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.
We describe various approaches that give matrix descriptions of compactified NS five-branes. As a result, we obtain matrix models for Yang-Mills theories with sixteen supersymmetries in dimensions $2,3,4$ and 5. The equivalence of the various approaches relates the Coulomb branch of certain gauge theories to the moduli space of instantons on $T^4$. We also obtain an equivalence between certain six-dimensional string theories. Further, we discuss how various perturbative and non-perturbative features of these Yang-Mills theories appear in their matrix formulations. The matrix model for four-dim…
We consider ways in which conventional supersymmetry can be embedded in the set of more general fermionic transformations proposed recently [\Ref{B}] as a framework in which to study $d=10$ super Yang-Mills. Solutions are exhibited which involve closed algebras of various numbers of supersymmetries together with their invariance groups: nine supersymmetries with $\GT {\times}\SO (1,1)$ invariance; eight supersymmetries with $\SO (7){\times}\SO (1,1)$ invariance; four supersymmetries with $\SO (3,1){\times}\U (3)$ invariance. We recover in this manner all previously known ways of adding finite …
Starting from N=1 scalar and vector supermultiplets in 2+1 dimensions, we construct superfields which constitute Lagrangians invariant under N=2 supersymmetries. We first recover the N=2 supersymmetric Abelian-Higgs model and then the N=2 pure super Yang-Mills model. The conditions for this elevation are consistent with previous results found by other authors.
In this paper we show that Yang-Mills theory in the Curci-Ferrari-Delbourgo-Jarvis gauge admits some up to now unknown local linear Ward identities. These identities imply some non-renormalization theorems with practical simplifications for perturbation theory. We show in particular that all renormalization factors can be extracted from two-point functions. The Ward identities are shown to be related to supergauge transformations in the superfield formalism for Yang-Mills theory. The case of non-zero Curci-Ferrari mass is also addressed.
Recently it has been shown how a topologically twisted version of ${\cal N}=4$ super Yang-Mills may be discretized in such a way as to preserve one scalar supersymmetry at nonzero lattice spacing. The remaining fifteen supersymmetries are broken by terms of ${\cal O}(a)$ where $a$ is the lattice spacing. One would like to know whether these remaining supersymmetries are regained in the continuum limit $a \to 0$ and, if not, how much tuning of the couplings in the lattice action is required. In this paper we derive the form of these additional twisted supersymmetries by combining a set of discr…
We study deformation of N=2 and N=4 super Yang-Mills theories, which are obtained as the low-energy effective theories on the (fractional) D3-branes in the presence of constant Ramond-Ramond 3-form background. We calculate the Lagrangian at the second order in the deformation parameter from open string disk amplitudes. In N=4 case we find that all supersymmetries are broken for generic deformation parameter but part of supersymmetries are unbroken for special case. We also find that classical vacua admit fuzzy sphere configuration. In N=2 case we determine the deformed supersymmetries. We rewr…
We study D-branes in the background of Euclidean AdS2xS2 with a graviphoton field turned on. As the background is not Ricci flat, the graviphoton field must have both self-dual and antiself-dual parts. This, in general, will break all the supersymmetries on the brane. However, we show that there exists a limit for which one can restore half of the supersymmetries. Further, we show that in this limit, the N=1/2 SYM Lagrangian on flat space can be lifted on to the Euclidean AdS2xS2 preserving the same amount of supersymmetries as in the flat case. We observe that without the C-dependent terms pr…
We consider theories consisting of a planar interface with $\N=4$ super-Yang-Mills on either side and varying gauge coupling across the interface. The interface does not carry any independent degrees of freedom, but is allowed to support local gauge invariant operators, included with independent interface couplings. In general, both conformal symmetry and supersymmetry will be broken, but for special arrangements of the interface couplings, these symmetries may be restored. We provide a systematic classification of all allowed interface supersymmetries. We find new theories preserving eight an…
We introduce an N=8 supersymmetric extension of the Bogomolny-type model for Yang-Mills-Higgs fields in 2+1 dimensions related with twistor string theory. It is shown that this model is equivalent to an N=8 supersymmetric U(n) chiral model in 2+1 dimensions with a Wess-Zumino-Witten-type term. Further reduction to 1+1 dimensions yields N=(8,8) supersymmetric extensions of the standard U(n) chiral model and Grassmannian sigma models.
We study deformed supersymmetries in N=2 super Yang-Mills theory in the Omega-backgrounds characterized by two complex parameters $ε_1, ε_2$. When one of the $ε$-parameters vanishes, the theory has extended supersymmetries. We compute the central charge of the algebra and obtain the deformed BPS monopole equation. We examine supersymmetries preserved by the equation.
We show that requiring sixteen supersymmetries in quantum mechanical gauge theory implies the existence of a web of constrained interactions. Contrary to conventional wisdom, these constraints extend to arbitrary orders in the momentum expansion.
N=2 supersymmetric Yang--Mills theories coupled to matter are considered in the Wess--Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge transformations and equations of motion. The difficulties hidden in such an algebraic structure are well known: almost always auxiliary fields can be introduced in order to put the formalism off--shell, but still the field dependent gauge transformations give rise to an infinite dimensional algebra quite hard to deal with. However, it is possible to avoid all the…
This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2 vector multiplet (VM) are embedded within. The central charges provide a plethora of information as to further symmetries of the Lagrangian. Several of these symmetries are calculated to second order. It is hoped that investigations such as these may yield avenues to help solve the auxiliary field closure problem for d = 4, N = 4, SUSY-YM and the d = 4, N = 2 Fayet-Hypermultiplet, without using an infinite number of auxiliary fields.
We construct the classical configurations of BPS states with 1/4 unbroken supersymmetries in four-dimensional N=4 SU(n+1) supersymmetric Yang-Mills theory, and discuss that these configurations correspond to string networks connecting (n+1) D3-branes in Type IIB string theory.
We give a unified approach to localization of maximally symmetric gauge theories on spheres, including $S^6$ and $S^7$. The approach follows Pestun's method of dimensionally reducing from 10 dimensional super Yang-Mills. The resulting theories have a reduced $R$-symmetry which includes an $SU(1,1)$ subgroup, except in four dimensions where, because of conformal invariance, the full flat-space $R$-symmetry is maintained, and in seven dimensions where $SU(1,1)$ is the flat-space $R$-symmetry. For the case of $S^6$ and $S^7$ we discuss the localization of these theories and also present new resul…
We extend a well-known D-brane construction of the AdS/dCFT correspondence to non-abelian defects. We focus on the bulk side of the correspondence and show that there exists a regime of parameters in which the low-energy description consists of two approximately decoupled sectors. The two sectors are gravity in the ambient spacetime, and a six-dimensional supersymmetric Yang-Mills theory. The Yang-Mills theory is defined on a rigid AdS_4 x S^2 background and admits sixteen supersymmetries. We also consider a one-parameter deformation that gives rise to a family of Yang-Mills theories on asympt…
Higher derivative terms in the effective action of certain Yang-Mills theories can be severely constrained by supersymmetry. We show that requiring sixteen supersymmetries in quantum mechanical gauge theory determines the $v^6$ term in the effective action. Even the numerical coefficient of the $v^6$ term is fixed in terms of lower derivative terms in the effective action.
Herein, we consider a topologically twisted version of maximally supersymmetric Yang-Mills theory in five dimensions which was introduced by Witten in 2011. We consider this theory on a five manifold of the form M_4 x I for M_4 an oriented Riemannian four manifold. The complete and unique action of the theory in bulk is written down and is shown to be invariant under two scalar supersymmetries.
We introduce a $N_c\times N_c$ matrix model with $\mathcal{N}=2$ supersymmetries and show its relation to the topological rigid string and the topological YM$_2$. This allows to connect the latter two theories directly. Moreover the construction leads to a new insight in the \ninfty limit. Finally a quantum mechanical matrix theory is proposed which may describe light-cone (light-front) dynamics of gauge fields.
After adding seven auxiliary scalar fields, the action for ten-dimensional super-Yang-Mills contains an equal number of bosonic and fermionic non-gauge fields. Besides being manifestly Lorentz and gauge-invariant, this action contains nine spacetime supersymmetries whose algebra closes off-shell. Octonions provide a convenient notation for displaying these symmetries.
We propose a nonperturbative definition of N=4 super Yang-Mills (SYM). We realize N=4 SYM on RxS^3 as the theory around a vacuum of the plane wave matrix model. Our regularization preserves sixteen supersymmetries and the gauge symmetry. We perform the 1-loop calculation to give evidences that the superconformal symmetry is restored in the continuum limit.
In this note we give a homological explanation of "pure spinors" in YM theories with minimal amount of supersymmetries. We construct A_{\infty} algebras A for every dimension D=3,4,6,10, which for D=10 coincides with homogeneous coordinate ring of pure spinors with coordinate lambda^{alpha}. These algebras are Bar-dual to Lie algebras generated by supersymmetries, written in components. The algebras have a finite number of higher multiplications. The main result of the present note is that in dimension D=3,6,10 the algebra A\otimes Λ[θ^α]\otimes Mat_n with a differential D is equivalent to Bat…
In spacetime dimension two, pure Yang-Mills possesses no physical degrees of freedom, and consequently it admits a supersymmetric extension to couple to an arbitrary number, N say, of Majorana-Weyl gauginos. This results in (N,0) super Yang-Mills. Further, its dimensional reduction to mechanics doubles the number of supersymmetries, from N to N+N, to include conformal supercharges, and leads to a superconformal Yang-Mills quantum mechanics with symmetry group OSp(N|2,R). We comment on its connection to AdS_2 \times S^{N-1} and reduction to a supersymmetric Calogero model.
We present interacting massive N=1 vector multiplet (VM) in nine dimensions (9D). Due to the identically-vanishing mass-term m(\Barλλ) \equiv 0 for (symplectic) pseudo-Majorana gaugino in 9D, we employ unconventional technique to give masses to fermions. In 9D, we consider the gauge group G for the VM (A_μ^I, λ^I , φ^I) (I = 1, 2, \cdots, dim G), where G is the Yang-Mills gauge group, and the gaugino λ^I is a pseudo-Majorana spinor. We break G by shifting the scalar φ^I, so that the gaugino λ^I as well as its super-partner gauge boson A_μ^I will get the same mass. The scalar φ^I plays the role…
We construct super Yang-Mills theories with ${\cal N}=2, 4$ supersymmetries on the two-dimensional square lattice keeping one or two supercharges exactly. Along the same line as the previous paper \cite{sugino}, the construction is based on topological field theory formulation. In order to resolve the problem of degenerate classical vacua encountered in the previous paper, we consider two kinds of modifications of the action. For one of them, any supersymmetry breaking terms do not need to be introduced, and the formulations exactly realize some of supersymmetries at the lattice level. Our lat…
We discuss BPS states preserving 1/4 supersymmetries of N=4 supersymmetric Yang-Mills theory as M2-branes holomorphically embedded and ending on M5-branes. We use techniques in electrodynamics to find the M2-brane configurations, and give some explicit examples. In case the M2-brane worldsheet has handles, the worldsheet moduli of the M2-brane is constrained in a discrete manner. Several aspects of multi-pronged strings in type IIB string theory are beautifully reproduced in the M-theory description. We also discuss the relation between the above construction and the D2-brane dynamics in type …
We explore maximally supersymmetric Yang-Mills theory with walls of impurities respecting half of the supersymmetries. The walls carry fundamental or bifundamental matter multiplets. We employ three-dimensional N=2 superspace language to identify the Higgs branch of this theory. We find that the vacuum conditions determining the Higgs branch are exactly the bow equations yielding Yang-Mills instantons on a multi-Taub-NUT space. Under electric-magnetic duality, the super Yang-Mills theory describing the bulk is mapped to itself, while the fundamental- and bifundamental-carrying impurity walls a…
We study a discretization of ${\cal N}=2$ super Yang-Mills theory which possesses a single exact supersymmetry at non-zero lattice spacing. This supersymmetry arises after a reformulation of the theory in terms of {\it twisted} fields. In this paper we derive the action of the other twisted supersymmetries on the component fields and study, using Monte Carlo simulation, a series of corresponding Ward identities. Our results for SU(2) and SU(3) support a restoration of these additional supersymmetries without fine tuning in the infinite volume continuum limit. Additionally we present evidence s…
We perform a systematic analysis on supersymmetric states in N=4 supersymmetric Yang-Mills theory (SYM) on R x S^3. We find a new set of 1/16 BPS equations and determine the precise configuration of the supersymmetric states by solving all 1/16 BPS equations when they are valued in Cartan subalgebra of a gauge group and the fermionic fields vanish. We also determine the number of supersymmetries preserved by the supersymmetric states varying the parameters of the BPS solutions. As a byproduct we present the complete set of such supersymmetric states in N=8 SYM on R x S^2 by carrying out dimens…
We consider N = 4 Yang-Mills theory on a flat four-torus with the R-symmetry current coupled to a flat background connection. The partition function depends on the coupling constant of the theory, but when it is expanded in a power series in the R-symmetry connection around the loci at which one of the supersymmetries is unbroken, the constant and linear terms are in fact independent of the coupling constant and can be computed at weak coupling for all non-trivial 't Hooft fluxes. The case of a trivial 't Hooft flux is difficult because of infrared problems, but the corresponding terms in the …
From One to Eight: Supersymmetry Restoration in Lattice 3D ${\cal N} = 4$ Super Yang--Mills
National Institute for Theoretical and Computational Sciences, School of Physics, and Mandelstam Institute for Theoretical Physics, University of the Witwatersrand（威特沃特斯兰德大学理论及计算科学国家研究所、物理学院和曼德尔斯坦理论物理研究所）
We study the effective action of quantum mechanical SU(N) Yang-Mills theories with sixteen supersymmetries and N>2. We show that supersymmetry requires that the eight fermion terms in the supersymmetric completion of the $v^4$ terms be one-loop exact. We also show that the twelve fermion terms in the supersymmetric completion of the $v^6$ terms are two-loop exact for N=3. For N>3, this no longer seems to be true; we are able to find non-renormalization theorems for only certain twelve fermion structures. We call these structures `generalized F-terms.' We argue that as the rank of the gauge gro…
In this paper we study the n-point correlation functions of two different families of local gauge invariant operators in N=4 supersymmetric Yang-Mills theory. The main idea is to consider the correlation functions of operators which all share a number of supersymmetries irrespective of their relative locations. We achieve this by equipping the operators with explicit space-time dependence. We provide evidence by different methods that these n-point correlators do not receive quantum corrections in perturbation theory and are hence given exactly by their tree-level result. The arguments rely on…
The scalar and vector topological Yang-Mills symmetries on Calabi-Yau manifolds geometrically define consistent sectors of Yang-Mills D=4,6 N=1 supersymmetry, which fully determine the supersymmetric actions up to twist. For a CY_2 manifold, both N=1,D=4 Wess and Zumino and superYang-Mills theory can be reconstructed in this way. A superpotential can be introduced for the matter sector, as well as the Fayet-Iliopoulos mechanism. For a CY_3 manifold, the N=1, D=6 Yang-Mills theory is also obtained, in a twisted form. Putting these results together with those already known for the D=4,8 N=2 case…
We study the noncommutative version of the extended ADHM construction in the eight dimensional U(1) Yang-Mills theory. This construction gives rise to the solutions of the BPS equations in the Yang-Mills theory, and these solutions preserve at least 3/16 of supersymmetries. In a wide subspace of the extended ADHM data, we show that the integer $k$ which appears in the extended ADHM construction should be interpreted as the $D4$-brane charge rather than the $D0$-brane charge by explicitly calculating the topological charges in the case that the noncommutativity parameter is anti-self-dual. We a…
We construct an octonionic instanton solution to the seven dimensional Yang-Mills theory based on the exceptional gauge group $G_2$ which is the automorphism group of the division algebra of octonions. This octonionic instanton has an extension to a solitonic two-brane solution of the low energy effective theory of the heterotic string that preserves two of the sixteen supersymmetries and hence corresponds to $N=1$ space-time supersymmetry in the (2+1) dimensions transverse to the seven dimensions where the Yang-Mills instanton is defined.
Global supersymmetries of the S-matrices of N = 2, 4, 8 supersymmetric Yang-Mills theories in three spacetime dimensions (without matter hypermultiplets) are shown to be SU(1|1), SU(2|2) and SU(2|2) X SU(2|2) respectively. These symmetries are not manifest in the off-shell Lagrangian formulations of these theories. A direct map between these symmetries and their representations in terms of the Yang-Mills degrees of freedom and the corresponding quantities in Chern-Simons-Matter theories with N >= 4 supersymmetry is also obtained. Dimensional reduction of the on-shell observables of the Yang-Mi…
Following the observation of Banks and Green that the D-instantons in AdS_5 correspond to the instantons in 4-dimensional supersymmetric Yang-Mills theory, we study in more detail this correspondence for individual instantons. The supergravity solution for a D-instanton in AdS_5 is found using the ansatz used previously for D-instantons in flat space. We check that the actions and supersymmetries match between the D-instanton solution and the Yang-Mills instanton. Generalizing this result, we propose that any supergravity solution satisfying the ansatz corresponds to a (anti-)self-dual Yang-Mi…
Domain walls in supersymmetric Yang-Mills are BPS configurations which preserve two supercharges of the parent theory and so their tensions are known exactly. On the other hand, they have been described as D-branes for the confining string. This leads to a description of their collective dynamics in terms of a 2+1 -dimensional gauge theory with two supersymmetries and a Chern-Simons term. We show that this open string description can capture the qualitative behaviour of the forces between the domain walls for an arbitrary configuration of n walls at leading order in 1/N, extending earlier calc…
We study singular time-dependent $\frac{1}{8}$-BPS configurations in the abelian sector of ${{\mathcal N}= 4}$ supersymmetric Yang-Mills theory that represent BPS string-like defects in ${{\mathbb R}\times S^3}$ spacetime. Such BPS strings can be described as intersections of the zeros of holomorphic functions in two complex variables with a 3-sphere. We argue that these BPS strings map to $\frac{1}{8}$-BPS surface operators under the state-operator correspondence of the CFT. We show that the string defects are holographically dual to noncompact probe D3-branes in global $AdS_5\times S^5$ that…
We study a three-dimensional U(k) Yang-Mills Chern-Simons theory with adjoint matter preserving two supersymmetries. According to Acharya and Vafa, this theory describes the low-energy worldvolume dynamics of BPS domain walls in four-dimensional N=1 SYM theory. We demonstrate how to obtain the same theory in a brane configuration of type IIB string theory that contains threebranes and fivebranes. A combination of string and field theory techniques allows us to re-formulate some of the well-known properties of N=1 SYM domain walls in a geometric language and to postulate a Seiberg-like duality …
We conjecture the form of the one-loop determinants for localized gauge theories with eight supersymmetries on $d$-dimensional spheres. Combining this with results for the localized action, we investigate the strong coupling behavior in the large $N$ limit for a continuous range of $d$. In particular, we find the $N$ dependence of the free energy for supersymmetric Yang-Mills with only a vector multiplet in $3<d<4$ and for maximally supersymmetric Yang-Mills in $3< d<6$. We also argue that this gives an effective way to regularize divergences after localization in $d=4$ for ${\mathcal N}=2$ ga…
We study the dimensional reduction of ten-dimensional super Yang-Mills theory in curved backgrounds with torsion. We examine the parallel spinor conditions and the constraints for the torsion parameters which preserve supersymmetry and gauge symmetry in four dimensions. In particular we examine the ten-dimensional Omega-background with the torsion which is identified with the R-symmetry Wilson line gauge fields. After the dimensional reduction, we obtain the Omega-deformed N=4 super Yang-Mills theory. Solving the parallel spinor conditions and the torsion constraints, we classify the deformed …
In this brief review, I summarize the current theoretical knowledge in supersymmetry on the lattice, with special emphasis on recent results in the framework of N=1 supersymmetric Yang Mills theory, Wess-Zumino model and Yang-Mills theory with extended supersymmetries.
Up to overall harmonic factors, the D8-brane solution of the massive type IIA supergravity theory is the product of nine-dimensional Minkowski space (the worldvolume) with the real line (the transverse space). We show that the equations of motion allow for the worldvolume metric to be generalised to an arbitrary Ricci-flat one. If this nine-dimensional Ricci-flat manifold admits Killing spinors, then the resulting solutions are supersymmetric and satisfy the usual Bogomol'nyi bound, although they preserve fewer than the usual one half of the supersymmetries. We describe the possible choices of…
We study D-instanton solutions in type IIB supergravity on $AdS_5\times T^{1,1}$, which has a dual ${\cal N}=1$ $SU(N)\times SU(N)$ super Yang-Mills theory. Apart from ordinary D(-1)-brane instantons, we discuss wrapped D1-branes over minimal 2-cycles and derive explicit solutions preserving half the supersymmetries. These solutions are identified with Yang-Mills instantons which are (anti)self-dual in both gauge group factors with instanton charge $(k,k')$. By examining the boundary behaviour of the solutions we discuss the coupling to the corresponding dual boundary operators, and identify t…
We consider the maximal super-Yang-Mills theory in 5 Euclidean dimensions with SO(5) R-symmetry and 16 supersymmetries. We argue that the strong coupling limit of this theory (with a possible UV completion) has an emergent time dimension and gives a description of the 5+1 dimensional Lorentz invariant (2,0) theory of the M5-brane, compactified on a timelike circle with radius R=g^2/4π^2 . Our discussion involves issues of quantization of Euclidean theories without time.
We construct d<=7 dimensional maximally supersymmetric Yang-Mills theories on a class of curved backgrounds with off-shell supercharges. The off-shell supersymmetry is mainly a generalization of on-shell supersymmetry constructed previously by Blau. We present several examples of backgrounds and discuss the number of the preserved supersymmetries on these backgrounds. We also construct another maximally supersymmetric Yang-Mills theories on S^3 by dimensional reducing along the R-direction of N=4 super Yang-Mills theory on RxS^3.
In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether these theories suffer from a sign problem. In this paper we address this issue by conducting simulations of the N=(2, 2) and N=(8, 8) supersymmetric Yang--Mills theories in two dimensions for the U(N) theories with N=2,3,4, using the new twisted lattice formulations. Our results provide evidence that these theories do not suffer from a sign problem in the conti…
A Yang-Mills solution is constructed on T^6 which corresponds to a brane configuration composed purely of 0-branes and 6-branes. This configuration breaks all supersymmetries and has an energy greater than the sum of the energies of its components; nonetheless, the configuration is stable classically, at least to quadratic order. An analogous construction is also given for a system of 0-branes and 8-branes on T^8. These constructions may prove to be useful for describing 6-branes and 8-branes in M(atrix) theory.
We consider the bosonic and fermionic symmetries of five-dimensional Maxwell- and Yang-Mills-Einstein supergravity theories on a spacetime with boundaries (isomorphic to M x S1/Z2). Due to the appearance of the "Chern-Simons" term, the classical action is not generally invariant under gauge and supersymmetries. Once bulk vector fields are allowed to propagate on the boundaries, there is an "inflow" governed by the rank-3 symmetric tensor that defines the five-dimensional theories. We discuss the requirements that invariance of the action imposes on new matter content and boundary conditions.
On any simply connected Sasaki-Einstein five dimensional manifold one can construct a super Yang-Mills theory which preserves at least two supersymmetries. We study the special case of toric Sasaki-Einstein manifolds known as $Y^{p,q}$ manifolds. We use the localisation technique to compute the full perturbative part of the partition function. The full equivariant result is expressed in terms of certain special function which appears to be a curious generalisation of the triple sine function. As an application of our general result we study the large $N$ behaviour for the case of single hyperm…
We study decoupling limits and S-dualities for noncommutative open string/ Yang-Mills theory in a gravity setup by considering an $SL(2,Z)$ invariant supergravity solution of the form ((F, D1), D3) bound state of type IIB string theory. This configuration can be regarded as D3-branes with both electric and magnetic fields turned on along one of the spatial directions of the brane and preserves half of the space-time supersymmetries of the string theory. Our study indicates that there exists a decoupling limit for which the resulting theory is an open string theory defined in a geometry with no…
For all types of N=4 anti-de Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the non-Abelian case. Manifestly N=4 supersymmetric Yang-Mills (SYM) actions are explicitly given in the cases of (2,2) and critical (4,0) AdS supersymmetries. The N=4 vector multiplets and the corresponding actions are then reduced to (2,0) AdS superspace, in which only N=2 supersymmetry is manifest. Using the off-shell structure of the N=4 vector multiplets, we provide complete N=4 SYM actions i…
We test the AdS/CFT correspondence by calculating Wilson loops in N = 4 super Yang-Mills theory on R*S^3 in the planar limit. Our method is based on a novel large-N reduction, which reduces the problem to Monte Carlo calculations in the plane-wave matrix model or the BMN matrix model, which is a 1d gauge theory with 16 supercharges. By using the gauge-fixed momentumspace simulation, we obtain results respecting 16 supersymmetries. We report on the Monte Carlo results for the BPS circular Wilson loop, which reproduce the exact result up to strong coupling. As a future prospect, we calculate a t…
Lattice Studies of Two-Dimensional Maximally Supersymmetric Yang-Mills Theory for Tests of Gauge-Gravity Duality
Indian Institute of Science Education and Research - Mohali（印度科学教育与研究学院-莫哈利分校）；University of the Witwatersrand（威特沃特斯兰德大学）；University of Liverpool（利物浦大学）
We use the recently proposed supergravity approach to large $N$ gauge theories to calculate ordinary and spatial Wilson loops of gauge theories in various dimensions. In this framework we observe an area law for spatial Wilson loops in four and five dimensional supersymmetric Yang-Mills at finite temperature. This can be interpreted as the area law of ordinary Wilson loops in three and four dimensional non-supersymmetric gauge theories at zero temperature which indicates confinement in these theories. Furthermore, we show that super Yang Mills theories with 16 supersymmetries at finite tempera…
We obtain D=4 de Sitter gravity coupled to SU(2) Yang-Mills gauge fields from an explicit and consistent truncation of D=11 supergravity via Kaluza-Klein dimensional reduction on a non-compact space. The ``internal'' space is a smooth hyperbolic 7-space (H^7) written as a foliation of two 3-spheres, on which the SU(2) Yang-Mills fields reside. The positive cosmological constant is completely fixed by the SU(2) gauge coupling constant. The explicit reduction ansatz enables us to lift any of the D=4 solutions to D=11. In particular, we obtain dS_2 in M-theory, where the nine-dimensional transver…
Continuum reduction and Monte Carlo simulation are used to calculate the heavy quark potential and the string tension in large N Yang-Mills theory in four dimensions. The potential is calculated out to a separation of nine lattice units on a lattice with extent six in each direction.
