We analyze the classical and quantum vacua of 2d $\mathcal{N}=(8,8)$ supersymmetric Yang-Mills theory with $SU(N)$ and $U(N)$ gauge group, describing the worldvolume interactions of $N$ parallel D1-branes with flat transverse directions $\mathbb{R}^8$. We claim that the IR limit of the $SU(N)$ theory in the superselection sector labeled $M \pmod{N}$ --- identified with the internal dynamics of $(M,N)$-string bound states of Type IIB string theory --- is described by the symmetric orbifold $\mathcal{N}=(8,8)$ sigma model into $(\mathbb{R}^8)^{D-1}/\mathbb{S}_D$ when $D=\gcd(M,N)>1$, and by a single massive vacuum when $D=1$, generalizing the conjectures of E. Witten and others. The full worldvolume theory of the D1-branes is the $U(N)$ theory with an additional $U(1)$ 2-form gauge field $B$ coming from the string theory Kalb-Ramond field. This $U(N)+B$ theory has generalized field configurations, labeled by the $\mathbb{Z}$-valued generalized electric flux and an independent $\mathbb{Z}_N$-valued 't Hooft flux. We argue that in the quantum mechanical theory, the $(M,N)$-string sector with $M$ units of electric flux has a $\mathbb{Z}_N$-valued discrete $θ$ angle specified by $M \pmod{N}$ dual to the 't Hooft flux. Adding the brane center-of-mass degrees of freedom to the $SU(N)$ theory, we claim that the IR limit of the $U(N) + B$ theory in the sector with $M$ bound F-strings is described by the $\mathcal{N}=(8,8)$ sigma model into ${\rm Sym}^{D} ( \mathbb{R}^8)$. We provide strong evidence for these claims by computing an $\mathcal{N}=(8,8)$ analog of the elliptic genus of the UV gauge theories and of their conjectured IR limit sigma models, and showing they agree. Agreement is established by noting that the elliptic genera are modular-invariant Abelian (multi-periodic and meromorphic) functions, which turns out to be very restrictive.
We study AdS backgrounds of N=4 supergravity in four space-time dimensions which preserve all sixteen supercharges. We show that the graviphotons have to form a subgroup of the gauge group that consists of an electric and a magnetic SO(3)_+ x SO(3)_-. Moreover, these N=4 AdS backgrounds are necessarily isolated points in field space which have no moduli.
We show that the maximally supersymmetric vacua of d=5 N=1 sugra remain maximally supersymmetric solutions when taking into account higher order corrections.
Higher curvature Lovelock gravity theories can have a number of maximally symmetric vacua with different values of the curvature. Critical surfaces in the space of Lovelock couplings separate regions with different numbers of such vacua, and there exist symmetry breaking regions with no maximally symmetric vacua. Especially in such regimes, it is interesting to ask what reduced symmetry vacua may exist. We study this question, focusing on vacua that are products of maximally symmetric spaces. For low order Lovelock theories, we assemble a map of such vacua over the Lovelock coupling space, dis…
Maximally extended, explicit and regular coverings of the Schwarzschild - de Sitter family of vacua are given, first in spacetime (generalizing a result due to Israel) and then for all dimensions $D$ (assuming a $D-2$ sphere). It is shown that these coordinates offer important advantages over the well known Kruskal - Szekeres procedure.
We analyze the scalar potentials of maximal gauged three-dimensional supergravities which reveal a surprisingly rich structure. In contrast to maximal supergravities in dimensions D>3, all these theories admit a maximally supersymmetric (N=16) ground state with negative cosmological constant Lambda<0, except for the gauge group SO(4,4)^2, for which Lambda=0. We compute the mass spectra of bosonic and fermionic fluctuations around these vacua and identify the unitary irreducible representations of the relevant background (super)isometry groups to which they belong. In addition, we find several …
We show that a generalised reduction of D=10 IIB supergravity leads, in a certain limit, to a maximally extended SO(2) gauged supergravity in D=9. We show the scalar potential of this model allows both Minkowski and a new type of domain wall solution to the Bogomol'nyi equations. We relate these vacua to type IIB D-branes.
We determine the conditions for maximally supersymmetric AdS_5 vacua of five-dimensional gauged N=2 supergravity coupled to vector-, tensor- and hypermultiplets charged under an arbitrary gauge group. In particular, we show that the unbroken gauge group of the AdS_5 vacua has to contain an U(1)_R-factor. Moreover we prove that the scalar deformations which preserve all supercharges form a Kahler submanifold of the ambient quaternionic Kahler manifold spanned by the scalars in the hypermultiplets.
An explicit proof of the existence of nontrivial vacua in the pure supersymmetric Yang-Mills theories with higher orthogonal SO(N), N>=7 or the G_2 gauge group defined on a 3-torus with periodic boundary conditions is given. Extra vacuum states are separated by an energy barrier from the perturbative vacuum A_i=0 and its gauge copies.
We argue that supersymmetric higher-dimension operators in the effective actions of M-theory and IIB string theory do not affect the maximally supersymmetric vacua: $adS_4\times S^7$ and $adS_7\times S^4$ in M-theory and $adS_5\times S^5$ in IIB string theory. All these vacua are described in superspace by a fixed point with all components of supertorsion and supercurvature being supercovariantly constant. This follows from 32 unbroken supersymmetries and allows us to prove that such vacua are exact.
We classify maximally supersymmetric backgrounds (vacua) of chiral (1,0) and (2,0) supergravities in six dimensions and, by reduction, also those of the minimal N=2 supergravity in five dimensions. Up to R-symmetry, the (2,0) vacua are in one-to-one correspondence with (1,0) vacua, and these in turn are locally isometric to Lie groups admitting a bi-invariant lorentzian metric with anti-selfdual parallelising torsion, which we classify. We then show that the five-dimensional vacua are homogeneous spaces arising canonically as the spaces of right cosets of spacelike one-parameter subgroups.
Classical vacuum - pure gauge - solutions of Euclidean two-dimensional SU(2) Yang-Mills theories are studied. Topologically non-trivial vacua are found in a class of gauge group elements isomorphic to $S_2$. These solutions are unexpectedly related to the solution of the non-linear O(3) model and to the motion of a particle in a periodic potential.
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 compute the number of massive vacua of N=4 supersymmetric Yang-Mills theory mass-deformed to preserve N=1 supersymmetry, for any gauge group G. We use semi-classical techniques and efficiently reproduce the known counting for A,B and C-type gauge groups, present the generating function for both O(2n) and SO(2n), and compute the supersymmetric index for gauge groups of exceptional type. A crucial role is played by the classification of nilpotent orbits, as well as global properties of their centralizers. We give illustrative examples of new features of our analysis for the D-type algebras.
We provide a simple derivation of the extremal values of the superpotential in massive vacua of N=1* SYM, making use of the required modular weight for the central charge of BPS walls interpolating between these vacua. This modular weight descends from the action of S-duality on the N=4 superalgebra which in turn is inherited from its classical action on the dyon spectrum. We show that this kinematic information, combined with minimal knowledge of the weak coupling asymptotics, is sufficient to determine the exact vacuum superpotentials in terms of Eisenstein series.
We discuss the existence of $θ$-vacua in pure Yang-Mills theory in two space-time dimensions. More precisely, a procedure is given which allows one to classify the distinct quantum theories possessing the same classical limit for an arbitrary connected gauge group G and compact space-time manifold M (possibly with boundary) possessing a special basepoint. For any such G and M it is shown that the above quantizations are in one-to-one correspondence with the irreducible unitary representations (IUR's) of $π_1(G)$ if M is orientable, and with the IUR's of $π_1(G)/2π_1(G)$ if M is nonorientable.
We investigate the vacuum structure of pure SU(N) N=1 super Yang-Mills. The theory is expected to possess N vacua with associated domain walls. We show that the newly extended version of the low energy effective Lagrangian for super Yang-Mills supports the BPS domain wall solutions associated with any two vacua aligned with the origin of the moduli space. For the two color theory the domain wall analysis is complete. We also find new non BPS domain wall solutions connecting any two vacua of the underling SU(N) super Yang-Mills theory not necessarely aligned. When two vacua are aligned with the…
We consider generic properties of the moduli space of vacua in $N=2$ supersymmetric Yang--Mills theory recently studied by Seiberg and Witten. We find, on general grounds, Picard--Fuchs type of differential equations expressing the existence of a flat holomorphic connection, which for one parameter (i.e. for gauge group $G=SU(2)$), are second order equations. In the case of coupling to gravity (as in string theory), where also ``gravitational'' electric and magnetic monopoles are present, the electric--magnetic S duality, due to quantum corrections, does not seem any longer to be related to $S…
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.
The moduli space of flat connections for maximally supersymmetric Yang-Mills theories, in a space-time of the form T^3xR, contains isolated points, corresponding to normalizable zero energy states, for certain simple gauge groups G. We consider the low energy effective field theories in the weak coupling limit supported on such isolated points and find that when quantized they consist of an infinite set of harmonic oscillators whose angular frequencies are completely determined by the Lie algebra of G. We then proceed to find the isolated flat connections for all simple G and subsequently spec…
It has recently been argued that the confining vacua of Yang-Mills theory in the far infrared can have topological degrees of freedom given by magnetic $\mathbb{Z}_q$ gauge field, both in the non-supersymmetric case and in the N=1 supersymmetric case. In this short note we give another piece of evidence by computing and matching the supersymmetric index of the pure super Yang-Mills theory both in the ultraviolet and in the infrared.
Two-dimensional SU(N) Yang-Mills theory is endowed with a non-trivial vacuum structure (k-sectors). The presence of k-sectors modifies the energy spectrum of the theory and its instanton content, the (Euclidean) space-time being compactified on a sphere. For the exact solution, in the limit in which the sphere is decompactified, a k-sector can be mimicked by the presence of k-fundamental charges at infinity, according to a Witten's suggestion. However, this property neither holds before decompactification nor for the genuine perturbative solution which corresponds to the zero-instanton contrib…
In this thesis we discuss recent new insights in the structure of the moduli space of flat connections of Yang-Mills theory on a 3-torus. Chapter 2 discusses the computation of Witten's index for 4-dimensional gauge theories, and the paradox that arises in comparing various computations. This was resolved by the discovery that for orthogonal and exceptional gauge groups, periodic flat connections exist that are contained in seperate, disconnected components of the moduli space. Chapter 3 and 4 discuss some aspects of the construction of holonomies parametrising vacua on such disconnected compo…
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.
We discuss a D3-D7 system in type IIB string theory. The near-horizon geometry is described by AdS^5 x X^5 where X^5 is a U(1) bundle over a Kahler-Einstein complex surface S with positive first Chern class c_1>0. The surface S can either be P^1 x P^1, P^2 or P_{n_1,...,n_k}, a blow up of P^2 at k points with 3\leq k\leq 8. The P^2 corresponds to the maximally supersymmetric AdS^5 x S^5 vacuum while the other cases lead to vacua with less supersymmetries. In the F-theory context they can be viewed as compactifications on elliptically fibered almost Fano 3-folds.
We formulate maximally supersymmetric Yang-Mills theory in five dimensions in light-cone superspace. The light-cone Hamiltonian is of the quadratic form and the theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory in four dimensions. We specifically study three-point counterterms and show how these counterterms vanish on-shell. This study is a preliminary to set up the technique in order to study possible four-point counterterms.
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 show how all known N=2, d=4,5,6 maximally supersymmetric vacua (Hpp-waves and aDSxS solutions) are related through dimensional reduction/oxidation preserving all the unbroken supersymmetries. In particular we show how the N=2, d=5 family of vacua (which are the near-horizon geometry of supersymmetric rotating black holes) interpolates between aDS_2xS^3 and aDS_3xS^2 in parameter space and how it can be dimensionally reduced to an N=2, d=4 dyonic Robinson-Bertotti solution with geometry aDS_2xS^2 and oxidized to an N=2, d=6 solution with aDS_3xS^3 geometry (which is the near-horizon of the s…
We study the N=1* supersymmetric gauge theories with gauge groups Sp(2n) and SO(2n+1). These theories are obtained from the corresponding N=4 supersymmetric Yang-Mills theories via a mass deformation. We show that the number of quantum vacua in the Sp(2n) theory is equal to the number of quantum vacua in the SO(2n+1) theory. This constitutes non-trivial support for S-duality between these theories. The verification of the equality of the number of quantum vacua involves a rather esoteric identity due to Ramanujan.
The main features of the cusp anomalous dimension in N=4 supersymmetri c Yang-Mills theory are reviewed. Moreover, the strong coupling expansion of the cusp derived is presented.
In this note, we describe supersymmetric backgrounds for the four-dimensional maximally supersymmetric Yang-Mills theory. As an extension of the method of Festuccia and Seiberg to sixteen supercharges in four dimensions, we utilize the coupling of the gauge theory to maximally extended conformal supergravity. Included among the fields of the conformal supergravity multiplet is the complexified coupling parameter of the gauge theory; therefore, backgrounds with spacetime varying coupling--such as appear in F-theory and Janus configurations--are naturally included in this formalism. We demonstra…
In the (non-supersymmetric) Yang-Mills theory in the large N limit there exists an infinite set of non-degenerate vacua. The distinct vacua are separated by domain walls whose tension determines the decay rate of the false vacua. I discuss the phenomenon from a field-theoretic point of view, starting from supersymmetric gluodynamics and then breaking supersymmetry, by introducing a gluino mass. By combining previously known results, the decay rate of the excited vacua is estimated, Γ\sim \exp (-const \times N^4). The fourth power of N in the exponent is a consequence of the fact that the wall …
A particular dimensional reduction of SU(2N) Yang--Mills theory on $Σ\times S^2$, with $Σ$ a Riemann surface, yields an $S(U(N) \times U(N))$ gauge theory on $Σ$, with a matrix Higgs field. The SU(2N) self-dual Yang--Mills equations reduce to Bogomolny equations for vortices on $Σ$. These equations are formally integrable if $Σ$ is the hyperbolic plane, and we present a subclass of solutions.
We use the embedding tensor formalism to analyse maximally symmetric backgrounds of N=2 gauged supergravities which have the full N=2 supersymmetry. We state the condition for N=2 vacua and discuss some of their general properties. We show that if the gauged isometries leave the SU(2) R-symmetry invariant, then the N=2 vacuum must be Minkowski. This implies that there are no AdS backgrounds with eight unbroken supercharges in the effective N=2 supergravity of six-dimensional SU(3) x SU(3) structure compactifications of type II string theory and M-theory. Combined with previous results on N=1 v…
$QCD_2$ with fermions in the adjoint representation is invariant under $SU(N)/Z_N$ and thereby is endowed with a non-trivial vacuum structure (k-sectors). The static potential between adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang-Mills theory with the same non-trivial structure. When the (Euclidean) space-time is compactified on a sphere $S^2$, Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of k-sectors modifies the energy spectrum of the theory and…
We identify configurations of intersecting branes that correspond to the meta-stable supersymmetry breaking vacua in the four-dimensional N=1 supersymmetric Yang-Mills theory coupled to massive flavors. We show how their energies, the stability properties, and the decay processes are described geometrically in terms of the brane configurations.
The question of whether BPS invariants are protected in maximally supersymmetric Yang-Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants ($F^4$) are indeed protected while the double-trace one-quarter BPS invariant ($d^2F^4$) is not protected at two loops in D=7, but is protected at three loops in D=6 in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotecte…
We present a simple class of warped-product vacuum (Ricci-flat) solutions to ten and eleven-dimensional supergravity, where the internal space is flat and the warp factor supports de Sitter (dS) and anti-de Sitter (AdS) vacua in addition to trivial Minkowski vacua. We outline the construction of consistent Kaluza-Klein (KK) reductions and show that, although our vacuum solutions are non-supersymmetric, these are closely related to the bosonic part of well-known maximally supersymmetric reductions on spheres. We comment on the stability of our solutions, noting that (A)dS$_3$ vacua pass routine…
Integrable spin chains in twisted maximally supersymmetric Yang-Mills theory
Instituto Galego de Física de Altas Enerxías (IGFAE) and Departamento de Física de Partículas, Universidade de Santiago de Compostela（加利西亚高能物理研究所和圣地亚哥德孔波斯特拉大学粒子物理系）；Institut für Physik, Humboldt-Universität zu Berlin（柏林洪堡大学物理研究所）
Existence of theta-vacuum states in Yang--Mills theories defined over asymptotically flat space-times examined taking into account not only the topology but the complicated causal structure of these space-times, too. By a result of Galloway apparently causality makes all vacuum states, seen by a distant observer, homotopically equivalent making the introduction of theta-terms unnecessary. But a more careful analysis shows that certain twisted classical vacuum states survive even in this case eventually leading to the conclusion that the concept of ``theta-vacua'' is meaningful in the case of g…
Flat connections for unitary gauge groups on a 3--torus with twisted boundary conditions as well as recently discovered periodic nontrivial flat connections with ``nondiagonalizable'' triples of holonomies for higher orthogonal and exceptional groups are constructed explicitly in terms of Jacobi theta functions with rational characteristics. The (fractional) Chern-Simons numbers of these vacuum gauge field configurations are verified by direct computation.
We study scalar potentials and the corresponding vacua of N=10 three dimensional gauged supergravity. The theory contains 32 scalar fields parametrizing the exceptional coset space $\frac{E_{6(-14)}}{SO(10)\times U(1)}$. The admissible gauge groups considered in this work involve both compact and non-compact gauge groups which are maximal subgroups of $SO(10)\times U(1)$ and $E_{6(-14)}$, respectively. These gauge groups are given by $SO(p)\times SO(10-p)\times U(1)$ for $p=6,...10$, $SO(5)\times SO(5)$, $SU(4,2)\times SU(2)$, $G_{2(-14)}\times SU(2,1)$ and $F_{4(-20)}$. We find many AdS$_3$ c…
The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the coefficient of the first potential ultraviolet divergence of planar (large N_c) maximally supersymmetric Yang-Mills theory in D = 5, which occurs at six loops. We show that the coefficient is nonvanishing. Furthermore, the numerical value of the divergence falls very close to an approximate exponential formula based on the coefficients of the divergences throu…
Instantons and their quantisation in pure Yang-Mills theory formulated in the background of de Sitter spacetime represented by spatially-closed ($k = 1$) Friedmann-Robertson-Walker metric are discussed. As for the classical treatment of the instanton physics, first, explicit instanton solutions are found and next, quantities like Pontryagin index and the semiclassical approximation to the inter-vacua tunnelling amplitude are evaluated. The Atiyah-Patodi-Singer index theorem is checked as well by constructing explicitly the normalizable fermion zero modes in this de Sitter spacetime instanton b…
The collinear factorization properties of two-loop scattering amplitudes in dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the AdS/CFT correspondence that the form of the large N_c L-loop amplitudes should be simple enough t…
We present an integral representation for the parity-even part of the two-loop six-point planar NMHV amplitude in terms of Feynman integrals which have simple transformation properties under the dual conformal symmetry. We probe the dual conformal properties of the amplitude numerically, subtracting the known infrared divergences. We find that the subtracted amplitude is invariant under dual conformal transformations, confirming existing conjectures through two-loop order. We also discuss the all-loop structure of the six-point NMHV amplitude and give a parametrization whose dual conformal inv…
We find analytic solutions of type IIB supergravity on geometries that locally take the form $\text{Mink}\times M_4\times \mathbb{C}$ with $M_4$ a generalised complex manifold. The solutions involve the metric, the dilaton, NSNS and RR flux potentials (oriented along the $M_4$) parametrised by functions varying only over $\mathbb{C}$. Under this assumption, the supersymmetry equations are solved using the formalism of pure spinors in terms of a finite number of holomorphic functions. Alternatively, the solutions can be viewed as vacua of maximally supersymmetric supergravity in six dimensions …
Integral invariants in maximally supersymmetric Yang-Mills theories are discussed in spacetime dimensions $4\leq D\leq 10$ for $SU(k)$ gauge groups. It is shown that, in addition to the action, there are three special invariants in all dimensions. Two of these, the single- and double-trace $F^4$ invariants, are of Chern-Simons type in $D=9,10$ and BPS type in $D\leq 8$, while the third, the double-trace of two derivatives acting on $F^4$, can be expressed in terms of a gauge-invariant super-$D$-form in all dimensions. We show that the super-ten-forms for $D=10$ $F^4$ invariants have interestin…
We provide explicit formulas for the number of vacua of four-dimensional pure N=1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators. These form a key ingredient in the semi-classical calculation of the number of massive vacua of N=1* gauge theories with gauge algebra su(n) compactified on a circle. Using arithmetic, we express that number in an SL(2,Z) duality invariant manner. We confirm our tally of massive vacua of the N=1* theories by a count of inequivalent extrema of the exact superpotential. Furthermore, we compu…
I consider N=1 U(N) gauge theory with matter in the adjoint, fundamental and anti-fundamental representations. Focusing on the equations defining the Riemann surface that describes the quantum theory, the gaugino condensates (and related superpotentials) are calculated in the limit of SU(N) gauge group, both in the pure theory and in the presence of matter. In the case without fundamental matter it is investigated the structure of the space of vacua. In particular it is discussed how different vacua can be related, in a way which finally helps to count them.
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 present the configurations of intersecting branes in type IIA string theory corresponding to the meta-stable supersymmetry breaking vacua(hep-th/0608063) in the four-dimensional N=1 supersymmetric Yang-Mills theory coupled massive flavors with adjoint matter where the superpotential has three deformed terms.
Recent analytical and numerical solutions of the above systems are reviewed. Discussed results include: a) exact construction of the supersymmetric vacua in two space-time dimensions, and b) precise numerical calculations of the coexisting continuous and discrete spectra in the four-dimensional system, together with the identification of dynamical supermultiplets and SUSY vacua. New construction of the gluinoless SO(9) singlet state, which is vastly different from the empty state, in the ten-dimensional model is also briefly summarized.
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.
We study $dS_4$ vacua within matter-coupled $N=4$ gauged supergravity in the embedding tensor formalism. We derive a set of conditions for the existence of $dS_4$ solutions by using a simple ansatz for solving the extremization and positivity of the scalar potential. We find two classes of gauge groups that lead to $dS_4$ vacua. One of them consists of gauge groups of the form $G_{\textrm{e}}\times G_{\textrm{m}}\times H$ with $H$ being a compact group and $G_{\textrm{e}}\times G_{\textrm{m}}$ a non-compact group with $SO(3)\times SO(3)$ subgroup and dynonically gauged. These gauge groups are …
We study the S-matrix of planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics; in particular, the higher-point amplitudes we consider can be obtained from those with lowest-points by a collinear uplifting. Based on a compact formula for one-loop N${}^2$MHV amplitudes, we use an equation proposed previously to compute, for the first time, the complete two-loop NMHV and three-loop M…
We calculate the exact eigenvalues of the adjoint scalar fields in the massive vacua of N=1* SUSY Yang-Mills with gauge group SU(N). This provides a field theory prediction for the distribution of D3 brane charge in the AdS dual. We verify the proposal of Polchinski and Strassler that the D3-brane's lie on a fuzzy sphere in the supergravity limit and determine the corrections to this distribution due to worldsheet and quantum effects. The calculation also provides several new results concerning the equilibrium configurations of the N-body Calogero-Moser Hamiltonian.
