Dilogarithm Identities in Conformal Field Theory

Dilogarithm identities for the central charges and conformal dimensions exist for at least large classes of rational conformally invariant quantum field theories in two dimensions. In many cases, proofs are not yet known but the numerical and structural evidence is convincing. In particular, close relations exist to fusion rules and partition identities. We describe some examples and ideas, and present some conjectures useful for the classification of conformal theories. The mathematical structures seem to be dual to Thurston's program for the classification of 3-manifolds.Comment: 14 pages, BONN-preprint. (a few minor changes, two major corrections in chapter 3, namely: (3.10) only holds in the case of the A series, Goncharovs conjecture is not an equivalence but rather an implication and a theorem

Orbifold resolutions with general profile

A very general class of resolved versions of the C/Z_N, T^2/Z_N and S^1/Z_2 orbifolds is considered and the free theory of 6D chiral fermions studied on it. As the orbifold limit is taken, localized 4D chiral massless fermions are seen to arise at the fixed points. Their number, location and chirality is found to be independent on the detailed profile of the resolving space and to agree with the result of hep-th/0409229, in which a particular resolution was employed. As a consistency check of the resolution procedure, the massive equation is numerically studied. In particular, for S^1/Z_2, the "resolved" mass--spectrum and wave functions in the internal space are seen to correctly reproduce the usual orbifold ones, as the orbifold limit is taken.Comment: 28 pages, 3 figures, typos corrected, references adde

Chiral zero-mode for abelian BPS dipoles

We present an exact normalisable zero-energy chiral fermion solution for abelian BPS dipoles. For a single dipole, this solution is contained within the high temperature limit of the SU(2) caloron with non-trivial holonomy.Comment: 9 pages, 1 figure (in 2 parts), presented at the workshop on "Confinement, Topology, and other Non-Perturbative Aspects of QCD", 21-27 Jan. 2002, Stara Lesna, Slovaki

Numerical Investigation of Monopole Chains

We present numerical results for chains of SU(2) BPS monopoles constructed from Nahm data. The long chain limit reveals an asymmetric behavior transverse to the periodic direction, with the asymmetry becoming more pronounced at shorter separations. This analysis is motivated by a search for semiclassical finite temperature instantons in the 3D SU(2) Georgi-Glashow model, but it appears that in the periodic limit the instanton chains either have logarithmically divergent action or wash themselves out.Comment: 14 pages, 6 figures; v2 minor changes, published versio

Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras

We prove the existence and associativity of the nonmeromorphic operator product expansion for an infinite family of vertex operator algebras, the triplet W-algebras, using results from P(z)-tensor product theory. While doing this, we also show that all these vertex operator algebras are C_2-cofinite.Comment: 21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is improved and one reference is adde

Supersymmetric Lorentz-Covariant Hyperspaces and self-duality equations in dimensions greater than (4|4)

We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel SO(3,1)-covariant superspaces, which we call hyperspaces, having dimensionality greater than (4|4) of traditional super-Minkowski space. As an application, we consider gauge fields on complexifications of these superspaces; and extending the concept of self-duality, we obtain classes of completely solvable equations analogous to the four-dimensional self-duality equations.Comment: 29 pages, late

AdS Superalgebras with Brane Charges

We consider the inclusion of brane charges in AdS_5 superalgebras that contain the maximal central extension of the super-Poincar\'e algebra on the boundary of AdS_5. For theories with N supersymmetries on the boundary, the maximal extension is OSp(1/8N,R), which contains the group $Sp(8N,R)\supset U(2N,2N) \supset SU(2,2)\times U(N)$ as extension of the conformal group. An ``intermediate'' extension to U(2N,2N/1) is also discussed, as well as the inclusion of brane charges in AdS_7 and AdS_4 superalgebras. BPS conditions in the presence of brane charges are studied in some details.Comment: Section on AdS_7 superalgebras and a description of AdS_4 superalgebras added, minor mistakes corrected, several references added; 13 pages, latex2

Dyons in N=4 Supersymmetric Theories and Three-Pronged Strings

We construct and explore BPS states that preserve 1/4 of supersymmetry in N=4 Yang-Mills theories. Such states are also realized as three-pronged strings ending on D3-branes. We correct the electric part of the BPS equation and relate its solutions to the unbroken abelian gauge group generators. Generic 1/4-BPS solitons are not spherically symmetric, but consist of two or more dyonic components held apart by a delicate balance between static electromagnetic force and scalar Higgs force. The instability previously found in three-pronged string configurations is due to excessive repulsion by one of these static forces. We also present an alternate construction of these 1/4-BPS states from quantum excitations around a magnetic monopole, and build up the supermultiplet for arbitrary (quantized) electric charge. The degeneracy and the highest spin of the supermultiplet increase linearly with a relative electric charge. We conclude with comments.Comment: 33 pages, two figures, LaTex, a footnote added, the figure caption of Fig.2 expanded, one more referenc

One Monopole with k Singularities

We present all charge one monopole solutions of the Bogomolny equation with k prescribed Dirac singularities for the gauge groups U(2), SO(3), or SU(2). We analyze these solutions comparing them to the previously known expressions for the cases of one or two singularities.Comment: 12 pages, LaTe

Goldstone models in D+1 dimensions, D=3,4,5, supporting stable and zero topological charge solutions

We study finite energy static solutions to a global symmetry breaking Goldstone model described by an isovector scalar field in D+1 spacetime dimensions. Both topologically stable multisolitons with arbitrary winding numbers, and zero topological charge soliton--antisoliton solutions are constructed numerically in D=3,4,5. We have explored the types of symmetries the systems should be subjected to, for there to exist multisoliton and soliton--antisoliton pairs in D=3,4,5,6. These findings are underpinned by constructing numerical solutions in the $D\le 5$ examples. Subject to axial symmetry, only multisolitons of all topological charges exist in even D, and in odd D, only zero and unit topological charge solutions exist. Subjecting the system to weaker than axial symmetries, results in the existence of all the possibilities in all dimensions. Our findings apply also to finite 'energy' solutions to Yang--Mills and Yang-Mills--Higgs systems, and in principle also sigma models.Comment: 29 pages, 6 figure