We obtain the action for a curved superconformal abelian M5 brane with the background R-symmetry gauge field turned on. We then restrict ourselves to superconformal M5 brane on a sphere times flat Minkowski space. We choose R-symmetry SO(1,4) instead of SO(5), which enables us to partially twist on Minkowski space and replace it by some curved Lorentzian manifold. We obtain M5 brane actions on $M_{1,1} \times S^4$ and $M_{1,2} \times S^3$ where actions and all fields, including the background gauge field, are real. Dimensional reduction along time gives real 5d SYM actions with nonabelian generalizations.
The construction of D-branes in N=2 superconformal minimal models, based on free field realization of N=2 super-Virasoro algebra unitary modules is represented.
We solve the Killing spinor equations of 6-dimensional (1,0) superconformal theories which include hyper-multiplets in all cases. We show that the solutions preserve 1,2,3,4 and 8 supersymmetries. We find models with self-dual string solitons which are smooth and supported by instantons with an arbitrary gauge group, and 3-brane solitons as expected from the M-brane intersection rules.
We analyze various brane configurations corresponding to field theories in three, four and five dimensions. We find brane configurations which correspond to three dimensional N=2 and four dimensional N=1 supersymmetric QCD theories with quartic superpotentials, in which what appear to be ``hidden parameters'' play an important role. We discuss the construction of five dimensional N=1 supersymmetric gauge theories and superconformal fixed points using branes, which leads to new five dimensional N=1 superconformal field theories. The same five dimensional theories are also used, in a surprising …
We derive the superconformal index of the world-volume theory on M2-branes probing the cone over an arbitrary Sasaki-Einstein seven-manifold. The index is expressed in terms of the cohomology groups of the cone. We match our supergravity results with known results from gauge theory. Along the way we derive the spectrum of short Kaluza-Klein multiplets on generic Sasaki-Einstein seven-manifolds.
We obtain the enropy of Schwarzschild and charged black holes in D>4 from superconformal gases that live on p=10-D dimensional brane-antibrane systems wrapped on T^p. The preperties of the strongly coupled superconformal theories such as the appearance of hidden dimensions (for p=1,4) and fractional strings (for p=5) are crucial for our results. In all cases, the Schwarzschild radius is given by the transverse fluctuations of the branes and antibranes due to the finite temperature. We show that our results can be generalized to multicharged black holes.
We investigate deformed superconformal symmetries on non(anti)commutative (super)spaces from the point of view of the Drinfel'd twisted symmetries. We classify all possible twist elements derived from an abelian subsector of the superconformal algebra. The symmetry breaking caused by the non(anti)commutativity of the (super)spaces is naturally interpreted as the modification of their coproduct emerging from the corresponding twist element. The remaining unbroken symmetries are determined by the commutative properties of those symmetry generators possessing the twist element. We also comment on…
It is shown that the two dimensional gravity, described either in the conformal gauge (the Liouville theory) or in the light cone gauge, when coupled to matter possesses an infinite number of twisted $N=2$ superconformal symmetries. The central charges of the $N=2$ algebra for the two gauge choices are in general different. Further, it is argued that the physical states in the light cone gauge theory can be obtained from the Liouville theory by a field redefinition.
We describe configurations of 5-branes and 7-branes which realize, when compactified on a circle, new isolated four-dimensional N=2 superconformal field theories recently constructed by Gaiotto. Our diagrammatic method allows to easily count the dimensions of Coulomb and Higgs branches, with the help of a generalized s-rule. We furthermore show that superconformal field theories with E6, E7, E8 flavor symmetry can be analyzed in a uniform manner in this framework; in particular we realize these theories at infinitely strongly-coupled limits of quiver theories with SU gauge groups.
We demonstrate how actions for interacting superconformal field theories in (p+1)-dimensions arise as a result of gauge fixing worldvolume diffeomorphisms and fermionic kappa-symmetry in actions for super-p-branes propagating in superbackgrounds of AdS(p+2)xS(D-p-2) geometry. The method of nonlinear realizations and coset spaces is used for getting an explicit form of supervielbeins and superconnections of the AdSxS superbackgrounds, which are required for the construction of the superconformal theories. Subtleties of consistent gauge fixing worldvolume symmetries of the branes are discussed.
We overview the main configurations of D-brane probes in the AdS_5 x X^5 background of type IIB string theory (X^5 being a Sasaki-Einstein manifold), and examine their most salient features from the point of view of the dual quiver superconformal field theory.
We study non-relativistic limits of the N=6 Chern-Simons-Matter theory that arises as a low-energy limit of the M2-brane gauge theory with background flux. The model admits several different non-relativistic limits and we find that the maximal supersymmetry we construct has 14 components of supercharges, which is a novel example of non-relativistic superconformal algebra in (1+2) dimension. We also investigate the other limits that realize less supersymmetries.
We study probe M5-branes in N=1 AdS5 solutions of M-theory that arise from M5-branes wrapped on a Riemann surface. Using the BPS condition from kappa-symmetry, we classify supersymmetric probe M5-branes that extend along all of AdS5 and intersect the Riemann surface at points. These can be viewed as punctures in the dual N=1 superconformal field theories. We find M5-branes that correspond to the two types of simple punctures previously studied in field theory. In addition, when the central charge is rational, we find a new class of M5-branes with a moduli space that includes two internal dimen…
We present a gauge-fixed M 5-brane action: a 6-dimensional field theory of a self-interacting (0,2) tensor multiplet with 32 worldvolume supersymmetries. The quadratic part of this action is shown to be invariant under rigid OSp(6,2|4) superconformal symmetry, with 16 supersymmetries and 16 special supersymmetries. We explore a deep relation between the superconformal symmetry on the worldvolume of the brane and symmetry of the near horizon anti-de Sitter infinite throat geometry of the M 5-brane in space-time.
We investigate the low energy physics of particles in the symmetric phase of the N=6 mass-deformed ABJM theory in terms of the superconformal nonrelativistic field theory with 14 supercharges. They describe the certain kind of excitations on M2 branes in the background of external four-form flux. We study the nonrelativistic superconformal algebra and their representations by using the operator-state correspondence with the related harmonic oscillator Hamiltonian. We find the unitarity bounds on the scaling dimension and particle number of any local operator, and comment on subtleties in compu…
We calculate and study the general superconformal index for the 6d U(N) (2,0) theory with four chemical potentials, from the indices of gauge theories on CP^2 x R. Our index agrees with the large N supergravity index on AdS_7 x S^4 at low energies, and also yields the negative 'Casimir energy' with an N^3 scaling which was recently calculated from a QFT on S^5. Our approach also suggests a systematic study of the (1,0) superconformal indices.
Due to the incompatibility of the nonlinear realization of superconformal symmetry and dilatation symmetry with the dilaton as the compensator field, in the present paper it shows an alternative mechanism of spontaneous breaking the N=2 superconformal symmetry to the N=0 case. By using the approach of nonlinear transformations it is found that it leads to a space-filling brane theory with Weyl scale W(1,3) symmetry. The dynamics of the resulting Weyl scale invariant brane, along with that of other Nambu-Goldstone fields, is derived in terms of the building blocks of the vierbein and the covari…
We explicitly construct a family of ${\cal N}=4$ superconformal mechanics of dyonic particles, generalizing the work of Anninos et al.\,\cite{Anninos:2013nra} to an arbitrary number of particles. These mechanics are obtained from a scaling limit of the effective Coulomb branch description of ${\mathcal N}=4$ quiver quantum mechanics describing D-branes in type II Calabi-Yau compactifications. In the supergravity description of these D-branes this limit changes the asymptotics to AdS$_2\times $S$^2\times$CY$_3$. We exhibit the $D(1,2;0)$ superconformal symmetry and conserved charges of the mech…
We study supersymmetric embeddings of D-brane probes of different dimensionality in the AdS_5xL^{abc} background of type IIB string theory. In the case of D3-branes, we recover the known three-cycles dual to the dibaryonic operators of the gauge theory and we also find a new family of supersymmetric embeddings. Supersymmetric configurations of D5-branes, representing fractional branes, and of spacetime filling D7-branes (which can be used to add flavor) are also found. Stable non supersymmetric configurations corresponding to fat strings and domain walls are found as well.
We write supersymmetry preserving conditions for infinite M5-branes intersecting on a (3+1)-dimensional space. In contrast to previously known solutions, these intersections are completely localized. We solve the equations for a particular class of configurations which in the near-horizon decoupling limit are dual to N_f = 2N_c Seiberg-Witten superconformal field theories with gauge group SU(N) and generalisations to SU(N)^n. We also discuss the relationship to D3-branes in the presence of an A_k singularity.
We extend the N=4 superconformal Chern-Simons theories of Gaiotto and Witten to those with additional twisted hyper-multiplets. The new theories are generically linear quiver gauge theories with the two types of hyper-multiplets alternating between gauge groups. Our construction includes the Bagger-Lambert model of SO(4) gauge group. A family of abelian theories are identified with those proposed earlier in the context of the M-crystal model for M2-branes probing (C^2/Z_n)^2 orbifolds. Possible extension with non-abelian BF couplings and string/M-theory realization are briefly discussed.
The Noether currents associated with the non-linearly realized super-Poincare' symmetries of the Green-Schwarz (Nambu-Goto-Akulov-Volkov) action for a non-BPS p=2 brane embedded in a N=1, D=4 target superspace are constructed. The R symmetry current, the supersymmetry currents, the energy-momentum tensor and the scalar central charge current are shown to be components of a world volume supercurrent. The centrally extended superconformal transformations are realized on the Nambu-Goldstone boson and fermion fields of the non-BPS brane. The superconformal currents form supersymmetry multiplets wi…
We investigate an AdS_4 x L_2 D5-brane in AdS_5 x X_5 space-time, in the context of AdS/dCFT correspondence. Here, X_5 is a Sasaki-Einstein manifold and L_2 is a submanifold of X_5. This brane has the same supersymmetry as the 3-dimensional N=1 superconformal symmetry if L_2 is a special Legendrian submanifold in X_5. In this case, this brane is supposed to correspond to a superconformal wall defect in 4-dimensional N=4 super Yang-Mills theory. We construct these new string backgrounds and show they have the correct supersymmetry, also in the case with non-trivial gauge flux on L_2. The simple…
In recent work, the superconformal quantum mechanics describing D0 branes in the AdS_2xS^2xCY_3 attractor geometry of a Calabi-Yau black hole with D4 brane charges p^A has been constructed and found to contain a large degeneracy of chiral primary bound states. In this paper it is shown that the asymptotic growth of chiral primaries for N D0 branes exactly matches the Bekenstein-Hawking area law for a black hole with D4 brane charge p^A and D0 brane charge N. This large degeneracy arises from D0 branes in lowest Landau levels which tile the CY_3xS^2 horizon. It is conjectured that such a multi-…
We test several expected isomorphisms between the U(N)xU(N) ABJM theory and (SU(N)xSU(N))/Z_N theory including the BLG theory by comparing their superconformal indices. From moduli space analysis, it is expected that this equivalence can hold if and only if the rank N and Chern-Simons level k are coprime. We also calculate the index of the ABJ theory and investigate whether some theories with identical moduli spaces are isomorphic or not.
We present several new examples of nontrivial 4d N=1 superconformal field theories. Some of these theories exhibit exotic global symmetries, including non-simply laced groups (such as $F_4$). They are obtained by studying threebrane probes in F-theory compactifications on elliptic Calabi-Yau threefolds. The geometry of the compactification encodes in a simple way the behavior of the gauge coupling and the Kähler potential on the Coulomb branch of these theories.
We construct a class of intersecting brane solutions with horizon geometries of the form adS_k x S^l x S^m x E^n. We describe how all these solutions are connected through the addition of a wave and/or monopoles. All solutions exhibit supersymmetry enhancement near the horizon. Furthermore we argue that string theory on these spaces is dual to specific superconformal field theories in two dimensions whose symmetry algebra in all cases contains the large N=4 algebra A_{gamma}. Implications for gauged supergravities are also discussed.
We study N=1 superconformal theories in four dimensions obtained wrapping M5 branes on a Riemann surface. We propose a method to determine from the spectral curve the scaling dimension of chiral operators in the SCFT. Whenever the R-symmetry has to be determined via a-maximization, our procedure allows us to determine the charge of chiral operators under the "trial" R-symmetry. Our proposal reduces to the correct prescription in the special case of N=2 theories of class S. We perform several consistency checks and apply our method to study some new SCFT's such as N=1 deformations of Argyres-Do…
The Bagger--Lambert construction of N = 8 superconformal field theories (SCFT) in three dimensions is based on 3-algebras. Three groups of researchers recently realized that an arbitrary semisimple Lie algebra can be incorporated by using a suitable Lorentzian signature 3-algebra. The SU(N) case is a candidate for the SCFT describing coincident M2-branes. However, these theories contain ghost degrees of freedom, which is unsatisfactory. We modify them by gauging certain global symmetries. This eliminates the ghosts from these theories while preserving all of their desirable properties. The res…
The N=1 superconformal circle theory consisting of a free boson and a free fermion is considered. At any radius the theory has standard Dirichlet and Neumann branes, but for rational radii there are additional superconformal boundary conditions that are labelled by elements in a quotient of SU(2). We analyse how these branes behave under the radius-changing bulk perturbation. As in the bosonic case, the bulk perturbation induces in general a boundary RG flow whose end-point is a superposition of Dirichlet or Neumann branes.
The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi-Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configurations in which a single D3-brane is wrapped on a cycle, and we do not take account of branes with multiple wrapping. We propose a formula that gives finite $N$ corrections to the index caused by such brane configurations. We compare the predictions of the formula for several examples with the results on the gauge theory side obtained by using localization for small si…
We study mass deformations of N=2 superconformal field theories with ADE global symmetries on a D3-brane. The N=2 Seiberg-Witten curves with ADE symmetries are determined by the Type IIB 7-brane backgrounds which are probed by a D3-brane. The Seiberg-Witten differentials $λ$ for these ADE theories are constructed. We show that the poles of $λ$ with residues are located on the global sections of the bundle in an elliptic fibration. It is then clearly seen how the residues transform in an irreducible representation of the ADE groups. The explicit form of $λ$ depends on the choice of a representa…
We propose a brane configuration for the (2+1)d, $\mathcal{N}=2$ superconformal theories (CFT$_3$) arising from M2-branes probing toric Calabi-Yau 4-fold cones, using a T-duality transformation of M-theory. We obtain intersections of M5-branes on a three-torus which form a 3d bipartite crystal lattice in a way similar to the 2d dimer models for CFT$_4$. The fundamental fields of the CFT$_3$ are M2-brane discs localized around the intersections, and the super-potential terms are identified with the atoms of the crystal. The model correctly reproduces the complete BPS spectrum of mesons and bary…
We realise the Shatashvili-Vafa superconformal algebra for $G_2$ string compactifications by combining Odake and free conformal algebras following closely the recent mathematical construction of twisted connected sum $G_2$ holonomy manifolds. By considering automorphisms of this realisation, we identify stringy analogues of two mirror maps proposed by Braun and Del Zotto for these manifolds.
This thesis first gives a background and review of the article hep-th/0102038, where we substantiated a conjectured duality between two a priori unrelated gauge theories, N=2 quiver theory and N=2 Seiberg-Witten theory. These gauge theories have different realisations as the worldvolume theories on different D-brane configurations. We showed that there is an identity between the spaces of vacua (moduli spaces) arising in the two theories, which suggests that the corresponding string theory pictures are dual. Second, the thesis gives a background and description of the analysis performed in the…
We study the large N limit of the interacting superconformal field theories associated with N M5 branes or M2 branes using the recently proposed relation between these theories and M theory on AdS spaces. We first analyze the spectrum of chiral operators of the 6d (0,2) theory associated with M5 branes in flat space, and find full agreement with earlier results obtained using its DLCQ description as quantum mechanics on a moduli space of instantons. We then perform a similar analysis for the D_N type 6d (0,2) theories associated with M5 branes at an R^5/Z_2 singularity, and for the 3d N=8 supe…
The classical superconformal actions of branes in adS superspaces have a closed form depending on a matrix $M^2$ quadratic in fermions, as found in hep-th/9805217. One can gauge-fix the local $κ$-symmetry using the Killing spinors of the brane in the bulk. We show that in such gauges the superconformal actions are simplified dramatically since $M^2=0$ in all cases. The relation between classical and gauge-fixed actions for these theories reflects the relation between the full superconformal algebra and its supersolvable subalgebra.
The particular model of d5 higher derivative gravity which is dual to ${\cal N}=2$ $Sp(N)$ SCFT is considered. A (perturbative) AdS black hole in such theory is constructed in the next-to-leading order of the AdS/CFT correspondence. The surface counterterms are fixed by the conditions required for a well-defined variational procedure and the finiteness of AdS space (when the brane goes to infinity). A dynamical brane is realized at the boundary of an AdS black hole with a radius that is larger than the horizon radius. The AdS/CFT correspondence dictates the parameters of the gravitational dual…
We explore further our recent generalization of the $\mathcal{N}=4$ superconformal Chern-Simons theories of Gaiotto and Witten. We find and construct explicitly theories of enhanced $\mathcal{N}=5$ or 6 supersymmetry, especially $\mathcal{N}=5$, $Sp(2M)\times O(N)$ and $\mathcal{N}=6$, $Sp(2M)\times O(2)$ theories. The $U(M)\times U(N)$ theory coincides with the $\mathcal{N}=6$ theory of Aharony, Bergman, Jafferis and Maldacena (ABJM). We argue that the $\mathcal{N}=5$ theory with $Sp(2N)\times O(2N)$ gauge group can be understood as an orientifolding of the ABJM model with $U(2N)\times U(2N)$…
We construct three dimensional Chern-Simons-matter theories with gauge groups U(N)xU(N) and SU(N)xSU(N) which have explicit N=6 superconformal symmetry. Using brane constructions we argue that the U(N)xU(N) theory at level k describes the low energy limit of N M2-branes probing a C^4/Z_k singularity. At large N the theory is then dual to M theory on AdS_4xS^7/Z_k. The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS_4xCP^3. For k=1 the theory is conjectured to describe N M2-branes in flat space, although our construction realiz…
We explore N=(1,0) superconformal six-dimensional theories arising from M5-branes probing a transverse A_k singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5-brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1,0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of qW-algebrae.
The supergravity dual of superconformal anomaly in a four-dimensional supersymmetric gauge theory is investigated. We consider a well-established dual correspondence between the ${\cal N}=1$ $SU(N+M)\times SU(N)$ supersymmetric gauge theory with two flavors of matter fields in the bifundamental representation of gauge group and the type IIB superstring in the space-time background furnished by the Klebanov-Strassler (K-S) solution. The D-brane configuration for these two dual theories consists of N D3 branes and M fractional $D3$ branes in the singular space-time composed of a direct product o…
We study a class of classical solutions of three-dimensional N=6 superconformal Chern-Simons theory coupled with U(N) \times U(N) bi-fundamental matter fields. Especially, time evolutions of fuzzy spheres are discussed for both massless and massive cases. For the massive case, there are a variety of solutions having different behaviors according to the value of the mass. In addition to the time-dependent solutions, we analyze non-BPS static solutions which represent parallel M5/M5 or M5/anti-M5-branes suspended by multiple M2-branes. These solutions are similar to the fundamental strings conne…
We investigate the AdS/CFT correspondence for quiver gauge theories realized on D3-branes put on abelian orbifolds by using the superconformal index. We assume that on the gravity side the finite $N$ corrections of the index are reproduced by D3-branes wrapped on three particular three-cycles in the internal space ${\cal Y}$, the abelian orbifold of $\boldsymbol{S}^5$. We first establish the relation between baryonic charges on the gauge theory side and the D3-brane wrapping numbers and holonomies on D3-branes. Then we confirm our proposal by comparing the results of localization for gauge the…
We present the superconformal gauge theory living on the world-volume of D3 branes probing the toric singularities with horizon the recently discovered Sasaki-Einstein manifolds L^{p,q,r}. Various checks of the identification are made by comparing the central charge and the R-charges of the chiral fields with the information that can be extracted from toric geometry. Fractional branes are also introduced and the physics of the associated duality cascade discussed.
Three-dimensional conformal theories with six supersymmetries and SU(4) R-symmetry describing stacks of M2-branes are here proposed to be related to generalized Jordan triple systems. Writing the four-index structure constants in an appropriate form, the Chern-Simons part of the action immediately suggests a connection to such triple systems. In contrast to the previously considered three-algebras, the additional structure of a generalized Jordan triple system is associated to a graded Lie algebra, which corresponds to an extension of the gauge group. In this note we show that the whole theory…
We present a nonabelian Lagrangian that appears to have $(2,0)$ superconformal symmetry and that can be coupled to a supergravity background. But for our construction to work, we have to break this superconformal symmetry by imposing as a constraint on top of the Lagrangian that the fields have vanishing Lie derivatives along a Killing direction.
We construct the T duals of certain type IIA brane configurations with one compact dimension (elliptic models) which contain orientifold planes. These configurations realize four-dimensional $\NN=2$ finite field theories. For elliptic models with two negatively charged orientifold six-planes, the T duals are given by D3 branes at singularities in the presence of O7-planes and D7-branes. For elliptic models with two oppositely charged orientifold planes, the T duals are D3 branes at a different kind of orientifold singularities, which do not require D7 branes. We construct the adequate orientif…
We show how the anti-de Sitter isometries of a brane solution of supergravity theory produce superconformal invariance of their world-volume action. In this way linear as well as non-linear superconformal actions are obtained in various dimensions. Two particular examples are a conformal action with the antisymmetric tensor in 6 dimensions in Pasti-Sorokin-Tonin formulation, and superconformal mechanics.
Quantum geometry of twisted Wess--Zumino--Witten branes is formulated in the framework of twisted Reflection Equation Algebras. It is demonstrated how the representation theory of these algebras leads to the correct classification and localisation of branes. A semiclassical formula for quantised brane positions is derived and shown to be consistent with earlier string-theoretic analyses.
The main focus of this lecture is on extended objects in adS*S bosonic backgrounds with unbroken supersymmetry. The backgrounds are argued to be exact, special consideration are given to the non-maximal supersymmetry case. The near horizon superspace construction is explained. The superconformal symmetry appears in the worldvolume actions as the superisometry of the near horizon superspace, like the superPoincare symmetry of GS superstring and BST supermembrane in the flat superspace. The issues in gauge fixing of local kappa-symmetry are reviewed. We describe the features of the gauge-fixed I…
We study the chiral ring of four-dimensional superconformal field theories obtained by wrapping M5-branes on a complex curve inside a Calabi-Yau three-fold. We propose a field theoretic construction of all the theories found by Bah, Beem, Bobev and Wecht by introducing new building blocks, and prove several $\mathcal{N} = 1$ dualities featuring the latter. We match the central charges with those computed from the M5-brane anomaly polynomial, perform the counting of relevant operators and analyze unitarity bound violations. As a byproduct, we compute the exact dimension of "heavy operators" obt…
We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a number of exotic and enlightening properties which do not occur in higher dimensional field theories. We see that superfield and superspace formalism is available for $\mathcal{N}\le 8$ superconformal mechanical models. We then discuss the M2-branes with a focus on the world-volume descriptions of the multiple M2-branes which are superconformal three-dimensi…
Recently, Gaiotto, Strominger and Yin have proposed a holographic dual description for the near-horizon physics of certain N=2 black holes in terms of the superconformal quantum mechanics on D0-branes in the attractor geometry. We provide further evidence for their proposal by applying it to the case of `small' black holes which have vanishing horizon area in the leading supergravity approximation. We consider 2-charge black holes in type IIA on $T^2 \times M$, where $M$ can be either $K_3$ or $T^4$, made up out of D0-branes and D4-branes wrapping $M$. We construct the corresponding superconfo…
Based on recent developments, in this letter we find 2+1 dimensional gauge theories with scale invariance and N=8 supersymmetry. The gauge theories are defined by a Lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theori…
The N=4, d=4 Yang-Mills conformal supersymmetry exhibits a very simple sub-sector described by four differential operators. The invariance under this subalgebra is big enough to determine the N=4 theory. Some attempts are done to interpret these differential operators.
We analyze the level-rank duality of omega_c-twisted D-branes of SU(N)_K (when N and K>2). When N or K is even, the duality map involves Z_2-cominimal equivalence classes of twisted D-branes. We prove the duality of the spectrum of an open string stretched between omega_c-twisted D-branes, and ascertain the relation between the charges of level-rank-dual omega_c-twisted D-branes.
