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.
In this paper, we construct Janus-type solutions of three-dimensional gauged supergravity with sixteen supersymmetries. We find solutions which correspond to interfaces between the same CFT on both sides, as well as RG-flow interfaces between CFTs with different numbers of supersymmetries and central charges. The solutions are obtained by solving the flow equations derived from the supersymmetry variations, and they preserve some fraction of the supersymmetries of the $\AdS_3$ vacua.
In this note we review the construction of topologically gauged M2 branes with 6 supersymmetries and discuss some of its properties. This is done using the 3-algebra formulation thereby covering all possible gauge groups. We will elaborate upon 1) the fundamental identity and its solutions noting, provided these gauged theories describe stacks of branes, the case of a single brane, 2) the chiral point solution to the field equations (occuring even for a single brane) that breaks the superconformal symmetries down to those of AdS_3 (TMG) supergravity, 3) physical parameters and how they scale i…
We study essentially non-Abelian backgrounds in the five dimensional N=4 gauged SU(2)$\times$U(1) supergravity. Static configurations that are invariant under either the SO(4) spatial rotations or with respect to the SO(3) rotations and translations along the fourth spatial coordinate are considered. By analyzing consistency conditions for the equations for supersymmetric Killing spinors we derive the Bogomol'nyi equations and obtain their globally regular solutions. The SO(4) symmetric configurations contain the purely magnetic non-Abelian fields together with the purely electric Abelian fiel…
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 study static, spherically symmetric, and purely magnetic solutions of SU(2) $\times$ SU(2) gauge supergravity in four dimensions. A systematic analysis of the supersymmetry conditions reveals solutions which preserve 1/8 of the supersymmetries and are characterized by a BPS-monopole-type gauge field and a globally hyperbolic, everywhere regular geometry. These present the first known example of non-Abelian backgrounds in gauge supergravity and in leading order effective string theory.
We show that all smooth Killing horizons with compact horizon sections of 4-dimensional gauged N=2 supergravity coupled to any number of vector multiplets preserve $2 c_1({\cal K})+4 \ell$ supersymmetries, where ${\cal K}$ is a pull-back of the Hodge bundle of the special Kähler manifold on the horizon spatial section. We also demonstrate that all such horizons with $c_1({\cal K})=0$ exhibit an SL(2,R) symmetry and preserve either 4 or 8 supersymmetries. If the orbits of the SL(2,R) symmetry are 2-dimensional, the horizons are warped products of AdS2 with the horizon spatial section. Otherwise…
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 study static, spherically symmetric, and purely magnetic solutions of the N=4 gauged supergravity in four dimensions. A systematic analysis of the supersymmetry conditions reveals solutions which preserve 1/4 of the supersymmetries and are characterized by a BPS-monopole-type gauge field and a globally hyperbolic, everywhere regular geometry. We show that the theory in which these solutions arise can be obtained via compactification of ten-dimensional supergravity on the group manifold. This result is then used to lift the solutions to ten dimensions.
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 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 …
We study some vacua of N=9 three dimensional gauged supergravity. The theory contains sixteen scalar fields parametrizing the exceptional coset space ${F_{4(-20)}}{SO(9)}$. Various AdS supersymmetric and some non-supersymmetric vacua are found in both compact and non-compact gaugings with gauge groups $SO(p)\times SO(9-p)$ for $p=0, 1, 2, 3, 4$, $G_{2(-14)}\times SL(2)$ and $Sp(1,2)\times SU(2)$. We also study many RG flow solutions, both analytic and numerical, interpolating between supersymmetric critical points in this theory. All the flows considered here are driven by a relevant operator …
Small instantons can play an important role in Yang-Mills theories whose gauge couplings are sizeable at small distances. An interesting class of theories where this could occur is in weakly-gauged holographic models (dual to Yang-Mills theories interacting with strongly-coupled CFTs), since gauge couplings are indeed enhanced towards the UV boundary of the 5D AdS space. However, contrary to expectations, we show that small instantons in these non-asymptotically-free models are highly suppressed and ineffective. This is due to the conservation of topological charge that forbids instantons to b…
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 formulate N=2 twisted super Yang-Mills theory with a gauged central charge by superconnection formalism in two dimensions. We obtain off-shell invariant supermultiplets and actions with and without constraints, which is in contrast with the off-shell invariant D=N=4 super Yang-Mills formulation with unavoidable constraints.
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…
In this paper, a new locally supersymmetric two brane Randall-Sundrum model is constructed. The construction starts from a D=5, N=2 gauged Yang-Mills/Einstein/tensor supergravity theory with scalar manifold M = SO(1,1) x SO(2,1) / SO(2) and gauge group U(1)_R x SO(2). Here, U(1)_R is a subgroup of the R-symmetry group SU(2)_R and SO(2) is a subgroup of the isometry group of M. Next, the U(1)_R gauge coupling g_R is replaced by g_R sgn(x^5) and the fifth dimension is compactified on S^1 / Z_2. The conditions of local supersymmetry for the bulk plus brane system admit a Randall-Sundrum vacuum so…
We present some multiplets of N=2 off-shell supergravity in five dimensions. One is the Super Yang-Mills multiplet, another one is the linear multiplet. The latter one is used to establish a general action formula from which we derive an action for the Super Yang-Mills multiplet. The Super Yang-Mills multiplet is used to construct the nonlinear multiplet with gauged SU(2). This nonlinear multiplet and the action formula for the Yang-Mills multiplet enable us to write down an SU(2) gauged supergravity which we finally truncate to arrive at gauged supergravity with gauge group SO(2).
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 investigate maximal gauged supergravity in seven dimensions and some of its solitonic solutions. By focusing on a truncation of the gauged SO(5) R-symmetry group to its U(1)^2 Cartan subgroup, we construct general two charge black holes that are asymptotically anti-de Sitter. We demonstrate that 1- and 2-charge black holes preserve 1/2 and 1/4 of the supersymmetries respectively. Additionally, we examine the odd-dimensional self-duality equation governing the three-form potential transforming as the 5 of SO(5), and provide some insight on the construction of membrane solutions in anti-de Si…
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.
We investigate to derive off-shell invariant twisted super Yang-Mills for N=2 in 2-dimensions and N=4 in 4-dimensions with a central charge by super connection ansatz formalism. We find off-shell invariant N=2 algebra with and without an extra constraint in 2-dimensions. On the other hand in 4-dimensions we find off-shell invariant N=4 twisted SUSY algebra including one central charge always with a constraint.
We give a detailed study of the critical points of the potentials of the simplest non-trivial N=2 gauged Yang-Mills/Einstein supergravity theories with tensor multiplets. The scalar field target space of these examples is SO(1,1)XSO(2,1)/SO(2). The possible gauge groups are SO(2)XU(1)_R and SO(1,1)XU(1)_R, where U(1)_R is a subgroup of the R-symmetry group SU(2)_R, and SO(2) and SO(1,1) are subgroups of the isometry group of the scalar manifold. The scalar potentials of these theories consist of a contribution from the U(1)_R gauging and a contribution that is due to the presence of the tensor…
We show that the massive Yang--Mills action having as a mass term the non-local operator introduced by Gubarov, Stodolsky, and Zakharov is classically equivalent to a principal gauged sigma model. The non-local mass corresponds to the topological term of the sigma model. The latter is obtained once the degrees of freedom implicitly generated in the non-local action are explicitly implemented as group elements. The non-local action is recovered by integrating out these group elements. In contrast to the usual gauge-fixed treatment, the sigma model point of view provides a safe framework in whic…
We consider the role of N=4 conformal supergravity in the relation between N=4 SYM theory and D=5 gauged supergravity expanded near the Anti de Sitter background. We discuss the structure of the SYM effective action in conformal supergravity background, in particular, terms related to conformal anomaly. Solving the leading-order Dirichlet problem for the metric perturbation in AdS background we explicitly compute the bilinear graviton term in the D=5 Einstein action, demonstrating its equivalence to the linearized Weyl tensor squared part of the gravitational effective action induced by SYM th…
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…
We derive the full Wess-Zumino-Witten term of a gauged chiral lagrangian in D=4 by starting from a pure Yang-Mills theory of gauged quark flavor in a flat, compactified D=5. The theory is compactified such that there exists a B_5 zero mode, and supplemented with quarks that are ``chirally delocalized'' with q_L (q_R) on the left (right) boundary (brane). The theory then necessarily contains a Chern-Simons term (anomaly flux) to cancel the fermionic anomalies on the boundaries. The constituent quark mass represents chiral symmetry breaking and is a bilocal operator in D=5 of the form: \bar{q}_L…
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.
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…
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…
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.
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.
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…
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 study holographic RG flow solutions within four-dimensional $N=4$ gauged supergravity obtained from type IIA and IIB string theories compactified on $T^6/\mathbb{Z}_2\times \mathbb{Z}_2$ orbifold with gauge, geometric and non-geometric fluxes. In type IIB non-geometric compactifications, the resulting gauged supergravity has $ISO(3)\times ISO(3)$ gauge group and admits an $N=4$ $AdS_4$ vacuum dual to an $N=4$ superconformal field theory (SCFT) in three dimensions. We study various supersymmetric RG flows from this $N=4$ SCFT to $N=4$ and $N=1$ non-conformal field theories in the IR. The flo…
A static, spherically symmetric and purely magnetic solution of the Einstein-Yang-Mills-Dilaton theory, found previously by numerical integration is shown to obey a system of first order Bogomol'nyi equations. As common for such equations, there is a tight relation to supersymmetry, in the present case to the N=4 gauged SU(2)$\times$SU(2) supergravity of Freedman and Schwarz. Specifically, the dilaton potential of the latter can be avoided by choosing one of the two gauge coupling constants to be imaginary. It is argued that this corresponds to a hitherto unknown N=4 gauged SU(2)$\times$SU(1,1…
This dissertation is devoted to deriving the bosonic sectors of certain gauged supergravities in various dimensions from reducing eleven-dimensional supergravity, type IIA and type IIB supergravities in ten dimensions on certain spherical spaces. Explicit non-linear Kaluza-Klein ansätze for reductions of eleven-dimensional supergravity and of type IIA and type IIB supergravities on $S^n$ and $S^n\times T^m$ are presented. Knowing explicit non-linear ansätze is proven to be very useful in finding super Yang-Mills operators of gauge theories via AdS/CFT correspondence. We present a sample calcul…
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 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.
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 present new supersymmetric black-hole solutions of the 4- and 5-dimensional gauged supergravity theories that one obtains by dimensional reduction on $T^{5}$ and $T^{6}$ of Heterotic supergravity with a triplet of Yang-Mills fields. The new ingredient of our solutions is the presence of dyonic non-Abelian fields which allows us to obtain a generalization of the BMPV black hole with two independent angular momenta and the first example of a supersymmetric, rotating, asymptotically-flat black hole with a regular horizon in 4 dimensions.
States on the Coulomb branch of N=4 super-Yang-Mills theory are studied from the point of view of gauged supergravity in five dimensions. These supersymmetric solutions provide examples of consistent truncation from type IIB supergravity in ten dimensions. A mass gap for states created by local operators and perfect screening for external quarks arise in the supergravity approximation. We offer an interpretation of these surprising features in terms of ensembles of brane distributions.
We investigate static non-abelian black hole solutions of anti-de Sitter Einstein-Yang-Mills-Dilaton gravity, which is obtained as a consistent truncation of five-dimensional maximal gauged supergravity. If the dilaton is (consistently) set to zero, the remaining equations of motion, with a spherically-symmetric ansatz, may be derived from a superpotential. The associated first-order equations admit an explicit solution supported by a non-abelian SU(2) gauge potential, which has a logarithmically growing mass term. In an extremal limit the horizon geometry becomes AdS$_2\times S^3$. If the dil…
We explicitly construct $N=10$ Chern-Simons gaged supergravity in three dimensions with non-semisimple gauge group $SO(5)\ltimes \mathbf{T}^{10}$. The gauge group is embedded in $E_{6(-14)}$ which is the isometry group of the 32-dimensional scalar manifold $E_{6(-14)}/SO(10)\times U(1)$. The resulting theory is on-shell equivalent to $SO(5)$ Yang-Mills gauged supergravity coming from dimensional reduction on $S^1$ of $SO(5)$ $N=5$ gauged supergravity in four dimensions. We discuss the spectrum of the corresponding reduction. The $SO(5)\ltimes \mathbf{T}^{10}$ gauged supergravity, describing th…
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 start by revisiting the problem of finding BPS solutions in $\mathcal{N}=4$ SU(2)$\times$SU(2) gauged supergravity. We report on a new supersymmetric solution in the Abelian sector of the theory, which describes a soliton that is regular everywhere. The solution is 1/4 BPS and can be obtained from a double analytic continuation of a planar solution found by Klemm in hep-th/9810090. Also in the Abelian sector, but now for a spherically symmetric ansatz we find a new solution whose supersymmetric nature was overlooked in the previous literature. Then, we move to the non-Abelian sector of the …
Six-dimensional N=(1,0) Einstein-Maxwell gauged supergravity is known to admit a (Minkowski)_4\times S^2 vacuum solution with four-dimensional N=1 supersymmetry. The massless sector comprises a supergravity multiplet, an SU(2) Yang-Mills vector multiplet, and a scalar multiplet. In this paper it is shown that, remarkably, the six-dimensional theory admits a fully consistent dimensional reduction on the 2-sphere, implying that all solutions of the four-dimensional N=1 supergravity can be lifted back to solutions in six dimensions. This provides a striking realisation of the idea, first proposed…
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 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…
The Ward identities are the relations which the complete Green functions of quantum fields satisfy if an original classical Lagrangian system is degenerate. A generic degenerate Lagrangian system of even and odd fields is considered. It is characterized by a hierarchy of reducible Noether identities and gauge supersymmetries parameterized by antifields and ghosts, respectively. In the framework of the BV quantization procedure, an original degenerate Lagrangian is extended to ghosts and antifields in order to satisfy the master equation. Replacing antifields with gauge fixing terms, one comes …
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 …
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.
We present a family of globally regular ${\cal N}=1$ vacua in the D=4, ${\cal N}=4$ gauged supergravity of Gates and Zwiebach. These solutions are labeled by the ratio $ξ$ of the two gauge couplings, and for $ξ=0$ they reduce to the supergravity monopole previously used for constructing the gravity dual of ${\cal N}=1$ super Yang-Mills theory. For $ξ>0$ the solutions are asymptotically anti de Sitter, but with an excess of the solid angle, and they reduce exactly to anti de Sitter for $ξ=1$. Solutions with $ξ<0$ are topologically $R^1\times S^3$, and for $ξ=-2$ they become $R^1\times S^3$ geom…
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…
