No abstract

Consequences of a strong version of the AdS/CFT correspondence for extremely stringy physics are examined. In particular, properties of N = 4 supersymmetric Yang-Mills theory are used to extract results about interacting tensionless strings and massless higher spin fields in an AdS5 × S 5 background. Furthermore, the thermodynamics of this model signals the presence of a Hawking-Page phase transition between AdS5 space and a "black hole"-like high temperature configuration even in the extreme string limit.

From the ordinary tensile string we derive a geometric action for the tensionless (T = 0) string and discuss its symmetries and field equations. The Weyl symmetry of the usual string is shown to be replaced by a global space-time conformal symmetry in the T → 0 limit. We present the explicit expressions for the generators of this group in the light-cone gauge. Using these, we quantize the theory in an operator form and require the conformal symmetry to remain a symmetry of the quantum theory. Modulo details concerning zero-modes that are discussed in the paper, this leads to the stringent restriction that the physical states should be singlets under space-time diffeomorphisms, hinting at a topological theory. We present the details of the calculation that leads to this conclusion.

We study the low energy effective theory describing the dynamics of Dparticles. This corresponds to the quantum mechanical system obtained by dimensional reduction of 9 + 1 dimensional supersymmetric Yang-Mills theory to 0 + 1 dimensions and can be interpreted as the non relativistic limit of the Born-Infeld action. We study the system of two like-charged D-particles and find evidence for the existence of non-BPS states whose mass grows like λ 1/3 over the BPS mass. We give a string interpretation of this phenomenon in terms of a linear potential generated by strings stretching from the two Dparticles. Some comments on the possible relations to black hole entropy and eleven dimensional supergravity are also given. 4 p is the dimension of the soliton: p = 0 for particle-like objects, p = 1 for strings etc. 5 Throughout the paper we use dimensionless units by setting α ′ = 1.

The strong version of Maldacena's AdS/CFT conjecture implies that the large N expansion of free N = 4 super-YM theory describes an interacting string theory in the extreme limit of high spacetime curvature relative to the string length. String states may then be understood as composed of SYM string bits. We investigate part of the low-lying spectrum of the tensionless (zero-coupling) limit and find a large number of states that are not present in the infinite tension (strong-coupling) limit, notably several massless spin two particles. We observe that all conformal dimensions are N -independent in the free SYM theory, implying that masses in the corresponding string theory are unchanged by string interactions. Degenerate string states do however mix in the interacting string theory because of the complicated N -dependence of general CFT two-point functions. Finally we verify the CFT crossing symmetry, which corresponds to the dual properties of string scattering amplitudes. This means that the SYM operator correlation functions define AdS dual models analogous to the Minkowski dual models that gave rise to string theory.