Gauge theory and the excision of repulson singularities

Abstract

We study brane configurations that give rise to large-N gauge theories with eight supersymmetries and no hypermultiplets. These configurations include a variety of wrapped, fractional, and stretched branes or strings. The corresponding spacetime geometries which we study have a distinct kind of singularity known as a repulson. We find that this singularity is removed by a distinctive mechanism, leaving a smooth geometry with a core having an enhanced gauge symmetry. The spacetime geometry can be related to large-N Seiberg-Witten theory.1 Understanding the physics of spacetime singularities is a challenge for any complete theory of quantum gravity. It has been shown that string theory resolves certain seeming singularities, such as orbifolds [1], flops [2], and conifolds [3], in the sense that their physics is completely nonsingular. On the other hand, it has also been argued that certain singularities should not be resolved, but rather must be disallowed configurations -in particular, negative mass Schwarzschild, which would correspond to an instability of the vacuum [4]. Also, in the study of perturbations of the AdS/CFT duality various singular spacetimes have been encountered, and at least some of these must be unphysical in the same sense as negative mass Schwarzschild. A more general understanding of singularities in string theory is thus an important goal.In this paper we study a naked singularity of a particular type [5,6,7], which has been dubbed the repulson. A variety of brane configurations in string theory appear to give rise to such a singularity. However, we will argue that this is not the case. Rather, as the name might suggest, the constituent branes effectively repel one another (in spite of supersymmetry), forming in the end a nonsingular shell.Our interest in this singularity arose from a search for new examples of gauge/gravity duality. In particular, the brane configurations that give rise to the repulson singularity have on their world-volumes pure D = 4, N = 2 gauge theory (or the equivalent in other dimensions), as opposed to the usual pure D = 4, N = 4, or D = 4, N = 2 with hypermultiplets. We do not precisely find such a duality, in the sense of using supergravity to calculate properties of the strongly coupled gauge theory, but we do find a striking parallel between the moduli space of the large-N SU(N) gauge theory and the fate that we have deduced for the singularity. We also find some clues which allow us to guess at aspects of a possible dual.

The enhançon, black holes, and the second law

“…When we reach V(r) = V * at some radius, new physics will come into play, and this is the "enhançon" locus of ref. [7]. This radius may be computed easily to be:…”

“…Now when the K3 volume reaches V * , at the enhançon radius, r e , the wrapped D5-branes will be unable to proceed supersymmetrically into smaller radius [7], due to the fact that their effective tensions are going through zero there. They are therefore forced to form an enhançon sphere at radius r e .…”

“…[7] that the probe, made of pure D5-branes, hangs up at the enhançon radius r e . Now we discover that ref.…”

“…At strong coupling (or large charges), where the D-branes have a non-trivial back-reaction on the geometry, for generic combinations of parameters it was shown in ref. [7] that this situation can give rise to regions of the naive spacetime solution where the tension of the wrapped brane is unphysical. This is simply because the volume of the K3 upon which the brane is wrapped can vary as a function of position transverse to the branes.…”

Evidence for a gravitational Myers effect

“…[1,2,3]). A second mechanism is that the singularity may be an artifact of the classical approximation and there are quantum effects which modify or shield its problematic nature [4,5,6]. If the singularity is naturally associated with a gauge field, the mechanism of shielding/resolving is by now well-understood.…”