Chiral Current Algebra Research Articles

Chiral boundary conditions for singletons and W-branes

We revisit the holographic dictionary for a free massless scalar in AdS3, focusing on the ‘singleton’ solutions for which the boundary profile is an arbitrary chiral function. We look for consistent boundary conditions which include this class of solutions. On one hand, we give a no-go argument that they cannot be interpreted within any boundary condition which preserves full conformal invariance. On the other hand, we show that such solutions fit naturally in a generalization of the Compère-Song-Strominger boundary conditions, which preserve a chiral Virasoro and current algebra. These observations have implications for the black hole deconstruction proposal, which proposes singleton solutions as candidate black hole microstate geometries. Our results suggest that the chiral boundary condition, which also contains the extremal BTZ black hole, is the natural setting for holographically interpreting the black hole deconstruction proposal.

RG flow of magnetic brane correlators

The magnetic brane solution to five-dimensional Einstein-Maxwell-Chern-Simons theory provides a holographic description of the RG flow from four-dimensional Yang-Mills theory in the presence of a constant magnetic field to a two-dimensional low energy CFT. We compute two-point correlators involving the U(1) current and the stress tensor, and use their leading IR behavior to confirm the existence of a single chiral current algebra, and of left-and right-moving Virasoro algebras in the low energy CFT. The common central charge of the Virasoro algebras is found to match the Brown-Henneaux formula, while the level of the current algebra is related to the Chern-Simons coupling. The coordinate reparametrizations produced by the Virasoro algebras on the AdS3 near-horizon geometry arise from physical non-pure gauge modes in the asymptotic AdS5 region, thereby providing a concrete example for the emergence of IR symmetries. Finally, we interpret the infinite series of sub-leading IR contributions to the correlators in terms of certain double-trace interactions generated by the RG flow in the low energy CFT.

Bosonization in Higher Dimensions via Noncommutative Field Theory

We propose the bosonization of a many-body fermion theory in D spatial dimensions through a noncommutative field theory on a (2D-1)-dimensional space. This theory leads to a chiral current algebra over the noncommutative space and reproduces the correct perturbative Hilbert space and excitation energies for the fermions. The validity of the method is demonstrated by bosonizing a two-dimensional gas of fermions in a harmonic trap.

Conformal Covariance Subalgebras

We give a direct Lie algebraic characterisation of conformal inclusions of chiral current algebras associated with compact, reductive Lie algebras. We use straightforward quantum field theoretic arguments and prove a long standing conjecture of Schellekens and Warner on grounds of unitarity and positivity of energy. We explore the structures found to characterise ``conformal covariance subalgebras'' and ``coset current algebras''.

QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS

We study the problem of recovering Wightman conserved currents from the canonical local implementations of symmetries which can be constructed in the algebraic framework of quantum field theory, in the limit in which the region of localization shrinks to a point. We show that, in a class of models of conformal quantum field theory in space-time dimension 1+1, which includes the free massless scalar field and the SU(N) chiral current algebras, the energy-momentum tensor can be recovered. Moreover we show that the scaling limit of the canonical local implementation of SO(2) in the free complex scalar field is zero, a manifestation of the fact that, in this last case, the associated Wightman current does not exist.

Classification of Subsystems for the Haag–Kastler Nets Generated by c = 1 Chiral Current Algebras

Let \(\mathcal{F}\) be the Haag--Kastler net generated by the \({s\hat u}\) (2) chiral current algebra at level 1. We classify the SL(2, \(\mathbb{R}\))-covariant subsystems \(\mathcal{B}\) ⊂ \(\mathcal{F}\) by showing that they are all fixed points nets \(\mathcal{F}\)H for some subgroup H of the gauge automorphisms group SO(3) of \(\mathcal{F}\). Then, using the fact that the net \(\mathcal{F}\)1 generated by the \({\hat u}\)(1) chiral current can be regarded as a subsystem of \(\mathcal{F}\), we classify the subsystems of \(\mathcal{F}\)1. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem \(\mathcal{F}_{{\text{1}}^{\mathbb{Z}_{\text{2}} } } \).

Axial U(1) symmetry breaking and the second Weinberg sum rule

A current-algebraic result due to Nieh is used to evaluate corrections to the second Weinberg sum rule due to the ${\mathrm{U}}_{A}(1)$ symmetry-breaking effective interactions. The 't Hooft interaction produces the dominant part of the second sum rule breaking terms both in the flavor-singlet and in the flavor-octet channels, whereas the Veneziano-Witten interaction leaves the second sum rule intact. This is a manifestation of the second sum rule's sensitivity to violations of the Feynman--Gell-Mann--Zweig ${\mathrm{U}}_{L}(6)\ifmmode\times\else\texttimes\fi{}{\mathrm{U}}_{R}(6)$ chiral current algebra. These predictions are compared with extant experimental data, tentatively favoring the 't Hooft interaction.

Toroidal compactification of heterotic 6D non-critical strings down to four dimensions

The low-energy limit of the 6D non-critical string theory with N = 1 SUSY and E 8 chiral current algebra compactified on T 2 is generically an N = 2 U(1) vector multiplet. We study the analog of the Seiberg-Witten solution for the low-energy effective action as a function of E 8 Wilson lines on the compactified torus and the complex modulus of that torus. The moduli space includes regions where the Seiberg-Witten curves for SU(2) QCD are recovered as well as regions where the newly discovered 4D theories with enhanced E 6, 7, 8 global symmetries appear.

A test of the chiral E8 current algebra on a 6D non-critical string

Compactifying the E 8 non-critical string in 6D down to 5D, the 6D strings give rise to particles and strings in 5D. Using the dual M-theory description compactified on an elliptically fibered Calabi-Yau we compare some of the 5D BPS states to what one expects from non-critical strings with an E 8 chiral current algebra. The E 8 multiplets of particle states comprise of 2-branes wrapping on irreducible curves together with bound states of several 2-branes.

Classification of the local extensions of the SU(3) chiral current algebra

All local extensions of the chiral algebra of observables are classified for SU3 level k conformal current algebra models. This method is based on analyzing the polynomial solutions of the corresponding Knizhnik–Zamolodchikov equations.

π+ and π0 polarizabilities from γγ→ππ datapolarizabilities from γγ→ππ data

We suggest the most model-independent and simple description of the γγ→ππ process near threshold in framework of S-matrix approach. The amplitudes contain the pion polarizabilities as free parameters and some general properties of ππ interaction. Application of these formulae for description of MARK-II[1] and Crystal Ball [2] data gives: (α − β)C = (6.6 ± 1.2) · 10−42cm3, (α − β)N = (− 0.7 ± 2.3) · 10−42cm3 (in units systeme 2=4πα) at the experimental values of ππ scattering lengthsa 0 0 =0.24,a 0 2 =−0.04. Both values are compatible with predictions of chiral models and current algebra.

Kähler-Chern-Simons theory and symmetries of anti-self-dual gauge fields

Kähler-Chern-Simons theory, which was proposed as a generalization of ordinary Chern-Simons theory, is explored in more detail. The theory describes anti-self-dual instantons on a four-dimensional Kähler manifold. The phase space is the space of gauge potentials, whose symplectic reduction by the constraints of anti-self-duality leads to the moduli space of instantons. We show that infinitesimal Bäcklund transformations, previously related to “hidden symmetries” of instantons, are canonical transformations generated by the anti-self-duality constraints. The quantum wave functions naturally lead to a generalized Wess-Zumino-Witten action, which in turn has associated chiral current algebras. The dimensional reduction of the anti-self-duality equations leading to integrable two-dimensional theories is briefly discussed in this framework.

Universality in quantum Hall systems

It is shown that the theory of the quantum Hall effect is closely related to Chern-Simons gauge theory and to rational conformal field theory. In particular, the equations of classical electromagnetism in quantum Hall systems are derived from a pure Chern-Simons action. This permits us to argue that the scaling limit of a quantum Hall system is described by quantum Chern-Simons theory, thereby explaining the discreteness of the set of values of the Hall conductivity. Using the equivalence of Chern-Simons theory to chiral current algebra, a general derivation of the existence of chiral currents circulating near the boundary edges of a quantum Hall system is found. It is indicated how to derive the effective Chern-Simons action of a quantum Hall system from the underlying quantum mechanics. Applications of our results to very weakly doped “high-temperature superconductors” are described.

VERTEX OPERATORS IN THE QUANTUM HALL EFFECT

The edge states of the quantum Hall effect carry representations of chiral current algebras and their associated groups. In the simplest case of a single filled Landau level, I demonstrate explicitly how the group action affects the many-body states, and why the Kac-Peterson cocycle appears in the group multiplication law. I show how these representations may be used to construct vertex operators which create localised edge excitations, and indicate how they are related to the bulk quasi-particles.

Odd dimensional gauge theories and current algebra

We quantize gauge field theories in odd dimensional space-time with actions including both a Chern-Simons term and a Yang-Mills term. Such theories will be referred to as CSYM theories. We show that there are deep connections between these theories and chiral anomalies and current algebra in even dimensional space-time. The classical canonical structure of the CSYM theories is intimately related to the algebraic properties of the consistent and covariant chiral anomalies. The quantization of the CSYM theories involves a one-cocycle which is the Wess-Zumino functional and, depending on the dimension of space-time and the gauge group, the consistent realization of gauge invariance at the quantum level imposes a quantization condition on the Chern-Simons coupling parameter. The associated cocycle behavior of physical states may be understood in terms of an Abelian functional curvature on the space of all spatial gauge fields. By considering the CSYM theories on a space-time with a spatial boundary we show that the algebra of Gauss law generators acquires a boundary-valued anomaly which is cohomologous to the Faddeev-Shatashvili proposal for the anomaly in the equal-time commutator of Gauss law operators in the theory of massless chiral fermions interacting with a gauge field in even dimensional space-time.

Current algebra from Chern-Simons theories

We analyze odd-dimensional gauge field theories with action including both a Chern-Simons and a Yang-Mills term. When space-time has a spatial boundary the commutator algebra of Gauss law constraints acquires a boundary-valued anomaly which is related to anomalous chiral fermionic current algebra. We further study the limit in which the Yang-Mills term is removed and compute the corresponding anomalous boundary current algebras of pure Chern-Simons theories.

Modular invariant QFT models of u(1) conformal current algebra

Local field representations of the U(1) chiral conformal current algebra are considered. They correnpond to the Virasoro central charge c=1. The locality condition singles out a denumerable set of models with basic charged fields of U(10 charge g = ± n , n = 1, 2, … . Modular invariant partition functions are constructed for all such models. The level-1 su(2) theory and the extended N = 2 super Virasoro model (for c = 1) are special cases.

Why are the isoscalar neutral current axial-vector couplings and isoscalar nucleon anomalous moments small?

By using an argument based on the realization of chiral current algebras, we explain why the isoscalar neutral current axial-vector coupling and the isoscalar nucleon anomalous moments are small. We give an argument which predicts, ( G A N(0))p/( G A N(0)) n = ( H A N(0)) p/( H A N(0)) n = k p/ k n ≈ 1.79/−1.91, where k p and k n are the anomalous moments of the proton and neutron, respectively. ( G A N(0)) p and ( H A N(0)) p are the weak neutral current axial-vector coupling and the induced pseudoscalar coupling for the proton, respectively.

Chiral solitons and current algebra

We investigate the possibility of a realistic hadrodynamics based solely on observable currents. The basic idea is to exploit the soliton generation in bosonic chiral theories as a mechanism for finding the fermionic representations of current algebra. A prototype realization is Skyrme's O(4) invariant theory of pions and nucleons. A comprehensive reexamination of this model in the context of chiral dynamics suffices to reveal a strikingly self-consistent dynamical picture. First a differential geometric formulation gives the proper framework for a chiral invariant quantum theory of solitons and allows a compact derivation of Skyrme's main results. While no exact analytic solution is found, the solitons are sufficiently localized so that their singularities can be properly isolated out for analysis. Using Witten's ansatz, a determination of the form of the 1-soliton singularity is obtained from the field equations. It is given by Cayley's steoreographic projection from S 3 to R 3 ⌣ {∞} ≈ S 3 ; a most suitable form for the proof of spinor structure. Williams' proof that the quantized 1-soliton sector gives rise to fermionic spin states is recalled. It is argued that the topological dynamics of this sector induce an invariance group K = SU(2) I ⊗ SU(2) J and its associated strong coupling isobaric spectrum for the nucleons. The associated current algebra is derived and resolves the main difficulties of the Sugawara-Sommerfield program. The signature of a field theoretical bootstrap is clear: massive nucleons as soliton bound states of Nambu-Goldstone bosons illustrate a dynamical mechanism dual to that of Nambu and Jona-Lasinio.

Spontaneous breakdown and current algebras

We demonstrate the equivalence of spontaneously brokenSU2×SU2 chiral invariance and current algebras in a field-theoretic model. The model consists of an isospinor Fermi field («nucleon») and an isovector, pseudoscalar, massless bound state («pion»). The spontaneous breakdown of the chiralSU2 symmetry induces anE3 symmetry at the observational level. Its consequences are examined and are shown to be equivalent to conventionalSU2×SU2 current algebra results.