Adel Bilal

Higher-derivative corrections to the non-Abelian Born–Infeld action

Abstract We determine higher-derivative terms in the open superstring effective action with U(N) gauge group up to and including order α′ 4 as can be extracted from 4 boson, 2 boson–2 fermion and 4xa0fermion string scattering amplitudes. This yields corrections to the non-Abelian Born–Infeld action involving higher derivatives as is relevant for studying D-branes beyond the slowly varying field approximation. While at order α′ 2 the action has recently been shown to be a symmetrised trace, this no longer is true at order α′ 3 or α′ 4 . We insist that these terms including higher derivatives are as important in a low-energy expansion as, e.g., the much-discussed α′ 4 F 6 terms. In particular, axa0computation of the fluctuation spectra at order α′ 4 has to take into account these nonsymmetrised trace higher-derivative terms computed here.

Supersymmetric non-abelian Born-Infeld revisited

We determine the non-abelian Born-Infeld action, including fermions, as it results from the four-point tree-level open superstring scattering amplitudes at order 02 . Wend that,after anappropriateeld redenition allterms at this order canbewrittenasasymmetrised trace. Weconfront thisactionwiththeresultsthat follow from kappa-symmetry and conclude that the recently proposed non-abelian kappa-symmetry cannot be extended to cubic orders in the Born-Infeld curvature.

On the origin of W-algebras

Abstract We show that the complex and projective structures on 2D Riemann surfaces are determined by the solutions to the linear differential equations obtained by the hamiltonian reduction of Sl(2, C ) connections by the gauge parabolic subgroup. The compatibility of complex (μ) and projective (T) structures appears as the associated zero-curvature condition on the reduced symplectic manifold and is nothing but the conformal Ward identity. Generalizing this construction to the reduction of Sl (n, C ) connections by the maximal parabolic gauge subgroup, we obtain generalized complex (μ, ρ,…) and projective (T, W, …) structures. From their compatibility conditions we explicitly obtain the Ward identities of Wn-gravity and the operator product expansions of the Wn-algebras. The associated linear differential equations (one of which involves the basic differential operator of the nth reduction of the KP hierarchy) allow for a geometric interpretation of the W-symmetries in terms of deformations of flag configurations in the jet bundle γ(n−1). We also show how to derive the Wn-Ward identities fromt he quantization of the (2 + 1)-dimensional Chern-Simons theory.

String theory and noncommutative field theories at one loop

By exploiting the boundary state formalism we obtain the string correlator between two internal points on the one loop open string world-sheet in the presence of a constant background B-field. From this derivation it is clear that there is an ambiguity when one tries to restrict the Green function to the boundary of the surface. We fix this ambiguity by showing that there is a unique form for the correlator between two points on the boundary which reproduces the one loop field theory results of different noncommutative field theories. In particular, we present the derivation of one loop diagrams for φ36 and φ44 scalar interactions and for Yang–Mills theory. From the 2-point function we are able to derive the one loop β-function for noncommutative gauge theory.

A remark on the N→∞ limit of WN-algebras

Abstract The (non-linearly) extended conformal algebras associated with su( N ) ( W N -algebras) contain operators W k (z) of dimensions k =2,3, …, N . We show that in the N →∞ limit, the quantum (commutator) algebra of the W k (z) reduces to their classical (Poisson bracket) algebra. In particular, this proves the closure — in the usual non-linear sense — of the quantum W ∞ algebra.

A note on the chiral anomaly in the AdS/CFT correspondence and 1/N2 correction

Abstract According to the AdS/CFT correspondence, the d=4, N =4 SU(N) SYM is dual to the Type IIB string theory compactified on AdS5×S5. A mechanism was proposed previously that the chiral anomaly of the gauge theory is accounted for to the leading order in N by the Chern–Simons action in the AdS5 SUGRA. In this paper, we consider the SUGRA/string action at one loop and determine the quantum corrections to the Chern–Simons action. While gluon loops do not modify the coefficient of the Chern–Simons action, spinor loops shift the coefficient by an integer. We find that for finite N, the quantum corrections from the complete tower of Kaluza–Klein states reproduce exactly the desired shift N2→N2−1 of the Chern–Simons coefficient, suggesting that this coefficient does not receive corrections from the other states of the string theory. We discuss why this is plausible.

Fusion and braiding in W-algebra extended conformal theories

Abstract We define the chiral conformal blocks of integer-spin extended (W-algebra) conformal theories by the fusion of elementary ones. The braid group representation matrices which realize the exchange algebra are computed. They are shown to coincide with the Boltzmann weights — in a certain limit of the spectral parameter — of the critical face models of Jimbo et al. In the unitary cases, where the extended conformal theories can be realized as cosets g k ⊕ g 1 / g k+1 , we relate the braiding matrices of the former to those of the ĝ WZW models. In this article we restrict ourselves to the case corresponding to symmetric tensor representations of An.

CP-violation and T-odd effects at LEP-II

Abstract LEP-II will be a tool to study CP -violation in processes involving vector bosons, and will test in particular the CP properties of the coupling of photons and Zs to W-pairs. While it is difficult to observe truly CP -odd effects, it is easy to measure T -odd ones. The latter can originate from CP -violation, or from radiative corrections involving the absorptive part of the scattering amplitude. T -odd effects are interesting in themselves, in that they accurately test the standard model and are sensitive to its unmeasured ingredients, such as the WW → WW scattering amplitude or the masses of the top quark and the elementary scalar. The prediction of the standard T -odd effects is a necessary stepping stone in the search for an honest-to-goodness violation of CP in the pure gauge sector. We thoroughly analyse the T -odd observables in the e + e − → W + W − process within the standard model, as well as the extra effects to be expected if the γ W + W − and/or ZW + W − vertices were to violate CP in a non-standard fashion.

Bosonization of ZN parafermions and su(2)N KAČ-Moody algebra

Abstract We extend Nemeschanskys bosonization to all parafermion currents of the Z N theory and give an alternative bosonization for the su (2) N Kac-Moody currents and the Z N parafermions, based on Wakimotos construction.

W-algebras from Chern-Simons theory

Abstract We show that the physical state conditions of SL(3, R ) Chern-Simons theory are equivalent to the Ward identities of the W (2) 3 --algebra. More precisely, choosing a specific polarization for quantizing the Chern-Simons theory, we can solve explicitly part of the Chern-Simons physical state conditions, while the remaining ones reduce to the Ward identities satisfied by the conformal blocks of the W (2) 3 -algebra extended conformal field theory (implying the OPEs). It is an obvious conjecture that a different choice of polarization leads to the Ward identities of W 3 = W (1) 3 and that these relations can be generalized to SL ( n , R ) Chern-Simons and W n .