Bo Sundborg

Stringy gravity, interacting tensionless strings and massless higher spins

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 × S5 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.

The moduli space and monodromies of N = 2 supersymmetric SO(2r + 1) Yang-Mills theory

Abstract We write down the weak-coupling limit of N = 2 supersymmetric Yang-Mills theory with arbitrary gauge group G . We find the weak-coupling monodromies represented in terms of Sp(2r, Z ) matrices depending on paths closed up to Weyl transformations in the Cartan space of complex dimension r , the rank of the group. There is a one to one relation between Weyl orbits of these paths and elements of a generalized braid group defined from G . We check that these weak-coupling monodromies behave correctly in limits of the moduli space corresponding to restrictions to subgroups. In the case of SO(2 r + 1) we write down the complex curve representing the solution of the theory. We show that the curve has the correct monodromies.

D-PARTICLE DYNAMICS AND BOUND STATES

We study the low energy effective theory describing the dynamics of D-particles. 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 nonrelativistic 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 λ1/3 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 D-particles. Some comments on the possible relations to black hole entropy and elevendimensional supergravity are also given.

Free large N supersymmetric Yang-Mills theory as a string theory

The strong version of Maldacenas AdS/CFT conjecture implies that the large-N expansion of free = 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.

Classical and quantized tensionless strings

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.

The zero tension limit of the superstring

Abstract We construct the limit T →0 of the superstring starting from a reformulation of the same limit for the bosonic string. The resulting action is manifestly 2D-diffeomorphism invariant as well as Siegel-invariant. It is also invariant under superconformal transformations in the ambient superspace. The model describes a collection of superparticles moving on a supernull surface. We propose it as a high energy limit of the superstring.

The zero tension limit of the spinning string

Abstract We construct the limit T →0 of the spinning string starting from a reformulation of the same limit for the bosonic string. The action closely resembles that of the spinning particle and just as in that case we can extend our action to N supersymmetries and gauge the associated global O( N ) symmetry. We also present a superspace formulation of the N =1 theory and a general discussion of how to introduce spinors in geometries with degenerate metrics.

Exceptional equivalences in N = 2 supersymmetric Yang-Mills theory

Abstract We find low-energy equivalences between N = 2 supersymmetric gauge theories with different simple gauge groups with and without matter. We give a construction of equivalences based on subgroups and find all examples with maximal simple subgroups. This is used to solve some theories with exceptional gauge groups G 2 and F 4 . We are also able to solve an E 6 theory on a codimension one submanifold of its moduli space.

Space-time symmetries of quantized tensionless strings

Abstract The tensionless limit of the free bosonic string is space-time conformally symmetric classically. Requiring invariance of the quantum theory in the light-cone gauge tests the reparametrization symmetry needed to fix this gauge. The full conformal symmetry gives stronger constraints than the Poincare subalgebra. We find that the symmetry may be preserved in any space-time dimension, but only if the spectrum is drastically reduced (part of this reduction is natural in a zero tension limit of the ordinary string spectrum). The quantum states are required to be symmetric (i.e. singlets) under space-time diffeomorphisms, except for the centre of mass wave function. We speculate on a relation to a topological phase of string theory.

Hamiltonian BRST quantization of the conformal string

We present a new formulation of the tensionless string (T = 0) where the space-time conformal symmetry is manifest. Using a Hamiltonian BRST scheme we quantize this Conformal String and find that it has critical dimension D = 2. This is in keeping with our classical result that the model describes massless particles in this dimension. It is also consistent with our previous results which indicate that quantized conformally symmetric tensionless strings describe a topological phase away from D = 2. We reach our result by demanding nilpotency of the BRST charge and consistency with the Jacobi identities. The derivation is presented in two different ways: in operator language and using mode expansions. Careful attention is paid to regularization, a crucial ingredient in our calculations.We present a new formulation of the tensionless string (