Consistency Conditions for Holographic Duality

We show that if the beta functions of a field theory are given by the gradient of a certain potential on the space of couplings, a gravitational background in one more dimension can express the renormalization group (RG) flow of the theory. The field theory beta functions and the gradient flow constraint together reconstruct the second order spacetime equations of motion. The RG equation reduces to the conventional gravitational computation of the spacetime quasilocal stress tensor, and a c-theorem holds true as a consequence of the Raychaudhuri equation. Conversely, under certain conditions, if the RG evolution of a field theory possesses a monotonic c-function, the flow of couplings can be expressed in terms of a higher dimensional gravitational background.Comment: LaTeX, 14 page

Strings on orbifold lines

The orbifold lines IIA/Script I8 and IIB/Script I8(-1)FL possess BPS discrete torsion variants which carry fundamental string (NSNS) charge. We show that these variants are actually classified by an integral electric field F from the twisted RR sector, and compute their tension and NSNS charge as a function of F. The analysis employs equivariant K-theory and the string creation phenomenon. The K-theory results demonstrate the corrections to cohomology in the case of torsion; it is found that 8 units of F are invisible at transverse infinity for IIA, and correspondingly 16 units for IIB

Brane Transfer Operations and T-Duality of Non-BPS States

Using the relation between D-brane charges and K-theory, we study non-BPS D-branes and their behavior under T-duality. We point out that in general compactifications, D-brane charges are classified by relative K-theory groups. T-duality is found to act as a symmetry between the relative K-theory groups in Type II and Type I/IA theories. We also study Type \tilde\IA theory (which contains an O8^- plane and an O8^+ plane), using K-theory and T-duality to identify its stable D-branes. Comparison with string theory constructions reveals two interesting effects. One of them involves the transfer of branes between O-planes, while in the other, a D-brane charge which seems conserved near one O-plane in fact decays due to the presence of another type of O-plane.Comment: 28 pages harvmac, 4 figures; Expanded argument for relative K-theory in subsection 2.2, and added explicit K-theory groups of a point in eq.(A.3) of the appendi

On the Complementarity of F-theory, Orientifolds, and Heterotic Strings

We study F-theory duals of six dimensional heterotic vacua in extreme regions of moduli space where the heterotic string is very strongly coupled. We demonstrate how to use orientifold limits of these F-theory duals to regain a perturbative string description. As an example, we reproduce the spectrum of a T^4/\ZZ_{4} orientifold as an F-theory vacuum with a singular $K3$ fibration. We relate this vacuum to previously studied heterotic $E_8\times E_8$ compactifications on $K3$.Comment: 36 pages, 4 eps figures, use harvmac and epsf. Typos correcte

The Operator Spectrum of the Six-dimensional (1,0) Theory

We study the large N operator spectrum of the (1,0) superconformal chiral six-dimensional theory with E_8 global symmetry. This spectrum is dual to the Kaluza-Klein spectrum of supergravity on AdS_7 X S^4/Z_2 with a ten-dimensional E_8 theory at its singular locus. We identify those operators in short multiplets of OSp(6,2|2), whose dimensions are exact for any N. We also discuss more general issues concerning AdS/CFT duality on orbifold supergravity backgrounds.Comment: 16pp, Late

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

Non-tachyonic open descendants of the 0B string theory

We use the crosscap constraint to construct open descendants of the 0B string compactified on $T^6 /Z_3$ and on $T^4/Z_2$ free of tachyons both in the closed and in the open unoriented sectors. In four dimensions the construction results in a Chan-Paton gauge group $U(8)\otimes U(12)\otimes U(12)$ with three generations of chiral fermions in the representations $(\overline{8},1,\overline{12}) +(8,12,1)+(1,\overline{66},1)+(1,1,66)$.Comment: 13 pages, Latex. Minor corrections. Final version to appear on Phys.Lett.