and highlights a potential ambiguity in the formalism.
Two-loop Gell-Mann-Low function is calculated for N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives. The integrals, which define it, are shown to be reduced to total derivatives and can be easily calculated analytically.
