The Coupling of Yang-Mills to Extended Objects

The coupling of Yang-Mills fields to the heterotic string in bosonic formulation is generalized to extended objects of higher dimension (p-branes). For odd p, the Bianchi identities obeyed by the field strengths of the (p+1)-forms receive Chern-Simons corrections which, in the case of the 5-brane, are consistent with an earlier conjecture based on string/5-brane duality.Comment: 14 Page

Plutarch on the childhood of Alcibiades

Almost four decades ago, Donald Russell published in this journal an analysis of the first sixteen chapters of theLife of Alkibiades, which consist largely of short self-contained anecdotes about Alkibiades' childhood, youth and early career (Russell 1966b). As Russell demonstrated, most of these anecdotes are juxtaposed without any causal link. Although there are the occasional chronological markers – indications, for example, that Alkibiades is getting older and passing from childhood to early manhood – some are plainly out of chronological order and it is impossible to extract a clear chronology from them. Russell argued, however, that to try to extract such a chronological narrative would be to misunderstand the function of this material, which is not to provide a narrative of Alkibiades' early years but rather to illuminate and illustrate his character.Russell's argument, in particular the stress on Plutarch's interest in character, was seminal; together with two other papers published at roughly the same time, it marked the beginning of a new appreciation of Plutarch as an author of literary merit. But Russell was rather less convinced of the logic of selection of the first five anecdotes, which relate to Alkibiades' youth and comprise some one-and-a-half pages of Teubner text (Alk.2–3).</jats:p

Putting String/Fivebrane Duality to the Test

According to string/fivebrane duality, the Green-Schwarz factorization of the $D=10$ spacetime anomaly polynomial $I_{12}$ into $X_4\, X_8$ means that just as $X_4$ is the anomaly polynomial of the $d=2$ string worldsheet so $X_8$ should be the anomaly polynomial of the $d=6$ fivebrane worldvolume. To test this idea we perform a fivebrane calculation of $X_8$ and find perfect agreement with the string one--loop result.Comment: 14 pages, CERN TH-6614/92, CTP-TAMU 60/9

Instanton Moduli and Brane Creation

We obtain new intersecting 5-brane, string and pp-wave solutions in the heterotic string on a torus and on a K3 manifold. In the former case the 5-brane is supported by Yang-Mills instantons, and in the latter case both the 5-brane and the string are supported by the instantons. The instanton moduli are parameterised by the sizes and locations of the instantons. We exhibit two kinds of phase transition in which, for suitable choices of the instanton moduli, a 5-brane and/or a string can be created. One kind of phase transition occurs when the size of an instanton vanishes, while the other occurs when a pair of Yang-Mills instantons coalesce. We also study the associated five-dimensional black holes and the implications of these phase transitions for the black-hole entropy. Specifically, we find that the entropy of the three-charge black holes is zero when the instantons are separated and of non-zero scale size, but becomes non-zero (which can be counted miscrospically) after either of the phase transitions.Comment: 18 pages, Late

Spectrum of D=6, N=4b Supergravity on AdS_3 x S^3

The complete spectrum of D=6, N=4b supergravity with n tensor multiplets compactified on AdS_3 x S^3 is determined. The D=6 theory obtained from the K_3 compactification of Type IIB string requires that n=21, but we let n be arbitrary. The superalgebra that underlies the symmetry of the resulting supergravity theory in AdS_3 coupled to matter is SU(1,1|2)_L x SU(1,1|2)_R. The theory also has an unbroken global SO(4)_R x SO(n) symmetry inherited from D=6. The spectrum of states arranges itself into a tower of spin-2 supermultiplets, a tower of spin-1, SO(n) singlet supermultiplets, a tower of spin-1 supermultiplets in the vector representation of SO(n) and a special spin-1/2 supermultiplet also in the vector representation of SO(n). The SU(2)_L x SU(2)_R Yang-Mills states reside in the second level of the spin-2 tower and the lowest level of the spin-1, SO(n) singlet tower and the associated field theory exhibits interesting properties.Comment: 37 pages, latex, 5 tables and 3 figures, typos corrected, a reference adde

Duality Symmetries and the Type II String Effective Action

We discuss the duality symmetries of Type II string effective actions in nine, ten and eleven dimensions. As a by-product we give a covariant action underlying the ten--dimensional Type IIB supergravity theory. We apply duality symmetries to construct dyonic Type II string solutions in six dimensions and their reformulation as solutions of the ten--dimensional Type IIB theory in ten dimensions.Comment: 19 pages, Latex, based on talk given at the Trieste conference on S-duality and Mirror Symmetry, June 199

D=6, N=1 String Vacua and Duality

We review the structure $D=6, N=1$ string vacua with emphasis on the different connections due to T-dualities and S-dualities. The topics discussed include: Anomaly cancellation; K3 and orbifold $D=6, N=1$ heterotic compactifications; T-dualities between $E_8\times E_8$ and $Spin(32)/Z_2$ heterotic vacua; non-perturbative heterotic vacua and small instantons; N=2 Type-II/Heterotic duality in D=4 ; F-theory/heterotic duality in D=6; and heterotic/heterotic duality in six and four dimensions.Comment: 52 pages, plain Latex. To appear in the proceedings of the APCTP Winter School on Duality, Mt. Sorak (Korea), February 199

Zero Modes for the D=11 Membrane and Five-Brane

There exist extremal p-brane solutions of $D\!=\!11$ supergravity for p=2~and~5. In this paper we investigate the zero modes of the membrane and the five-brane solutions as a first step toward understanding the full quantum theory of these objects. It is found that both solutions possess the correct number of normalizable zero modes dictated by supersymmetry.Comment: Minor typos corrected, one reference added, agrees with published version. 9 RevTeX pages, 1 figure include

Supercharges, Killing Spinors and Intersecting Gauge Five-branes

We obtain new solutions where a string and a pp-wave lie in the common worldvolume directions of the non-standard intersection of two gauge 5-branes in the heterotic string. The two 5-branes are supported by independent SU(2) Yang-Mills instantons in their respective (non-overlapping) transverse spaces. We present a detailed study of the unbroken supersymmetry, focusing especially on a comparison between a direct construction of Killing spinors and a counting of zero eigenvalues in the annticommutator of supercharges. The results are in agreement with some previous arguments, to the effect that additional zero eigenvalues resulting from a ``fine-tuning'' between positive-energy and negative-energy contributions from different components in an intersection are spurious, and should not be taken as an indication of supersymmetry enhancements. These observations have a general applicability that goes beyond the specific example we study in this paper.Comment: Latex, 23 pages; minor revisions, and references adde

On the strongly coupled heterotic string

We analyze in detail the anomaly cancellation conditions for the strongly coupled $E_8 \times E_8$ heterotic string introduced by Horava and Witten and find new features compared to the ten-dimensional Green-Schwarz mechanism. We project onto ten dimensions the corresponding Lagrangian of the zero-mode fields. We find that it has a simple interpretation provided by the conjectured heterotic string/fivebrane duality. The part which originates from eleven-dimensions is naturally described in fivebrane language. We discuss physical couplings and scales in four dimensions.Comment: Latex, 14 pages, Misprints correcte