Abstract
String theory on AdS3 has a solvable single-trace irrelevant deformation that is closely related to Toverline{T} . For one sign of the coupling, it leads to an asymptotically linear dilaton spacetime, and a corresponding Hagedorn spectrum. For the other, the resulting spacetime has a curvature singularity at a finite radial location, and an upper bound on the energies of states. Beyond the singularity, the signature of spacetime is flipped and there is an asymptotically linear dilaton boundary at infinity. We study the properties of black holes and fundamental strings in this spacetime, and find a sensible picture. The singularity does not give rise to a hard ultraviolet wall for excitations -one must include the region beyond it to understand the theory. The size of black holes diverges as their energy approaches the upper bound, as does the location of the singularity. Fundamental strings pass smoothly through the singularity, but if their energy is above the upper bound, their trajectories are singular. From the point of view of the boundary at infinity, this background can be thought of as a vacuum of Little String Theory which contains a large number of negative strings.
Highlights
We study the properties of black holes and fundamental strings in this spacetime, and find a sensible picture
As should be clear from the above comments, in our view it is important to improve the understanding of the backgrounds of [1] and related ones, since they constitute one of the only cases where holography can be studied in detail in a situation where the UV theory is not a CFT
We continued the study of string theory in the backgrounds M+3 (4.2), (4.3), and M−3 (4.4), which correspond to the current-current deformation (4.1) of string theory on AdS3 with positive and negative coupling, respectively
Summary
The construction of [1] is quite general, but it will be sufficient for our purposes to consider a special case, type II string theory on R4,1 × T 4 × S1, in the presence of k Neveu-Schwarz fivebranes (NS5-branes) wrapping T 4×S1 and p fundamental strings wrapping the S1, with n units of momentum on the S1. Where g = eΦ0 is the string coupling far from the branes, related to the ten dimensional Newton constant in flat spacetime by. The parameter r0 above is a non-extremality parameter Taking it to zero, and setting the momentum on the S1, n, to zero, gives the supersymmetric geometry describing p fundamental strings and k NS5-branes in asymptotically flat spacetime. For r0 > 0, (2.1) describes a black brane in flat spacetime. It has an outer horizon at r = r0 and an inner one at r = 0. The thermodynamics of the outer horizon can be used to learn about the properties of highly excited states with the charges (p, k, n) in string theory.
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