Chemistry of Chern-Simons Supergravity: reduction to a BPS kink, oxidation to M-theory and thermodynamical aspects

Abstract

We construct a supersymmetric extension of the two dimensional KaluzaKlein-reduced gravitational Chern-Simons term, and globally study its solutions, labelled by mass and U (1) charge c. The kink solution is BPS, and in an appropriate conformal frame all solutions asymptotically approach AdS. The thermodynamics of the Hawking effect yields interesting behavior for the specific heat and hints at a Hawking-Page-like transition at T critical ∼ c 3/2 . We address implications for higher dimensions ("oxidation"), in particular D=3,4 and 11, and comment briefly on AdS/CFT aspects of the kink.

All supersymmetric solutions ofN= 2,D= 4 gauged supergravity

“…It is interesting to note that (35) is similar to the action that arises from Kaluza-Klein reduction of the three-dimensional gravitational Chern-Simons term [30], with the only difference that here B is a fundamental field, whereas the field arising in [30] is the curl of a vector potential. If we use the ansatz B = x κ , equations (33) and (34) are satisfied for κ = 2 and κ = −1/3. The former value of κ yields the BPS solution [5]…”

“…In the special case δ 0 = 0 we recover the kink solution considered above. This solutions has been recently further analyzed in [33], where it was interpreted as a soliton consisting of photons kept together by gravity.…”

An action for the exact string black hole

“…For the Kaluza-Klein reduced gravitational Chern-Simons theory [25] this observation turned out to be pivotal for a successful application of first order gravity methods [26] and supersymmetrization [27].…”

“…Undoing the exponential representation implied by (2.7) and inserting p = 2/k amounts to 27) which is equivalent to (1.3).…”

“…Provided the relation (3.14) holds the pre-potential always exists. 27 For the ESBH (+)/ESNS (−) it reads…”