We show that configurations of multiple D-branes related by SU(N) rotations will preserve unbroken supersymmetry. This includes cases in which two D-branes are related by a rotation of arbitrarily small angle, and we discuss some of the physics of this. In particular, we discuss a way of obtaining 4D chiral fermions on the intersection of Dbranes.We also rephrase the condition for unbroken supersymmety as the condition that a 'generalized holonomy group' associated with the brane configuration and manifold is reduced, and relate this condition (in Type IIA string theory) to a condition in eleven dimensions.June 1996 (revised)

We argue that vacua of string theory which asymptote at weak coupling to linear dilaton backgrounds are holographic. The full string theory in such vacua is "dual" to a theory without gravity in fewer dimensions. The dual theory is generically not a local quantum field theory. Excitations of the string vacuum, which can be studied in the weak coupling region using worldsheet methods, give rise to observables in the dual theory. An interesting example is string theory in the near-horizon background of parallel NS5-branes, the CHS model, which is dual to the decoupled NS5-brane theory ("little string theory"). This duality can be used to study some of the observables in this theory and some of their correlation functions. Another interesting example is the "old" matrix model, which gives a holographic description of two dimensional string theory. 8/98

We consider various aspects of compactifications of the Type I/heterotic Spin(32)/Z 2 theory on K3. One family of such compactifications includes the standard embedding of the spin connection in the gauge group, and is on the same moduli space as the compactification of the heterotic E 8 × E 8 theory on K3 with instanton numbers (8,16). Another class, which includes an orbifold of the Type I theory recently constructed by Gimon and Polchinski and whose field theory limit involves some topological novelties, is on the moduli space of the heterotic E 8 × E 8 theory on K3 with instanton numbers (12,12). These connections between Spin(32)/Z 2 and E 8 × E 8 models can be demonstrated by T duality, and permit a better understanding of nonperturbative gauge fields in the (12,12) model. In the transformation between Spin(32)/Z 2 and E 8 × E 8 models, the strong/weak coupling duality of the (12,12) E 8 × E 8 model is mapped to T duality in the Type I theory. The gauge and gravitational anomalies in the Type I theory are canceled by an extension of the Green-Schwarz mechanism.

Giant gravitons in AdS 5 × S 5 , and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three sources: (a) topological considerations in orbifolds, (b) computation of protected correlators using free field theory and (c) a Matrix model argument. The last argument applies to AdS 7 × S 4 and the dual (2, 0) theory, where we use algebraic aspects of the fuzzy 4-sphere to compute the expectation value of a giant graviton operator along the Coulomb branch of the theory.

We study the (2, 0) superconformal theories in six dimensions, which arise from the lowenergy limit of k coincident 5-branes, using their discrete light-cone formulation as a superconformal quantum mechanical sigma model. We analyze the realization of the superconformal symmetry in the quantum mechanics, and the realization of primary operators.As an example we compute the spectrum of chiral primary states in symmetric Spin(5) R representations. To facilitate the analysis we introduce and briefly discuss a new class of Lorentz non-invariant theories, which flow in the IR to the (2, 0) superconformal field theories but differ from them in the UV.