Superconformal Currents Research Articles

The large N limit of OPEs in symmetric orbifold CFTs with mathcal{N} = (4, 4) supersymmetry

We explore the OPE of certain twist operators in symmetric product (SN) orbifold CFTs, extending our previous work [1] to the case of mathcal{N} = (4, 4) supersymmetry. We consider a class of twist operators related to the chiral primaries by spectral flow parallel to the twist. We conjecture that at large N, the OPE of two such operators contains only fields in this class, along with excitations by fractional modes of the superconformal currents. We provide evidence for this by studying the coincidence limits of two 4-point functions to several non-trivial orders. We show how the fractional excitations of the twist operators in our restricted class fully reproduce the crossing channels appearing in the coincidence limits of the 4-point functions.

The conformal supercurrents in diverse dimensions and conserved superconformal currents

Given a conserved and traceless energy-momentum tensor and a conformal Killing vector, one obtains a conserved current. We generalise this construction to superconformal theories in three, four, five and six dimensions with various amounts of supersymmetry by working in the appropriate superspaces.

Formula omitted] superconformal symmetry of [formula omitted] Chern–Simons theory

We demonstrate that the general D=3, N=5 Chern–Simons matter theory possesses a full OSp(5|4) superconformal symmetry, and construct the corresponding superconformal currents. The closure of the superconformal algebra is verified in detail. We also show that the conserved OSp(6|4) superconformal currents in the general N=6 theory can be obtained as special cases of the OSp(5|4) currents by enhancing the R-symmetry of the N=5 theory from USp(4) to SU(4).

OSp(4|4)superconformal currents in three-dimensionalN=4Chern-Simons quiver gauge theories

We prove explicitly that the general D=3, N=4 Chern-Simons-matter (CSM) theory has a complete OSp(4|4) superconformal symmetry, and construct the corresponding conserved currents. We re-derive the OSp(5|4) superconformal currents in the general N=5 theory as special cases of the OSp(4|4) currents by enhancing the supersymmetry from N=4 to N=5. The closure of the full OSp(4|4) superconformal algebra is verified explicitly.

Two-dimensional supersymmetric sigma models on almost-product manifolds and non-geometry

In this paper we study the relation between the target space geometry of (1, 1) sigma models and the factorization of the associated superconformal theory, at the classical level. It turns out that the superconformal currents T± factorize as , with and conserved separately, provided that the target space admits projectors P(±) and Q(±) (that is, a pair of almost-product structures), compatible with the Riemannian structure of the target space, and covariantly constant with respect to the two torsionful connections ∇(±) that arise naturally from the sigma model. It is a surprising result that the integrability of the projectors is not an obstruction for the associated symmetries and to form copies of the superconformal algebra. While one expects to be able to define a superconformal theory associated with a particular Riemannian submanifold defined by an integrable projector, a consequence of the above result is that there are no obstructions to defining a superconformal theory associated with non-integrable projectors. We show that this notion of non-geometry encompasses the locally non-geometric examples that arise in the T-duality inspired doubled formulations. In addition, we derive the general conditions for (2, 2) supersymmetry to be realized in the projective sense. This extends the relation between (2, 2) sigma models and bi-Hermitian geometry to the non-geometric setting. For the bosonic subsector we propose a BRST-type approach to defining the physical degrees of freedom in the non-geometric scenario.

From world-sheet supersymmetry to super target spaces

We investigate the relation between N=(2,2) superconformal Lie group WZNW models and Lie supergroup WZNW models. The B-twist of an exactly marginal perturbation of the world-sheet superconformal sigma model is the supergroup model. Moreover, the superconformal currents are expressed in terms of Lie superalgebra currents in the twisted theory. As applications, we find protected sectors and boundary actions in the supergroup sigma model. A special example is the relation between string theory on AdS_3 x S^3 x T^4 in the RNS formalism and the U(1,1|2) x U(1|1) x U(1|1) supergroup WZNW model.

Correlators of N = 1 superconformal currents

We give an explicit expression for the M-point correlator of the superconformal current in two-dimensional N = 1 superconformal field theories.

Domain walls, the extended superconformal algebra and the supercurrent

The presence of a domain wall is shown to require a tensorial central charge extension of the superconformal algebra. The currents associated with the conformal central charges are constructed as space–time moments of the SUSY tensorial central charge current. The supercurrent is obtained and it contains the R symmetry current, the SUSY spinor currents, the energy–momentum tensor and the SUSY tensorial central charge currents as its component currents. All tensorial central charge extended superconformal currents are constructed from the supercurrent. The superconformal currents' and the conformal tensorial central charge currents' (non-)conservation equations are expressed in terms of the generalized trace of the supercurrent. It is argued that although the SUSY tensorial central charges are uncorrected, the conformal tensorial central charges receive radiative corrections.

Superconformal symmetry in linear sigma model on supermanifolds

We consider a gauged linear sigma model in two dimensions with Grassmann odd chiral superfields. We investigate the Konishi anomaly of this model and find out the condition for realization of superconformal symmetry on the world-sheet. When this condition is satisfied, the theory is expected to flow into conformal theory in the infrared limit. We construct superconformal currents explicitly and study some properties of this world-sheet theory from the point of view of conformal field theories.

Superconformal symmetry, the supercurrent, and non-BPS brane dynamics

The Noether currents associated with the nonlinearly realized super-Poincare symmetries of the Green-Schwarz (Nambu-Goto-Akulov-Volkov) action for a non-Bogomol'nyi-Prasad-Sommerfield (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 with the world-volume conformal central charge current and special conformal current being the primary components of the supersymmetry multiplets containing all the currents. Correspondingly the superconformal symmetry breaking terms form supersymmetry multiplets the components of which are obtainable as supersymmetry transformations of the primary currents' symmetry breaking terms.

Nonlinear realization of supersymmetry and superconformal symmetry

Nonlinear realizations describing the spontaneous breakdown of supersymmetry and $R$-symmetry are constructed using the Goldstino and $R$-axion fields. The associated $R$-current, supersymmetry current and energy-momentum tensor are shown to be related under the nonlinear supersymmetry transformations. Nonlinear realizations of the superconformal algebra carried by these degrees of freedom are also displayed. The divergences of the $R$ and dilatation currents are related to the divergence of the superconformal currents through nonlinear supersymmetry transformations which in turn relates the explicit breakings of these symmetries.

Some Systematics of the Coupling Constant Dependence ofN=4 Yang-Mills

The operator, τ, that generates infinitesimal changes of the coupling constant in N = 4 Yang-Mills sits in the same supermultiplet as the superconformal currents. We show how superconformal current Ward identities determine a class of terms in the operator product expansion of τ with any other operator. In certain cases, this leads to constraints on the coupling dependence of correlation functions in N = 4 Yang-Mills. As an application, we demonstrate the exact non-renormalization of two and certain three-point correlation functions of BPS operators.

Making the hyper-Kähler structure ofN=2quantum string manifest

We show that the Lorentz covariant formulation of N=2 string in a curved space reveals an explicit hyper--K\"ahler structure. Apart from the metric, the superconformal currents couple to a background two--form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra.

Unitary minimal models of Script SScript W(3/2,3/2,2) superconformal algebra and manifolds ofG2holonomy

The SW(3/2,3/2,2) superconformal algebra is a W algebra with two free parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2. The algebra is proved to be the symmetry algebra of the coset (su(2)+su(2)+su(2))/su(2). At the central charge c=21/2 the algebra coincides with the superconformal algebra associated to manifolds of G_2 holonomy. The unitary minimal models of the SW(3/2,3/2,2) algebra and their fusion structure are found. The spectrum of unitary representations of the G_2 holonomy algebra is obtained.

Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory

The one-instanton contributions to various correlation functions of supercurrents in four-dimensional N=4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory.Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS5*S5 background. This is in line with the suggested AdS/Yang-Mills correspondence. The relation between Yang--Mills instantons and D-instantons is further confirmed by the explicit form of the classical D-instanton solution in the AdS5*S5 background and its associated supermultiplet of zero modes. Speculations are made concerning instanton effects in the large-N_c limit of the SU(N_c) Yang-Mills theory.

Superconformal ward identities and N = 2 Yang-Mills theory

A reformulation of the superconformal Ward identities that combines all the superconformal currents and the associated parameters in one multiplet is given for theories with rigid N = 1 or N = 2 supersymmetry. This form of the Ward identities is applied to the spontaneously broken N = 2 Yang-Mills theory and used to derive a condition on the low energy effective action. This condition is satisfied by the solution proposed by Seiberg and Witten.

Worldsheets with extended supersymmetry

We determine the equations which govern the gauge symmetries of worldsheets with local supersymmetry of arbitrary rank ( N, N′), and their possible anomalies. Both classical and ghost conformally invariant multiplets of the left or right sector are assembled into the components of a single O(N)-superfield. The component with ghost number zero of this superfield is the N-supersymmetric generalization of the Beltrami differential. In a Lagrangian approach, and after gauge-fixing, it becomes the super-moduli of Riemann surfaces coupled to local supersymmetry of rank N. It is also the source of all linear superconformal currents derived from ordinary operator product techniques. The interconnection between BRST invariant actions with different values of N ⩾ 3, and their possible link to topological 2D-gravity coupled to topological sigma models, are shown by straightforward algebraic considerations.

N = 2 superconformal invariance in two-dimensional quantum field theories

We construct N = 2 superconformal currents, vertex operators and four-point correlation functions using chiral superfields. The method generalizes works by Thorn and by Dotsenko and Fateev. In particular the discrete families of degenerate representations given in works by Di Vecchia et al. and Boucher et al. arise naturally, thereby constituting a derivation of the N = 2 superconformal dimensions of these representations. Finally, unitary representations of the N = 2 algebra in the twisted sector are constructed out of free fermions based on the model of Di Vecchia et al.

Improved Minkowski-space currents and residual shifts in theN=1 superspace-translation tensor

The general structure of the improved superconformal and super-Poincare currents obtained from the minimal superspace-translation tensor is given. A necessary condition for the residual shifts in this tensor follows from the requirement of shift invariance of these currents.

Supercurrents, renormalization and anomalies

A renormalized supercurrent is constructed for the massive and massless supersymmetric gφ 3 model of Wess and Zumino. Its pivotal position in the study of the superconformal group is demonstrated. All anomalies occurring in the superconformal currents' Ward identities are shown to be directly related to the Callan-Symanzik functions β and γ. These turn out to be mass independent under suitable off-shell normalization conditions.