We review what has been learnt and what remains unknown about the physics of hot enhancons following studies in supergravity. We recall a rather general family of static, spherically symmetric, non-extremal enhancon solutions describing D4 branes wrapped on K3 and discuss physical aspects of the solutions. We embed these solutions in the six dimensional supergravity describing type IIA strings on K3 and generalize them to have arbitrary charge vector. This allows us to demonstrate the equivalence with a known family of hot fractional D0 brane solutions, to widen the class of solutions of this second type and to carry much of the discussion across from the D4 brane analysis. In particular we argue for the existence of a horizon branch for these branes.
The system was the first setup in which a supergravity dual of pure @math SYM theory with no hypermultiplets was studied @cite_9 . It was constructed by wrapping BPS D-branes on a K3 manifold, and studying the resulting geometry. From the supergravity point of view, the system exhibited a novel singularity resolution mechanism. Naively, there appeared to be a naked timelike singularity in the space transverse to the branes, dubbed the repulson, because a massive particle would feel a repulsive potential which becomes infinite in magnitude at a finite radius from the naive position of the branes. Probing the background with a wrapped D-brane, however, showed that the @math source D-branes do not, in fact, sit at the origin. Rather, they expand to form a shell of branes, inside of which the geometry does not, after all, become singular.
@cite_9
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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. The enhancon mechanism removes a family of time-like singularities from certain supergravity spacetimes by forming a shell of branes on which the exterior geometry terminates. The problematic interior geometry is replaced by a new spacetime, which in the prototype extremal case is simply flat. We show that this excision process, made inevitable by stringy phenomena such as enhanced gauge symmetry and the vanishing of certain D-branes' tension at the shell, is also consistent at the purely gravitational level. The source introduced at the excision surface between the interior and exterior geometries behaves exactly as a shell of wrapped D6-branes, and in particular, the tension vanishes at precisely the enhancon radius. These observations can be generalised, and we present the case for non-extremal generalisations of the geometry, showing that the procedure allows for the possibility that the interior geometry contains an horizon. Further knowledge of the dynamics of the enhancon shell itself is needed to determine the precise position of the horizon, and to uncover a complete physical interpretation of the solutions. We construct new supersymmetric solutions of D = 11 supergravity describing n orthogonally “overlapping” membranes and fivebranes for n = 2,…,8. Overlapping branes arise after separating intersecting branes in a direction transverse to all of the branes. The solutions, which generalize known intersecting brane solutions, preserve at least 2−n of the supersymmetry. Each pairwise overlap involves a membrane overlapping a membrane in a 0-brane, a fivebrane overlapping a fivebrane in a 3-brane or a membrane overlapping a fivebrane in a string. After reducing n overlapping membranes to obtain n overlapping D-2-branes in D = 10, T-duality generates new overlapping D-brane solutions in type IIA and type IIB string theory. Uplifting certain type IIA solutions leads to the D = 11 solutions. Some of the new solutions reduce to dilaton black holes in D = 4. Additionally, we present a D = 10 solution that describes two D-5-branes overlapping in a string. T-duality then generates further D = 10 solutions and uplifting one of the type IIA solutions gives a new D = 11 solution describing two fivebranes overlapping in a string. We construct the most general supersymmetric configuration of @math -branes and @math -branes on a 6-torus. It contains arbitrary numbers of branes at relative @math angles. The corresponding supergravity solutions are constructed and expressed in a remarkably simple form, using the complex geometry of the compact space. The spacetime supersymmetry of the configuration is verified explicitly, by solution of the Killing spinor equations, and the equations of motion are verified too. Our configurations can be interpreted as a 16-parameter family of regular extremal black holes in four dimensions. Their entropy is interpreted microscopically by counting the degeneracy of bound states of @math -branes. Our result agrees in detail with the prediction for the degeneracy of BPS states in terms of the quartic invariant of the E(7,7) duality group.