Eguchi-Hanson Solitons

We present a new class of solutions in odd dimensions to Einstein’s equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson(A)dS metrics, with the added feature of having Lorentzian signatures. They provide an affirmative answer to the open question as to whether or not there exist solutions with negative cosmological constant that asymptotically approach AdS5/Γ, but have less energy than AdS5/Γ. We present evidence that these solutions are the lowest-energy states within their asymptotic class. Weakly coupled non-abelian gauge theories on non-simply connected manifolds can have ground states of much lower energy than one might naively expect. For example, a U(N) gauge theory on a torus ofm-dimensions whose typical length is L can have its lowest energy states of order 1/ (NL) (instead of 1/L) if N of the fields are arranged to be periodic after traversing one circle N times [1]. By introducing such locally flat but globally nontrivial connections, the effective size of the compact space is thereby increased by a factor of N , correspondingly reducing the spectrum of states. A string-theoretic interpretation of this phenomenon is that of the low-energy excitations of one D-brane wrapped N times around a circle, where the U(N) gauge theory describes the low energy excitations of N D-branes wrapped on the torus. The N open strings connecting distinct D-branes in the latter case become EMail: [email protected] EMail: [email protected]