Cascading Quivers from Decaying D-branes

We use an argument analogous to that of Kachru, Pearson and Verlinde to argue that cascades in L^{a,b,c} quiver gauge theories always preserve the form of the quiver, and that all gauge groups drop at each step by the number M of fractional branes. In particular, we demonstrate that an NS5-brane that sweeps out the S^3 of the base of L^{a,b,c} destroys M D3-branes.Comment: 11 pages, 1 figure; v2: references adde

From E_8 to F via T

We argue that T-duality and F-theory appear automatically in the E_8 gauge bundle perspective of M-theory. The 11-dimensional supergravity four-form determines an E_8 bundle. If we compactify on a two-torus, this data specifies an LLE_8 bundle where LG is a centrally-extended loopgroup of G. If one of the circles of the torus is smaller than sqrt(alpha') then it is also smaller than a nontrivial circle S in the LLE_8 fiber and so a dimensional reduction on the total space of the bundle is not valid. We conjecture that S is the circle on which the T-dual type IIB theory is compactified, with the aforementioned torus playing the role of the F-theory torus. As tests we reproduce the T-dualities between NS5-branes and KK-monopoles, as well as D6 and D7-branes where we find the desired F-theory monodromy. Using Hull's proposal for massive IIA, this realization of T-duality allows us to confirm that the Romans mass is the central extension of our LE_8. In addition this construction immediately reproduces the conjectured formula for global topology change from T-duality with H-flux.Comment: 25 pages, 4 eps figure

New Duality Transformations in Orbifold Theory

We find new duality transformations which allow us to construct the stress tensors of all the twisted sectors of any orbifold A(H)/H, where A(H) is the set of all current-algebraic conformal field theories with a finite symmetry group H \subset Aut(g). The permutation orbifolds with H = Z_\lambda and H = S_3 are worked out in full as illustrations but the general formalism includes both simple and semisimple g. The motivation for this development is the recently-discovered orbifold Virasoro master equation, whose solutions are identified by the duality transformations as sectors of the permutation orbifolds A(D_\lambda)/Z_\lambda.Comment: 48 pages,typos correcte

Loop Groups, Kaluza-Klein Reduction and M-Theory

We show that the data of a principal G-bundle over a principal circle bundle is equivalent to that of a \hat{LG} = U(1) |x LG bundle over the base of the circle bundle. We apply this to the Kaluza-Klein reduction of M-theory to IIA and show that certain generalized characteristic classes of the loop group bundle encode the Bianchi identities of the antisymmetric tensor fields of IIA supergravity. We further show that the low dimensional characteristic classes of the central extension of the loop group encode the Bianchi identities of massive IIA, thereby adding support to the conjectures of hep-th/0203218.Comment: 26 pages, LaTeX, utarticle.cls, v2:clarifications and refs adde

The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 IV. Orientation Orbifolds Include Orientifolds

In this fourth paper of the series, I clarify the somewhat mysterious relation between the large class of {\it orientation orbifolds} (with twisted open-string CFT's at $\hat c=52$) and {\it orientifolds} (with untwisted open strings at $c=26$), both of which have been associated to division by world-sheet orientation-reversing automorphisms. In particular -- following a spectral clue in the previous paper -- I show that, even as an {\it interacting string system}, a certain half-integer-moded orientation orbifold-string system is in fact equivalent to the archetypal orientifold. The subtitle of this paper, that orientation orbifolds include and generalize standard orientifolds, then follows because there are many other orientation orbifold-string systems -- with higher fractional modeing -- which are not equivalent to untwisted string systems.Comment: 22 pages, typos correcte

The Loop Group of E8 and Targets for Spacetime

The dimensional reduction of the E8 gauge theory in eleven dimensions leads to a loop bundle in ten dimensional type IA string theory. We show that the restriction to the Neveu-Schwarz sector leads naturally to a sigma model with target space E8 with the ten-dimensional spacetime as the source. The corresponding bundle has a structure group the group of based loops, whose classifying space we study. We explore some consequences of this proposal such as possible Lagrangians and existence of flat connections.Comment: 17 pages, main section improved, change in title, reference and acknowledgement adde

The orbifold-string theories of permutation-type: II. Cycle dynamics and target space-time dimensions

We continue our discussion of the general bosonic prototype of the new orbifold-string theories of permutation type. Supplementing the extended physical-state conditions of the previous paper, we construct here the extended Virasoro generators with cycle central charge $\hat{c}_j(\sigma)=26f_j(\sigma)$, where $f_j(\sigma)$ is the length of cycle $j$ in twisted sector $\sigma$. We also find an equivalent, reduced formulation of each physical-state problem at reduced cycle central charge $c_j(\sigma)=26$. These tools are used to begin the study of the target space-time dimension $\hat{D}_j(\sigma)$ of cycle $j$ in sector $\sigma$, which is naturally defined as the number of zero modes (momenta) of each cycle. The general model-dependent formulae derived here will be used extensively in succeeding papers, but are evaluated in this paper only for the simplest case of the "pure" permutation orbifolds.Comment: 32 page

Two Large Examples in Orbifold Theory: Abelian Orbifolds and the Charge Conjugation Orbifold on su(n)

Recently the operator algebra and twisted vertex operator equations were given for each sector of all WZW orbifolds, and a set of twisted KZ equations for the WZW permutation orbifolds were worked out as a large example. In this companion paper we report two further large examples of this development. In the first example we solve the twisted vertex operator equations in an abelian limit to obtain the twisted vertex operators and correlators of a large class of abelian orbifolds. In the second example, the twisted vertex operator equations are applied to obtain a set of twisted KZ equations for the (outer-automorphic) charge conjugation orbifold on su(n \geq 3).Comment: 58 pages, v2: three minor typo