Galois Modular Invariants of WZW Models

The set of modular invariants that can be obtained from Galois transformations is investigated systematically for WZW models. It is shown that a large subset of Galois modular invariants coincides with simple current invariants. For algebras of type B and D infinite series of previously unknown exceptional automorphism invariants are found.Comment: phyzzx macros, 38 pages. NIKHEF-H/94-3

Twisted Open Strings from Closed Strings: The WZW Orientation Orbifolds

Including {\it world-sheet orientation-reversing automorphisms} $\hat{h}_{\sigma} \in H_-$ in the orbifold program, we construct the operator algebras and twisted KZ systems of the general WZW {\it orientation orbifold} $A_g (H_-) /H_-$. We find that the orientation-orbifold sectors corresponding to each $\hat{h}_{\sigma} \in H_-$ are {\it twisted open} WZW strings, whose properties are quite distinct from conventional open-string orientifold sectors. As simple illustrations, we also discuss the classical (high-level) limit of our construction and free-boson examples on abelian $g$.Comment: 65 pages, typos correcte

Ghost Systems: A Vertex Algebra Point of View

Fermionic and bosonic ghost systems are defined each in terms of a single vertex algebra which admits a one-parameter family of conformal structures. The observation that these structures are related to each other provides a simple way to obtain character formulae for a general twisted module of a ghost system. The U(1) symmetry and its subgroups that underly the twisted modules also define an infinite set of invariant vertex subalgebras. Their structure is studied in detail from a W-algebra point of view with particular emphasis on Z_N-invariant subalgebras of the fermionic ghost system.Comment: 20 pages, plain Te

Unification Bounds on the Possible N=2 Supersymmetry Breaking Scale

In this letter, the possible appearance of N=2 supersymmetry at a low energy scale is investigated in the context of unified theories. Introducing mirror particles for all the gauge and matter multiplets of the Minimal Supersymmetric extension of the Standard Model (MSSM), the measured values of sin^2 \theta_W and \alpha_3(M_Z) indicate that the N=2 threshold scale M_{S_2} cannot be lower than \sim 10^{14}GeV. If the U(1) normalization coefficient k is treated as a free parameter, M_{S_2} can be as low as 10^9 GeV. On the other hand, if mirror quarks and leptons are absent and a non-standard value for k is used, N=2 supersymmetry breaking could in principle occur at the electroweak scale.Comment: 10 pages, LATEX, 2 eps figure

Galois currents and the projective kernel in Rational Conformal Field Theory

The notion of Galois currents in Rational Conformal Field Theory is introduced and illustrated on simple examples. This leads to a natural partition of all theories into two classes, depending on the existence of a non-trivial Galois current. As an application, the projective kernel of a RCFT, i.e. the set of all modular transformations represented by scalar multiples of the identity, is described in terms of a small set of easily computable invariants

The complete superconformal index for N=6 Chern-Simons theory

We calculate the superconformal index for N=6 Chern-Simons-matter theory with gauge group U(N) X U(N) at arbitrary allowed value of the Chern-Simons level k. The calculation is based on localization of the path integral for the index. Our index counts supersymmetric gauge invariant operators containing inclusions of magnetic monopole operators, where latter operators create magnetic fluxes on 2-sphere. Through analytic and numerical calculations in various sectors, we show that our result perfectly agrees with the index over supersymmetric gravitons in AdS_4 X S^7/Z_k in the large N limit. Monopole operators in nontrivial representations of U(N) X U(N) play important roles. We also comment on possible applications of our methods to other superconformal Chern-Simons theories.Comment: 49 pages, uses youngtab.st

Six-Dimensional Supergravity on S^3 X AdS_3 and 2d Conformal Field Theory

In this paper we study the relation between six-dimensional supergravity compactified on S^3 X AdS_3 and certain two-dimensional conformal field theories. We compute the Kaluza-Klein spectrum of supergravity using representation theory; these methods are quite general and can also be applied to other compactifications involving anti-de Sitter spaces. A detailed comparison between the spectrum of the two-dimensional conformal field theory and supergravity is made, and we find complete agreement. This applies even at the level of certain non-chiral primaries, and we propose a resolution to the puzzle of the missing states recently raised by Vafa. As a further illustration of the method the Kaluza-Klein spectra of F-theory on M^6 X S^3 X AdS_3 and of M-theory on M^6 X S^2 X AdS_3 are computed, with M^6 some Calabi-Yau manifold.Comment: 32 pages, LaTeX; minor corrections, reference adde

A new topological aspect of the arbitrary dimensional topological defects

We present a new generalized topological current in terms of the order parameter field $\vec \phi$ to describe the arbitrary dimensional topological defects. By virtue of the $$-mapping method, we show that the topological defects are generated from the zero points of the order parameter field $\vec \phi$, and the topological charges of these topological defects are topological quantized in terms of the Hopf indices and Brouwer degrees of $\phi$-mapping under the condition that the Jacobian $$. When $J(\frac \phi v)=0$, it is shown that there exist the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, we detail the bifurcation of generalized topological current and find different directions of the bifurcation. The arbitrary dimensional topological defects are found splitting or merging at the degenerate point of field function $\vec \phi$ but the total charge of the topological defects is still unchanged.Comment: 24 pages, 10 figures, Revte