arXiv subjects

Mark A. Walton

Publications and source records attributed to Mark A. Walton.

27 records · Page 2Linked to original sources

arXiv2003

PP-wave Green-Schwarz superstring, polygon divergent structure and conformal field theory

In the semi-light cone gauge $g_{ab}=e^{2ϕ}δ_{ab}$, $\barγ^+θ=0$, we evaluate the $ϕ$-dependent effective action for the pp-wave Green-Schwarz (GS) superstring in both harmonic and group coordinates. When we compute the fermionic $ϕ$-dependent effective action in harmonic coordinates, we find a new triangular one-loop Feynman diagram. We show that the bosonic $ϕ$-dependent effective action cancels with the fermionic one, indicating that the pp-wave GS superstring is a conformal field theory. We introduce the group coordinates preserving $SO(4)\times SO(4)$ and conformal symmetry. Group coordinates are interesting because vertex operators take simple forms in them. The new feature in group coordinates is that there are logarithmic divergences from n-gons, so that the divergent structure is more complicated than in harmonic coordinates. After summing over all contributions from n-gons, we show that in group coordinates, the GS superstring on pp-wave RR background is still a conformal field theory.

hep-th↗

arXiv2002

D-branes in asymmetrically gauged WZW models and axial-vector duality

We construct D-branes in a left-right asymmetrically gauged WZW model, with the gauge subgroup embedded differently on the left and the right of the group element. The symmetry-preserving boundary conditions for the group-valued field $g$ are described, and the corresponding action is found. When the subgroup $H=U(1)$, we can implement T-duality on the axially gauged WZW action; an orbifold of the vectorially gauged theory is produced. For the parafermion $SU(2)/U(1)$ coset model, a $σ$-model is obtained with vanishing gauge field on D-branes. We show that a boundary condition surviving from the SU(2) parent theory characterizes D-branes in the parafermion theory, determining the shape of A-branes. The gauge field on B-branes is obtained from the boundary condition for A-branes, by the orbifold construction and T-duality. These gauge fields stabilize the B-branes.

hep-th↗

arXiv2002

Maximally symmetric D-branes in gauged WZW models

Gluing conditions are proposed to characterize the D-branes in gauged WZW models. From them the boundary conditions for the group-valued and the subgroup-valued fields are determined. We construct a gauged WZW action for open strings that coincides classically with those written previously, when the gluing conditions are imposed.

hep-th↗

arXiv2001

Fusion multiplicities as polytope volumes: N-point and higher-genus su(2) fusion

We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess-Zumino-Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain convex polytopes, and write them explicitly as multiple sums measuring those volumes. We focus on su(2), but discuss higher-point (N>3) and higher-genus fusion in a general way. The method follows that of our previous work on tensor product multiplicities, and so is based on the concepts of generalised Berenstein-Zelevinsky diagrams, and virtual couplings. As a by-product, we also determine necessary and sufficient conditions for non-vanishing higher-point fusion multiplicities. In the limit of large level, these inequalities reduce to very simple non-vanishing conditions for the corresponding tensor product multiplicities. Finally, we find the minimum level at which the higher-point fusion and tensor product multiplicities coincide.

hep-th↗

arXiv2001

su(N) tensor product multiplicities and virtual Berenstein-Zelevinsky triangles

Information on su(N) tensor product multiplicities is neatly encoded in Berenstein-Zelevinsky triangles. Here we study a generalisation of these triangles by allowing negative as well as non-negative integer entries. For a fixed triple product of weights, these generalised Berenstein-Zelevinsky triangles span a lattice in which one may move by adding integer linear combinations of so-called virtual triangles. Inequalities satisfied by the coefficients of the virtual triangles describe a polytope. The tensor product multiplicities may be computed as the number of integer points in this convex polytope. As our main result, we present an explicit formula for this discretised volume as a multiple sum. As an application, we also address the problem of determining when a tensor product multiplicity is non-vanishing. The solution is represented by a set of inequalities in the Dynkin labels. We also allude to the question of when a tensor product multiplicity is greater than a given non-negative integer.

math-ph↗

arXiv2001

Purely affine elementary su(N) fusions

We consider three-point couplings in simple Lie algebras -- singlets in triple tensor products of their integrable highest weight representations. A coupling can be expressed as a linear combination of products of finitely many elementary couplings. This carries over to affine fusion, the fusion of Wess-Zumino-Witten conformal field theories, where the expressions are in terms of elementary fusions. In the case of su(4) it has been observed that there is a purely affine elementary fusion, i.e., an elementary fusion that is not an elementary coupling. In this note we show by construction that there is at least one purely affine elementary fusion associated to every su(N>3).

hep-th↗

arXiv2001

On the level-dependence of Wess-Zumino-Witten three-point functions

Three-point functions of Wess-Zumino-Witten models are investigated. In particular, we study the level-dependence of three-point functions in the models based on algebras $su(3)$ and $su(4)$. We find a correspondence with Berenstein-Zelevinsky triangles. Using previous work connecting those triangles to the fusion multiplicities, and the Gepner-Witten depth rule, we explain how to construct the full three-point functions. We show how their level-dependence is similar to that of the related fusion multiplicity. For example, the concept of threshold level plays a prominent role, as it does for fusion.

hep-th↗

arXiv2001

Affine su(3) and su(4) fusion multiplicities as polytope volumes

Affine su(3) and su(4) fusion multiplicities are characterised as discretised volumes of certain convex polytopes. The volumes are measured explicitly, resulting in multiple sum formulas. These are the first polytope-volume formulas for higher-rank fusion multiplicities. The associated threshold levels are also discussed. For any simple Lie algebra we derive an upper bound on the threshold levels using a refined version of the Gepner-Witten depth rule.

hep-th↗

arXiv1994

On the Classification of Diagonal Coset Modular Invariants

We relate in a novel way the modular matrices of GKO diagonal cosets without fixed points to those of WZNW tensor products. Using this we classify all modular invariant partition functions of $su(3)_k\oplus su(3)_1/su(3)_{k+1}$ for all positive integer level $k$, and $su(2)_k\oplus su(2)_\ell/su(2)_{k+\ell}$ for all $k$ and infinitely many $\ell$ (in fact, for each $k$ a positive density of $\ell$). Of all these classifications, only that for $su(2)_k\oplus su(2)_1/su(2)_{k+1}$ had been known. Our lists include many new invariants.

hep-th↗